2330:. They are distinguished from fouling deposits, which form from material originating ex-situ. Corrosion deposits should not be confused with fouling deposits formed by ex-situ generated corrosion products. Corrosion deposits will normally have composition related to the composition of the substrate. Also, the geometry of the metal-oxide and oxide-fluid interfaces may allow practical distinction between the corrosion and fouling deposits. An example of corrosion fouling can be formation of an iron oxide or oxyhydroxide deposit from corrosion of the carbon steel underneath. Corrosion fouling should not be confused with fouling corrosion, i.e., any of the types of corrosion that may be induced by fouling.
2610:. The periodic sharp variations in the apparent fouling amount often correspond to the moments of system shutdowns, startups or other transients in operation. The periodic variations are often interpreted as periodic removal of some of the deposit (perhaps deposit re-suspension due to pressure pulses, spalling due thermal stresses, or exfoliation due to redox transients). Steam blanketing has been postulated to occur between the partially spalled deposits and the heat transfer surface. However, other reasons are possible, e.g., trapping of air inside the surface deposits during shutdowns, or inaccuracy of temperature measurements during transients ("temperature streaming").
691:
2564:- This can occur when fouling rate is quantified by monitoring heat transfer. Relatively small amounts of deposit can improve heat transfer, relative to clean surface, and give an appearance of "negative" fouling rate and negative total fouling amount. Negative fouling is often observed under nucleate-boiling heat-transfer conditions (deposit improves bubble nucleation) or forced-convection (if the deposit increases the surface roughness and the surface is no longer "hydraulically smooth"). After the initial period of "surface roughness control", the fouling rate usually becomes strongly positive.
2385:
2481:
The normalized fouling rate (also in kg/ms) will additionally account for the concentration of the foulant in the process fluid (kg/kg) during preceding operations, and is useful for comparison of fouling rates between different systems. It is obtained by dividing the fouling rate by the foulant concentration. The fouling rate constant (m/s) can be obtained by dividing the normalized fouling rate by the mass density of the process fluid (kg/m).
667:
58:
375:
2620:
683:
3582:, cleaning with high-velocity water jets ("water lancing"), recirculating ("blasting") with metal, sponge or other balls, or propelling offline mechanical "bullet-type" tube cleaners. Whereas chemical cleaning causes environmental problems through the handling, application, storage and disposal of chemicals, the mechanical cleaning by means of circulating cleaning balls or offline "bullet-type" cleaning can be an
3296:
363:
170:
155:
3403:. Some plants employ foreign-object exclusion program (to eliminate the possibility of salient introduction of unwanted materials, e.g., forgetting tools during maintenance). Acoustic monitoring is sometimes employed to monitor for fretting by detached parts. In the case of micro fouling, water purification is achieved with extensive methods of water treatment,
3196:. The underlying physical picture for this model is that of a two-layer deposit consisting of consolidated inner layer and loose unconsolidated outer layer. Such a bi-layer deposit is often observed in practice. The above model simplifies readily to the older model of simultaneous deposition and re-entrainment (which neglects consolidation) when λ
2600:- In this scenario, the fouling rate increases with time; the rate of deposit buildup accelerates with time (perhaps until it becomes transport limited). Mechanistically, this scenario can develop when fouling increases the surface roughness, or when the deposit surface exhibits higher chemical propensity to fouling than the pure underlying metal.
3570:) are an option for some applications. Modern components are typically required to be designed for ease of inspection of internals and periodic cleaning. On-line fouling monitoring systems are designed for some application so that blowing or cleaning can be applied before unpredictable shutdown is necessary or damage occurs.
537:, the ingress of macro fouling into the cooling tower basin is possible through open canals or by the wind. Sometimes, parts of the cooling tower internals detach themselves and are carried into the cooling water circuit. Such substances can foul the surfaces of heat exchangers and may cause deterioration of the relevant
915:
temperature and thus will foul the cooling surfaces. Salts with "inverse" or "retrograde" solubility will foul the heating surfaces. An example of the temperature dependence of solubility is shown in the figure. Calcium sulfate is a common precipitation foulant of heating surfaces due to its retrograde solubility.
2968:
2420:
Bacterial fouling can occur under either aerobic (with oxygen dissolved in water) or anaerobic (no oxygen) conditions. In practice, aerobic bacteria prefer open systems, when both oxygen and nutrients are constantly delivered, often in warm and sunlit environments. Anaerobic fouling more often occurs
353:
This article is primarily devoted to the fouling of industrial heat exchangers, although the same theory is generally applicable to other varieties of fouling. In cooling technology and other technical fields, a distinction is made between macro fouling and micro fouling. Of the two, micro fouling is
918:
Precipitation fouling can also occur in the absence of heating or vaporization. For example, calcium sulfate decreases its solubility with decreasing pressure. This can lead to precipitation fouling of reservoirs and wells in oil fields, decreasing their productivity with time. Fouling of membranes
3371:
increases because the heat exchangers have to be designed in larger sizes to compensate for the heat-transfer loss due to fouling. To the output losses listed above, one needs to add the cost of down-time required to inspect, clean, and repair the components (millions of dollars per day of shutdown
2722:
consists of transport to the surface and subsequent attachment. Deposit removal is either through deposit dissolution, particle re-entrainment, or deposit spalling, erosive wear, or exfoliation. Fouling results from foulant generation, foulant deposition, deposit removal, and deposit consolidation.
2480:
The most straightforward way to quantify fairly uniform fouling is by stating the average deposit surface loading, i.e., kg of deposit per m of surface area. The fouling rate will then be expressed in kg/ms, and it is obtained by dividing the deposit surface loading by the effective operating time.
2369:
Solidification fouling occurs when a component of the flowing fluid "freezes" onto a surface forming a solid fouling deposit. Examples may include solidification of wax (with a high melting point) from a hydrocarbon solution, or of molten ash (carried in a furnace exhaust gas) onto a heat exchanger
326:
Other terms used in the literature to describe fouling include deposit formation, encrustation, crudding, deposition, scaling, scale formation, slagging, and sludge formation. The last six terms have a more narrow meaning than fouling within the scope of the fouling science and technology, and they
3553:
On the component design level, fouling can often (but not always) be minimized by maintaining a relatively high (for example, 2 m/s) and uniform fluid velocity throughout the component. Stagnant regions need to be eliminated. Components are normally overdesigned to accommodate the fouling
2447:
Composite fouling is common. This type of fouling involves more than one foulant or more than one fouling mechanism working simultaneously. The multiple foulants or mechanisms may interact with each other resulting in a synergistic fouling which is not a simple arithmetic sum of the individual
323:, organic) or a non-living substance (inorganic). Fouling is usually distinguished from other surface-growth phenomena in that it occurs on a surface of a component, system, or plant performing a defined and useful function and that the fouling process impedes or interferes with this function.
4232:
914:
on temperature or presence of evaporation will often be the driving force for precipitation fouling. The important distinction is between salts with "normal" or "retrograde" dependence of solubility on temperature. Salts with the "normal" solubility increase their solubility with increasing
4204:
3172:
3549:
has been a subject of controversy as to its effectiveness for fouling control since the 1950s. The prevailing opinion is that it simply "does not work". Nevertheless, some studies suggest that it may be effective under some conditions to reduce buildup of calcium carbonate deposits.
3554:
anticipated between cleanings. However, a significant overdesign can be a design error because it may lead to increased fouling due to reduced velocities. Periodic on-line pressure pulses or backflow can be effective if the capability is carefully incorporated at the design time.
3573:
Chemical or mechanical cleaning processes for the removal of deposits and scales are recommended when fouling reaches the point of impacting the system performance or an onset of significant fouling-induced degradation (e.g., by corrosion). These processes comprise pickling with
2531:
of the deposits will likely influence the probability of underdeposit corrosion. Deposit composition can also be important - even minor components of the deposits can sometimes cause severe corrosion of the underlying metal (e.g., vanadium in deposits of fired boilers causing
3798:
J. Moghadasi, H. Müller-Steinhagen, M. Jamialahmadi, and A. Sharif, "Scale
Deposition in Porous Media and their Removal by EDTA Injection ", ECI Engineering Conferences International Symposium Series, Heat Exchanger Fouling and Cleaning VII, July 1–6, 2007 - Tomar, Portugal.
4101:
400:
Piping, flow channels – reduces flow, increases pressure drop, increases upstream pressure, increases energy expenditure, may cause flow oscillations, slugging in two-phase flow, cavitation; may increase flow velocity elsewhere, may induce vibrations, may cause flow
4143:
C.W. Turner, S.J. Klimas, "Modelling the Effect of
Surface Chemistry on Particle Fouling Under Flow-Boiling Conditions", Proceeding of Heat Exchanger Fouling: Fundamental Approaches and Technical Solutions, 2001, July 8–13, Davos, Switzerland, AECL Report
4229:
2539:
There is no general rule on how much deposit can be tolerated, it depends on the system. In many cases, a deposit even a few micrometers thick can be troublesome. A deposit in a millimeter-range thickness will be of concern in almost any application.
4201:
2511:), localized fouling, packing of confined regions with deposits, creation of occlusions, "crevices", "deposit tubercles", or sludge piles. Such deposit structures can create environment for underdeposit corrosion of the substrate material, e.g.,
3362:
plants, fouling may reduce the gained output ratio by two-digit percentages (the gained output ratio is an equivalent that puts the mass of generated distillate in relation to the steam used in the process). The extra electrical consumption in
1702:
particles, i.e., particles smaller than about 1 μm in at least one dimension (but which are much larger than atomic dimensions). Particles are transported to the surface by a number of mechanisms and there they can attach themselves, e.g., by
898:
2741:
3539:, polymethacrylic acid, usually with a molecular weight lower than 10000). For fired boilers, aluminum or magnesium additives can lower the melting point of ash and promote creation of deposits which are easier to remove. See also
2576:- In this scenario, the fouling rate decreases with time, but never drops to zero. The deposit thickness does not achieve a constant value. The progress of fouling can be often described by two numbers: the initial fouling rate (a
4047:
H. M. Herro (Nalco
Chemical Company), "Deposit-Related Corrosion in Industrial Cooling Water Systems", Presented at the National Association of Corrosion Engineers Corrosion ’89 meeting, New Orleans, Louisiana, April 17–21, 1989
1711:. Note that the attachment of colloidal particles typically involves electrical forces and thus the particle behaviour defies the experience from the macroscopic world. The probability of attachment is sometimes referred to as "
4181:
Xu Zhi-Ming, ZHANG Zhong-Bin, and YANG Shan-Rang, "Costs due to utility fouling in China", ECI Engineering
Conferences International Symposium Series, Heat Exchanger Fouling and Cleaning VII, July 1–6, 2007 - Tomar, Portugal.
2021:
3303:
Fouling is ubiquitous and generates tremendous operational losses, not unlike corrosion. For example, one estimate puts the losses due to fouling of heat exchangers in industrialized nations to be about 0.25% of their
2594:). This is often the case for relatively soft or poorly adherent deposits in areas of fast flow. The asymptote is usually interpreted as the deposit loading at which the deposition rate equals the deposit removal rate.
3032:
2606:- Here, fouling loading generally increases with time (often assuming a generally linear or falling rate), but, when looked at in more detail, the fouling progress is periodically interrupted and takes the form of
2548:
Deposit on a surface does not always develop steadily with time. The following fouling scenarios can be distinguished, depending on the nature of the system and the local thermohydraulic conditions at the surface:
2491:
In heat transfer equipment, where the primary concern is often the effect of fouling on heat transfer, fouling can be quantified by the increase of the resistance to the flow of heat (mK/W) due to fouling (termed
3604:
4090:
D.H. Lister, ""Corrosion products in power generating systems". In: Fouling of Heat
Exchanger Equipment", E.F. Somerscales and J.G. Knudsen (eds.), Hemisphere Pub. Corp., Washington, DC, USA, 1981, pp.135-200.
2558:- Sometimes, a near-nil fouling rate is observed when the surface is new or very clean. This is often observed in biofouling and precipitation fouling. After the "induction period", the fouling rate increases.
673:
buildup inside a pipe reduces liquid flow through the pipe and reduces thermal conduction from the liquid to the outer pipe shell. Both effects will reduce the pipe's overall thermal efficiency when used as a
2732: [ rate of accumulation of unconsolidated deposit ] = [ rate of deposition ] - [ rate of re-entrainment of unconsolidated deposit ] - [ rate of consolidation of unconsolidated deposit ]
3766:
G.A. Mansoori "Physicochemical Basis of
Arterial Blockage / Fouling. Prediction and Prevention." Department of Chemical Engineering, University of Illinois at Chicago, on-line publication, September 2001
1306:
3282:
1401:
3728:
Joshua M. Hawkes, "The
Simulation and Study of Conditions Leading to Axial Offset Anomaly in Pressurized Water Reactors", Georgia Institute of Technology Master of Science Thesis, December 2004.
1209:
4219:
J.C. Cowan and D.J. Weintritt, "Water-Formed Scale
Deposits. A Comprehensive Study of the Prevention, Control, Removal and Use of Mineral Scale", Gulf Publishing Company, Houston, Texas, 1976.
694:
Temperature dependence of the solubility of calcium sulfate (3 phases) in pure water. The water is pressurized so that it can be maintained in the liquid state at the elevated temperatures.
2084:
1928:
3890:
Goode, Kylee R.; Asteriadou, Konstantia; Robbins, Phillip T.; Fryer, Peter J. (March 2013). "Fouling and
Cleaning Studies in the Food and Beverage Industry Classified by Cleaning Type".
2686:
Sometimes fouling autoretardation, i.e., reduction (or potentially enhancement) of crystallisation/attachment rate due to changes in the surface conditions caused by the fouling deposit;
718:. These are most often water solutions, but non-aqueous precipitation fouling is also known. Precipitation fouling is a very common problem in boilers and heat exchangers operating with
4081:
V.P. Brusakov, "Law for the
Deposition of Materials on Heat-Transmitting Surfaces under the Action of Thermoelectric Effects", Atomnaya Energiya, Vol.30, No.1, pp.10-14, January 1971.
3732:
3308:. Another analysis estimated (for 2006) the economical loss due to boiler and turbine fouling in China utilities at 4.68 billion dollars, which is about 0.169% the country GDP.
2726:
For the modern model of fouling involving deposition with simultaneous deposit re-entrainment and consolidation, the fouling process can be represented by the following scheme:
2182:
1637:
3503:
can reduce fouling in many systems, mainly by interfering with the crystallization, attachment, or consolidation steps of the fouling process. Examples for water systems are:
2127:
4186:
3803:
1683:
3944:
Sadeghinezhad, E.; Kazi, S. N.; Dahari, M.; Safaei, Mohammad Reza; Sadri, Rad; Badarudin, A. (14 April 2014). "A Comprehensive Review of Milk Fouling on Heated Surfaces".
1779:
2735:
Following the above scheme, the basic fouling equations can be written as follows (for steady-state conditions with flow, when concentration remains constant with time):
2338:
Chemical reactions may occur on contact of the chemical species in the process fluid with heat transfer surfaces. In such cases, the metallic surface sometimes acts as a
1578:
3818:"Modeling PWR Fuel Corrosion Product Deposition and Growth Processes (5)", Technical Report 1009734, Electric Power Research Institute, Palo Alto, California, USA, 2004.
2370:
surface. The surface needs to have a temperature below a certain threshold; therefore, it is said to be subcooled in respect to the solidification point of the foulant.
397:, decreases heat flux, increases temperature on the hot side, decreases temperature on the cold side, induces under-deposit corrosion, increases use of cooling water;
3319:), increased pressure drop, flow blockages, flow redistribution inside components, flow instabilities, induced vibrations (possibly leading to other problems, e.g.,
3694:"Marine fouling and its prevention"; prepared for Bureau of Ships, Navy Dept, Woods Hole Oceanographic Institution, United States, Navy Dept. Bureau of Ship, 1952.
2413:
Bacteria can form biofilms or slimes. Thus the organisms can aggregate on surfaces using colloidal hydrogels of water and extracellular polymeric substances (EPS) (
2238:
2211:
1836:
1809:
1536:
1507:
1478:
762:
2963:{\displaystyle {\begin{cases}{dm/dt}=k_{d}C_{m}\rho -\lambda _{r}m_{r}(t)\\{dm_{r}/dt}=k_{d}C_{m}\rho -\lambda _{r}m_{r}(t)-\lambda _{c}\cdot m_{r}(t)\end{cases}}}
3751:
4228:"Dispersants for Tube Fouling Control: Volume 2: Short-Term Trial at ANO-2", Report 1003144, Electric Power Research Institute, Palo Alto, California, USA, 2001
3558:
capability is always incorporated into steam generators or evaporators to control the accumulation of non-volatile impurities that cause or aggravate fouling.
1856:
1733:
1449:
1427:
2484:
Deposit thickness (μm) and porosity (%) are also often used for description of fouling amount. The relative reduction of diameter of piping or increase of the
449:
Injection/spray nozzles (e.g., a nozzle spraying a fuel into a furnace) – incorrect amount injected, malformed jet, component inefficiency, component failure;
3384:
The most fundamental and usually preferred method of controlling fouling is to prevent the ingress of the fouling species into the cooling water circuit. In
2346:
occurs in cooling water for the chemical industry which has a minor content of hydrocarbons. Systems in petroleum processing are prone to polymerization of
2590:- Here, the fouling rate decreases with time, until it finally reaches zero. At this point, the deposit thickness remains constant with time (a horizontal
2361:
Fouling through an ionic reaction with an evolution of an inorganic solid is commonly classified as precipitation fouling (not chemical reaction fouling).
4267:
A. Szkatula, M. Balanda, M. Kopec, "Magnetic treatment of industrial water. Silica activation". Eur. Phys. J.Applied Physics, 1, vol. 18, p. 41-49, 2002
3917:
Changani, S.D.; Belmar-Beiny, M.T.; Fryer, P.J. (May 1997). "Engineering and chemical factors associated with fouling and cleaning in milk processing".
2259:
Particles larger than those of colloidal dimensions may also foul e.g., by sedimentation ("sedimentation fouling") or straining in small-size openings.
903:
The calcium carbonate that forms through this reaction precipitates. Due to the temperature dependence of the reaction, and increasing volatility of CO
303:
4061:"Steam Generator Thermal Performance Degradation Case Studies", Report TR-110018, Electric Power Research Institute, Palo Alto, California, USA, 1998
1639:- kinetic rate constants for the transport, the surface reaction, and the overall deposition reaction, respectively; with the dimension of m/s (when
3200:=0. In the absence of consolidation, the asymptotic fouling is always anticipated by this older model and the fouling progress can be described as:
4172:
H. Mueller-Steinhagen and A.P. Watkinson, "Fouling of Heat Exchanger--New Approaches to Solve Old Problem", Heat Transfer Engineering, 26(2), 2005.
3516:
1939:
3167:{\displaystyle m(t)={{k_{d}C_{m}\rho } \over {\lambda }}\left(t\lambda _{c}+{{\lambda _{r}} \over {\lambda }}\left(1-e^{-\lambda t}\right)\right)}
934:
The following lists some of the industrially common phases of precipitation fouling deposits observed in practice to form from aqueous solutions:
2406:, plants, and animals on surfaces, such as ships and submarine hulls, or piping and reservoirs with untreated water. This can be accompanied by
3358:
station, typical losses could be 20 MW and up (up to 100% if the station shuts down due to fouling-induced component degradation). In seawater
2262:
With time, the resulting surface deposit may harden through processes collectively known as "deposit consolidation" or, colloquially, "aging".
2468:) experienced (presumably) abiotic fouling of solar panels by dust particles from the Martian atmosphere. Some of the deposits subsequently
3828:
Ruckenstein, Eli; Prieve, Dennis C. (1973). "Rate of deposition of Brownian particles under the action of London and double-layer forces".
3771:
3729:
3644:
Løge, Isaac A.; Bentzon, Jakob R.; Klingaa, Christopher G.; Walther, Jens H.; Anabaraonye, Benaiah U.; Fosbøl, Philip L. (February 2022).
2252:. A maximum fouling rate is usually observed when the fouling particles and the substrate exhibit opposite electrical charge, or near the
4065:
2729: [ rate of deposit accumulation ] = [ rate of deposition ] - [ rate of re-entrainment of unconsolidated deposit ]
4251:
3339:
input to compensate for the reduced output caused by fouling, and an increased use of cooling water in once-through cooling systems.
492:
Living organisms – deposition of excess minerals (e.g., calcium, iron, copper) in tissues is (sometimes controversially) linked to
1216:
4102:"Theoretical framework for predicting inorganic fouling in membrane distillation and experimental validation with calcium sulfate"
1865:
An alternative to using the sticking probability is to use a kinetic attachment rate constant, assuming the first order reaction:
4183:
3800:
3206:
1313:
3587:
3327:, premature failure of electrical heating elements, and a large number of other often unanticipated problems. In addition, the
296:
4268:
3709:
Siobhán Francesca E. Boerlage, "Scaling and Particulate Fouling in Membrane Filtration Systems", Taylor & Francis; 2001,
2680:
Induction period, i.e., a near-nil fouling rate at the initial period of fouling (observed only for some fouling mechanisms);
2649:, but may also occur by inertial coasting/impaction, particle interception by the surface (for particles with finite sizes),
2683:
Foulant crystallisation on the surface (or attachment of the colloidal particle, or chemical reaction, or bacterial growth);
2429:), which produce sulfide and often cause corrosion of ferrous metals (and other alloys). Sulfide-oxidizing bacteria (e.g.,
2358:
of organic matter. The food industry, for example milk processing, also experiences fouling problems by chemical reactions.
330:
Fouling phenomena are common and diverse, ranging from fouling of ship hulls, natural surfaces in the marine environment (
319:
is the accumulation of unwanted material on solid surfaces. The fouling materials can consist of either living organisms (
1135:
4282:
3372:
in lost revenue in a typical power plant), and the cost of actually doing this maintenance. Finally, fouling is often a
1698:") or in gas progresses by a mechanism different than precipitation fouling. This process is usually most important for
907:
with increasing temperature, the scaling is higher at the hotter outlet of the heat exchanger than at the cooler inlet.
3748:
2310:
is also of industrial significance. The particles can be either solid or liquid. The common examples can be fouling by
644:
Solidification fouling - when components of the flowing fluid with a high-melting point freeze onto a subcooled surface
4287:
122:
3714:
289:
141:
94:
2027:
1871:
927:. Similarly, precipitation fouling can occur because of solubility changes induced by other factors, e.g., liquid
4202:
Herve BODINEAU and Thierry SOLLIER, "Tube support plate clogging up of French steam generators", Eurosafe webpage
3619:
2580:
to the fouling curve at zero deposit loading or zero time) and the fouling rate after a long period of time (an
4311:
101:
79:
3855:
Bowen, Bruce D; Epstein, Norman (October 1979). "Fine particle deposition in smooth parallel-plate channels".
1933:
and then the transport and attachment kinetic coefficients are combined as two processes occurring in series:
3423:. The generation of the corrosion products in the water piping systems is often minimized by controlling the
3188:
This model reproduces either linear, falling, or asymptotic fouling, depending on the relative values of k, λ
2327:
641:
Chemical reaction fouling, for example, decomposition or polymerization of organic matter on heating surfaces
4316:
2315:
2248:
phenomenon, this fouling mechanism can be very sensitive to factors that affect colloidal stability, e.g.,
17:
423:– increases pressure drop, increases energy expenditure, reduces flux, membrane failure (in severe cases);
3500:
2641:
Foulant transport from the bulk of the process fluid to the fouling surface. This transport is often by
2493:
2240:
are the concentration of the particle foulant at the interface and in the bulk fluid, respectively; kg m.
252:
108:
3583:
3367:-operated coolers is also easily in the two-digit area. In addition to the operational costs, also the
3011:
is the mass loading of the removable (i.e., unconsolidated) fraction of the surface deposit (kg/m); and
2134:
1589:
242:
4049:
2095:
4321:
3609:
2520:
2497:
2422:
1050:
742:
538:
443:
257:
173:
2750:
2623:
Schematics of the fouling process consisting of simultaneous foulant deposition and deposit removal.
690:
90:
4326:
3546:
3485:. One of the most important unoxidizable biocides is a mixture of chloromethyl-isothiazolinone and
2426:
1642:
75:
3789:
T.R. Bott, "Fouling of Heat Exchangers (Chemical Engineering Monographs)", Elsevier Science, 1995.
2507:
is of primary concern, it is important to note non-uniformity of deposit thickness (e.g., deposit
1741:
2512:
2314:, or fouling of air-cooled components by dust in air. The mechanisms are discussed in article on
1543:
483:
262:
68:
3768:
1584:
for the crystallization reaction and the overall deposition process, respectively, dimensionless
386:
Examples of components that may be subject to fouling and the corresponding effects of fouling:
3331:
costs should be (but typically are not) considered. The ecological costs arise from the use of
3305:
2719:
2457:
2433:), on the other hand, can produce sulfuric acid, and can be involved in corrosion of concrete.
2389:
893:{\displaystyle {\ce {\mathsf {{Ca(HCO3)2}_{(aqueous)}->{CaCO3(v)}+{CO2}\!{\uparrow }+H2O}}}}
232:
2977:
m is the mass loading of the deposit (consolidated and unconsolidated) on the surface (kg/m);
2697:
2674:
1858:
for colloidal particles is a function of both the surface chemistry, geometry, and the local
923:
systems can occur due to differential solubility of barium sulfate in solutions of different
541:. They may also create flow blockages, redistribute the flow inside the components, or cause
35:
4062:
3986:
Hong Lu, "Composite Fouling of Heat Exchanger Surfaces", Nova Science Books, New York, 2007.
3717:
2439:
serve as an example of larger animals that have caused widespread fouling in North America.
3864:
2253:
2216:
2189:
1814:
1787:
1712:
1514:
1485:
1456:
715:
614:
4248:
3998:"Growth mechanisms of composite fouling: The impact of substrates on detachment processes"
2488:
can be of particular interest when the impact of fouling on pressure drop is of interest.
8:
4258:", Public Works Technical Bulletin 420-49-34, U.S. Army Corps of Engineers, 15 June 2001.
4100:
Warsinger, David M.; Tow, Emily W.; Swaminathan, Jaichander; Lienhard V, John H. (2017).
3614:
3448:
3420:
3416:
3408:
3373:
2407:
2384:
1838:
are the kinetic rate constants for deposition and transport, respectively. The value of
990:
749:
475:
277:
247:
212:
3868:
3376:
of serious degradation problems that may limit the life of components or entire plants.
4019:
3969:
3677:
3320:
3287:
where m is the maximum (asymptotic) mass loading of the deposit on the surface (kg/m).
1841:
1718:
1434:
1412:
394:
327:
also have meanings outside of this scope; therefore, they should be used with caution.
237:
217:
4154:
Kern, D.O.; Seaton, R.E. (1959). "A theoretical analysis of thermal surface fouling".
3930:
3695:
2700:, which account for deposit losing its porosity and becoming more tenacious with time;
931:, liquid degassing, redox potential changes, or mixing of incompatible fluid streams.
657:
Composite fouling, whereby fouling involves more than one foulant or fouling mechanism
4023:
3961:
3876:
3710:
3681:
3559:
3540:
3316:
2712:
2581:
2516:
2504:
2485:
2465:
2430:
2245:
1581:
1538:- equilibrium concentration of the substance at the conditions of the interface, kg/m
938:
928:
753:
367:
347:
331:
207:
176:
115:
3973:
2402:
or biological fouling is the undesirable accumulation of micro-organisms, algae and
1128:
The deposition rate by precipitation is often described by the following equations:
4306:
4301:
4126:
4116:
4009:
3953:
3926:
3899:
3872:
3837:
3667:
3657:
3646:"Scale attachment and detachment: The role of hydrodynamics and surface morphology"
3563:
3536:
3440:
2693:
2658:
2554:
1012:
964:
703:
602:
513:
matter of either biological or inorganic origin, for example industrially produced
420:
39:
4255:
4236:
4208:
4190:
4121:
4069:
3957:
3807:
3775:
3755:
3736:
3532:
3524:
3504:
3412:
3404:
2650:
2265:
The common particulate fouling deposits formed from aqueous suspensions include:
1859:
1072:
998:
974:
956:
920:
738:
699:
598:
486:
with time; plugging; in some cases complete stoppage of flow in a matter of days;
427:
3996:
Løge, Isaac A.; Anabaraonye, Benaiah U.; Fosbøl, Philip Loldrup (October 2022).
3605:
International Convention on the Control of Harmful Anti-fouling Systems on Ships
354:
the one that is usually more difficult to prevent and therefore more important.
3672:
3555:
3528:
3400:
3364:
2654:
2646:
2469:
2414:
2343:
2249:
1113:
1106:
980:
924:
734:
675:
581:
405:
390:
335:
158:
4014:
3997:
3662:
3645:
2631:
Generation or ingress of the species that causes fouling ("foulant sourcing");
2421:
in closed systems when sufficient nutrients are present. Examples may include
430:– increases temperature of the element, increases corrosion, reduces lifespan;
4295:
3624:
3489:-isothiazolinone. Also applied are dibrom nitrilopropionamide and quaternary
3470:
3385:
3355:
3351:
3347:
2666:
2607:
2533:
2355:
2295:
2281:
2016:{\displaystyle k_{d}=\left({\frac {1}{k_{a}}}+{\frac {1}{k_{t}}}\right)^{-1}}
534:
456:
343:
339:
267:
4036:
3903:
3586:
alternative. In some heat-transfer applications, mechanical mitigation with
3965:
3494:
3436:
3368:
3359:
2670:
2461:
2436:
2393:
1704:
1036:
635:
452:
437:
2417:, lipids, nucleic acids, etc.). The biofilm structure is usually complex.
4130:
3841:
3591:
2662:
1708:
730:
620:
162:
517:. Such matter enters into the cooling water circuit through the cooling
3432:
3396:
3392:
3328:
2704:
2528:
2399:
2379:
2351:
2269:
1080:
911:
719:
647:
518:
497:
468:
462:
320:
180:
2689:
Deposit dissolution (or re-entrainment of loosely attached particles);
2634:
Foulant transport with the stream of the process fluid (most often by
562:
Tools and other "foreign objects" accidentally left after maintenance;
3512:
3459:
3444:
3443:), control of oxygen dissolved in water (for example, by addition of
3312:
2642:
2635:
2591:
2285:
2273:
1699:
1044:
1040:
1024:
1002:
960:
946:
723:
711:
670:
631:
624:
610:
379:
202:
2627:
Fouling of a system can be modelled as consisting of several steps:
666:
465:
in airplanes – inaccurate or incorrect indication of airplane speed;
350:
on teeth or deposits on solar panels on Mars, among other examples.
57:
3490:
3462:
3324:
3290:
3022:
This system of equations can be integrated (taking that m = 0 and m
2524:
2508:
2339:
2311:
2289:
2277:
1099:
1084:
1076:
1066:
1062:
1058:
1054:
1020:
1016:
1008:
950:
651:
542:
479:
374:
227:
197:
30:
This article is about fouling in engineering. For uses of the term
2619:
2570:- The fouling rate can be steady with time. This is a common case.
2472:. This illustrates the universal nature of the fouling phenomena.
4099:
3579:
3520:
3482:
3466:
3455:
3428:
3332:
2577:
2403:
2307:
1095:
994:
942:
682:
433:
411:
46:
3594:
cleaning methods are available for many specific applications.
3486:
3478:
3295:
2347:
2326:
Corrosion deposits are created in-situ by the corrosion of the
1480:- concentration of the substance in the bulk of the fluid, kg/m
1091:
1032:
1028:
984:
968:
571:
514:
510:
3747:"Spark Plug Faces", brochure "Bosch Spark Plugs 0307", Part 1
3454:
For water systems at relatively low temperatures, the applied
752:- always prevailing in natural water - and the poorly soluble
3943:
3474:
3389:
1695:
1301:{\displaystyle {\frac {dm}{dt}}={k_{r}}(C_{i}-C_{e})^{n_{1}}}
707:
606:
565:
526:
493:
3342:
For example, "normal" fouling at a conventionally fired 500
489:
Teeth – promotes tooth or gum disease, decreases aesthetics;
446:– axial offset anomaly, may need to de-rate the power plant;
362:
169:
154:
3889:
3575:
3567:
3508:
3343:
3336:
3277:{\displaystyle m(t)=m^{*}\left(1-e^{-\lambda _{r}t}\right)}
2956:
2708:
2299:
1396:{\displaystyle {\frac {dm}{dt}}=k_{d}(C_{b}-C_{e})^{n_{2}}}
748:
As an example, the equilibrium between the readily soluble
577:
530:
272:
436:
barrels - increases chamber pressure; hampers loading for
3916:
3643:
3311:
The losses initially result from impaired heat transfer,
882:
859:
836:
819:
801:
788:
522:
2354:, waxes, etc.). High tube wall temperatures may lead to
417:
Solar panels – decreases the electrical power generated;
3830:
Journal of the Chemical Society, Faraday Transactions 2
3424:
2696:
or differential solubility in temperature gradient) or
1509:- concentration of the substance at the interface, kg/m
813:
807:
791:
775:
414:– reduces efficiency, increases probability of failure;
3299:
Cost relations between the individual types of fouling
3995:
3892:
Comprehensive Reviews in Food Science and Food Safety
3209:
3035:
2744:
2219:
2192:
2137:
2098:
2030:
1942:
1874:
1844:
1817:
1790:
1744:
1721:
1645:
1592:
1546:
1517:
1488:
1459:
1437:
1415:
1316:
1219:
1138:
765:
623:
fouling, i.e., accumulation of particles, typically
3427:
of the process fluid (typically alkalinization with
3335:
for the avoidance of biofouling, from the increased
2692:
Deposit consolidation on the surface (e.g., through
1429:- mass of the material (per unit surface area), kg/m
593:
As to micro fouling, distinctions are made between:
2184:
are the kinetic rate constants for deposition, m/s,
2129:
is the rate of the deposition by particles, kg m s,
1204:{\displaystyle {\frac {dm}{dt}}=k_{t}(C_{b}-C_{i})}
459:– inaccurate or incorrect measurement of flow rate;
82:. Unsourced material may be challenged and removed.
27:
Accumulation of unwanted material on solid surfaces
4093:
3276:
3166:
2962:
2232:
2205:
2176:
2121:
2078:
2015:
1922:
1850:
1830:
1803:
1773:
1727:
1677:
1631:
1572:
1530:
1501:
1472:
1443:
1421:
1395:
1300:
1203:
892:
756:, the following chemical equation may be written:
3827:
863:
4293:
3291:Economic and environmental importance of fouling
2997:- mass fraction of foulant in the fluid (kg/kg);
2543:
357:
3946:Critical Reviews in Food Science and Nutrition
408:, increases fuel usage, reduces maximum speed;
2302:and other relatively coarse suspended matter.
2079:{\displaystyle {\frac {dm}{dt}}={k_{d}}C_{b}}
1923:{\displaystyle {\frac {dm}{dt}}={k_{a}}C_{i}}
297:
3854:
3523:, and other "film-forming" amines), organic
3388:and other major industrial installations of
2475:
2333:
737:, the concentration of salts may exceed the
617:(e.g., calcium carbonate or calcium sulfate)
338:components through ingredients contained in
729:Through changes in temperature, or solvent
630:Corrosion fouling, i.e., in-situ growth of
4153:
3004:is the re-entrainment rate constant (1/s);
1694:Fouling by particles suspended in water ("
698:Scaling or precipitation fouling involves
304:
290:
4120:
4013:
3705:
3703:
3671:
3661:
3395:, macro fouling is avoided by way of pre-
3018:is the consolidation rate constant (1/s).
2364:
949:usually at t > ~50 °C, or rarely
885:
873:
850:
827:
810:
779:
770:
142:Learn how and when to remove this message
3857:Journal of Colloid and Interface Science
3315:damage (in particular under-deposit and
3294:
2618:
2383:
689:
681:
665:
661:
373:
361:
168:
153:
38:. For fouling on membrane surfaces, see
3588:dynamic scraped surface heat exchangers
3350:unit accounts for output losses of the
910:In general, the dependence of the salt
366:cross-section of a condenser tube with
14:
4294:
3919:Experimental Thermal and Fluid Science
3785:
3783:
3700:
2987:is the deposition rate constant (m/s);
2408:microbiologically influenced corrosion
1689:
1124:) from extremely pure, low-iron water.
877:
869:
854:
845:
831:
796:
783:
559:Detached internal parts of components;
471:electrodes in cars – engine misfiring;
342:or gases, and even the development of
4037:Mars Pathfinder - Dust Settling (MAE)
3493:compounds. For underwater ship hulls
597:Scaling or precipitation fouling, as
2614:
2442:
2321:
634:deposits, for example, magnetite on
80:adding citations to reliable sources
51:
3780:
2665:(in condensation and evaporation),
378:cross-section of a brass tube with
24:
3511:), long-chain aliphatic amines or
3379:
2451:
2350:or deposition of heavy fractions (
2270:iron oxides and iron oxyhydroxides
25:
4338:
4276:
3590:is an option. Also ultrasonic or
2392:in Northern France, covered with
2177:{\displaystyle k_{a},k_{t},k_{d}}
1632:{\displaystyle k_{t},k_{r},k_{d}}
686:Extreme boiler pipe scale buildup
3566:, or of low surface energy like
3469:compounds, chlorine and bromide
3354:of 5 MW and more. In a 1,300 MW
2673:(acting on rotating particles),
2122:{\displaystyle {\frac {dm}{dt}}}
588:
504:
404:Ship hulls – creates additional
56:
4261:
4241:
4222:
4213:
4195:
4175:
4166:
4147:
4137:
4084:
4075:
4055:
4041:
4030:
3989:
3980:
3937:
3910:
3883:
3848:
3821:
3620:Steam generator (nuclear power)
580:, parts of plants up to entire
67:needs additional citations for
3812:
3792:
3760:
3741:
3722:
3688:
3637:
3458:may be classified as follows:
3219:
3213:
3045:
3039:
2990:ρ is the fluid density (kg/m);
2950:
2944:
2915:
2909:
2827:
2821:
2306:Fouling by particles from gas
1377:
1350:
1282:
1255:
1198:
1172:
865:
840:
822:
745:of solids (usually crystals).
13:
1:
3931:10.1016/S0894-1777(96)00141-0
3631:
2544:Progress of fouling with time
2373:
2342:. For example, corrosion and
1678:{\displaystyle n_{1}=n_{2}=1}
358:Components subject to fouling
4156:British Chemical Engineering
4122:10.1016/j.memsci.2017.01.031
4002:Chemical Engineering Journal
3958:10.1080/10408398.2012.752343
3877:10.1016/0021-9797(79)90184-X
3650:Chemical Engineering Journal
1774:{\displaystyle k_{d}=Pk_{t}}
7:
4109:Journal of Membrane Science
3597:
3562:(for example, very smooth,
3501:Chemical fouling inhibitors
3026:= 0 at t = 0) to the form:
1573:{\displaystyle n_{1},n_{2}}
533:. In closed circuits, like
521:from sources like the open
509:Macro fouling is caused by
253:Metal-induced embrittlement
10:
4343:
4283:Crude Oil Fouling research
3584:environmentally friendlier
2377:
1213:Surface crystallisation:
1051:Aluminium oxide hydroxides
444:pressurized water reactors
243:Liquid metal embrittlement
44:
29:
4015:10.1016/j.cej.2022.137008
3663:10.1016/j.cej.2021.132583
3610:Oilfield scale inhibition
2521:stress corrosion cracking
2498:heat transfer coefficient
2496:"), or by development of
2476:Quantification of fouling
2470:spontaneously cleaned off
2423:sulfate-reducing bacteria
2334:Chemical reaction fouling
539:heat transfer coefficient
421:Reverse osmosis membranes
258:Stress corrosion cracking
165:, fouled by macro fouling
4249:Magnetic Water Treatment
3547:Magnetic water treatment
2647:turbulent-eddy diffusion
2523:, or localized wastage.
2427:sulfur-reducing bacteria
190:Mechanical failure modes
45:Not to be confused with
34:outside technology, see
3904:10.1111/1541-4337.12000
3481:cleavers, unoxidizable
3346:(net electrical power)
2677:, and other mechanisms.
2458:Mars Exploration Rovers
627:particles, on a surface
263:Sulfide stress cracking
3300:
3278:
3168:
2964:
2624:
2584:to the fouling curve).
2396:
2365:Solidification fouling
2234:
2207:
2178:
2123:
2080:
2017:
1924:
1852:
1832:
1805:
1775:
1729:
1679:
1633:
1574:
1532:
1503:
1474:
1445:
1423:
1397:
1302:
1205:
894:
695:
687:
679:
650:, like settlements of
383:
371:
233:Hydrogen embrittlement
184:
166:
4312:Hydraulic engineering
3298:
3279:
3169:
2965:
2675:thermoelectric effect
2622:
2387:
2235:
2233:{\displaystyle C_{b}}
2208:
2206:{\displaystyle C_{i}}
2179:
2124:
2081:
2018:
1925:
1853:
1833:
1831:{\displaystyle k_{t}}
1806:
1804:{\displaystyle k_{d}}
1776:
1730:
1680:
1634:
1575:
1533:
1531:{\displaystyle C_{e}}
1504:
1502:{\displaystyle C_{i}}
1475:
1473:{\displaystyle C_{b}}
1446:
1424:
1398:
1303:
1206:
895:
722:and often results in
693:
685:
669:
662:Precipitation fouling
377:
365:
172:
157:
36:Foul (disambiguation)
3842:10.1039/F29736901522
3560:Low-fouling surfaces
3449:corrosion inhibitors
3386:steam power stations
3207:
3033:
2742:
2598:Accelerating fouling
2513:intergranular attack
2503:If under-deposit or
2254:point of zero charge
2244:Being essentially a
2217:
2190:
2135:
2096:
2028:
1940:
1872:
1842:
1815:
1788:
1742:
1719:
1713:sticking probability
1643:
1590:
1544:
1515:
1486:
1457:
1435:
1413:
1314:
1217:
1136:
763:
484:petroleum production
476:petroleum reservoirs
76:improve this article
4317:Transport phenomena
3869:1979JCIS...72...81B
3673:20.500.11850/517338
3615:Particle deposition
3564:implanted with ions
3421:ion-exchange resins
3417:electrodeionization
2256:of either of them.
1690:Particulate fouling
991:Magnesium hydroxide
884:
861:
838:
821:
803:
790:
750:calcium bicarbonate
474:Production zone of
393:surfaces – reduces
248:Mechanical overload
4254:2011-12-15 at the
4235:2011-07-10 at the
4207:2011-07-26 at the
4189:2009-05-12 at the
4068:2011-07-10 at the
3806:2009-05-12 at the
3774:2010-05-30 at the
3754:2009-12-29 at the
3735:2006-09-17 at the
3447:), or addition of
3399:and cooling water
3301:
3274:
3164:
2960:
2955:
2625:
2588:Asymptotic fouling
2562:"Negative" fouling
2500:(W/mK) with time.
2494:fouling resistance
2397:
2316:aerosol deposition
2230:
2203:
2174:
2119:
2076:
2013:
1920:
1848:
1828:
1801:
1771:
1725:
1675:
1629:
1570:
1528:
1499:
1470:
1441:
1419:
1393:
1298:
1201:
977:(e.g., beerstone);
890:
872:
849:
826:
778:
773:
768:
696:
688:
680:
395:thermal efficiency
384:
372:
185:
167:
3952:(12): 1724–1743.
3580:complexing agents
3541:process chemicals
3317:crevice corrosion
3125:
3083:
2615:Fouling modelling
2582:oblique asymptote
2505:crevice corrosion
2486:surface roughness
2443:Composite fouling
2431:Acidithiobacillus
2322:Corrosion fouling
2246:surface chemistry
2117:
2049:
1997:
1977:
1893:
1851:{\displaystyle P}
1728:{\displaystyle P}
1582:order of reaction
1444:{\displaystyle t}
1422:{\displaystyle m}
1335:
1238:
1157:
1090:Copper (metallic
939:Calcium carbonate
887:
875:
852:
829:
812:
781:
772:
754:calcium carbonate
368:calcium carbonate
314:
313:
208:Corrosion fatigue
179:with residues of
152:
151:
144:
126:
16:(Redirected from
4334:
4322:Water technology
4271:
4265:
4259:
4245:
4239:
4226:
4220:
4217:
4211:
4199:
4193:
4179:
4173:
4170:
4164:
4163:
4151:
4145:
4141:
4135:
4134:
4124:
4106:
4097:
4091:
4088:
4082:
4079:
4073:
4059:
4053:
4045:
4039:
4034:
4028:
4027:
4017:
3993:
3987:
3984:
3978:
3977:
3941:
3935:
3934:
3914:
3908:
3907:
3887:
3881:
3880:
3852:
3846:
3845:
3825:
3819:
3816:
3810:
3796:
3790:
3787:
3778:
3764:
3758:
3745:
3739:
3726:
3720:
3707:
3698:
3692:
3686:
3685:
3675:
3665:
3641:
3537:polyacrylic acid
3533:polyelectrolytes
3525:phosphonic acids
3505:chelating agents
3441:sodium phosphate
3283:
3281:
3280:
3275:
3273:
3269:
3268:
3267:
3263:
3262:
3234:
3233:
3173:
3171:
3170:
3165:
3163:
3159:
3158:
3154:
3153:
3152:
3126:
3124:
3119:
3118:
3117:
3107:
3102:
3101:
3084:
3082:
3077:
3073:
3072:
3063:
3062:
3052:
2969:
2967:
2966:
2961:
2959:
2958:
2943:
2942:
2930:
2929:
2908:
2907:
2898:
2897:
2882:
2881:
2872:
2871:
2859:
2852:
2847:
2846:
2820:
2819:
2810:
2809:
2794:
2793:
2784:
2783:
2771:
2764:
2694:Ostwald ripening
2659:diffusiophoresis
2555:Induction period
2388:A fragment of a
2239:
2237:
2236:
2231:
2229:
2228:
2212:
2210:
2209:
2204:
2202:
2201:
2183:
2181:
2180:
2175:
2173:
2172:
2160:
2159:
2147:
2146:
2128:
2126:
2125:
2120:
2118:
2116:
2108:
2100:
2085:
2083:
2082:
2077:
2075:
2074:
2065:
2064:
2063:
2050:
2048:
2040:
2032:
2022:
2020:
2019:
2014:
2012:
2011:
2003:
1999:
1998:
1996:
1995:
1983:
1978:
1976:
1975:
1963:
1952:
1951:
1929:
1927:
1926:
1921:
1919:
1918:
1909:
1908:
1907:
1894:
1892:
1884:
1876:
1857:
1855:
1854:
1849:
1837:
1835:
1834:
1829:
1827:
1826:
1810:
1808:
1807:
1802:
1800:
1799:
1780:
1778:
1777:
1772:
1770:
1769:
1754:
1753:
1734:
1732:
1731:
1726:
1684:
1682:
1681:
1676:
1668:
1667:
1655:
1654:
1638:
1636:
1635:
1630:
1628:
1627:
1615:
1614:
1602:
1601:
1579:
1577:
1576:
1571:
1569:
1568:
1556:
1555:
1537:
1535:
1534:
1529:
1527:
1526:
1508:
1506:
1505:
1500:
1498:
1497:
1479:
1477:
1476:
1471:
1469:
1468:
1450:
1448:
1447:
1442:
1428:
1426:
1425:
1420:
1402:
1400:
1399:
1394:
1392:
1391:
1390:
1389:
1375:
1374:
1362:
1361:
1349:
1348:
1336:
1334:
1326:
1318:
1307:
1305:
1304:
1299:
1297:
1296:
1295:
1294:
1280:
1279:
1267:
1266:
1254:
1253:
1252:
1239:
1237:
1229:
1221:
1210:
1208:
1207:
1202:
1197:
1196:
1184:
1183:
1171:
1170:
1158:
1156:
1148:
1140:
1073:Aluminosilicates
899:
897:
896:
891:
889:
888:
883:
880:
868:
862:
860:
857:
844:
843:
837:
834:
820:
817:
816:
804:
802:
799:
794:
789:
786:
442:Nuclear fuel in
428:heating elements
306:
299:
292:
187:
186:
147:
140:
136:
133:
127:
125:
84:
60:
52:
40:Membrane fouling
21:
4342:
4341:
4337:
4336:
4335:
4333:
4332:
4331:
4327:Water treatment
4292:
4291:
4279:
4274:
4266:
4262:
4256:Wayback Machine
4246:
4242:
4237:Wayback Machine
4227:
4223:
4218:
4214:
4209:Wayback Machine
4200:
4196:
4191:Wayback Machine
4180:
4176:
4171:
4167:
4152:
4148:
4142:
4138:
4104:
4098:
4094:
4089:
4085:
4080:
4076:
4070:Wayback Machine
4060:
4056:
4046:
4042:
4035:
4031:
3994:
3990:
3985:
3981:
3942:
3938:
3915:
3911:
3888:
3884:
3853:
3849:
3826:
3822:
3817:
3813:
3808:Wayback Machine
3797:
3793:
3788:
3781:
3776:Wayback Machine
3765:
3761:
3756:Wayback Machine
3746:
3742:
3737:Wayback Machine
3727:
3723:
3708:
3701:
3693:
3689:
3642:
3638:
3634:
3629:
3600:
3413:reverse osmosis
3405:microfiltration
3382:
3380:Fouling control
3293:
3258:
3254:
3250:
3246:
3239:
3235:
3229:
3225:
3208:
3205:
3204:
3199:
3195:
3191:
3184:
3180:
3142:
3138:
3131:
3127:
3120:
3113:
3109:
3108:
3106:
3097:
3093:
3089:
3085:
3078:
3068:
3064:
3058:
3054:
3053:
3051:
3034:
3031:
3030:
3025:
3017:
3010:
3003:
2996:
2986:
2954:
2953:
2938:
2934:
2925:
2921:
2903:
2899:
2893:
2889:
2877:
2873:
2867:
2863:
2848:
2842:
2838:
2834:
2831:
2830:
2815:
2811:
2805:
2801:
2789:
2785:
2779:
2775:
2760:
2753:
2746:
2745:
2743:
2740:
2739:
2651:electrophoresis
2617:
2574:Falling fouling
2546:
2478:
2454:
2452:Fouling on Mars
2445:
2415:polysaccharides
2382:
2376:
2367:
2336:
2324:
2224:
2220:
2218:
2215:
2214:
2197:
2193:
2191:
2188:
2187:
2168:
2164:
2155:
2151:
2142:
2138:
2136:
2133:
2132:
2109:
2101:
2099:
2097:
2094:
2093:
2070:
2066:
2059:
2055:
2054:
2041:
2033:
2031:
2029:
2026:
2025:
2004:
1991:
1987:
1982:
1971:
1967:
1962:
1961:
1957:
1956:
1947:
1943:
1941:
1938:
1937:
1914:
1910:
1903:
1899:
1898:
1885:
1877:
1875:
1873:
1870:
1869:
1860:thermohydraulic
1843:
1840:
1839:
1822:
1818:
1816:
1813:
1812:
1795:
1791:
1789:
1786:
1785:
1765:
1761:
1749:
1745:
1743:
1740:
1739:
1720:
1717:
1716:
1692:
1663:
1659:
1650:
1646:
1644:
1641:
1640:
1623:
1619:
1610:
1606:
1597:
1593:
1591:
1588:
1587:
1564:
1560:
1551:
1547:
1545:
1542:
1541:
1522:
1518:
1516:
1513:
1512:
1493:
1489:
1487:
1484:
1483:
1464:
1460:
1458:
1455:
1454:
1436:
1433:
1432:
1414:
1411:
1410:
1385:
1381:
1380:
1376:
1370:
1366:
1357:
1353:
1344:
1340:
1327:
1319:
1317:
1315:
1312:
1311:
1290:
1286:
1285:
1281:
1275:
1271:
1262:
1258:
1248:
1244:
1243:
1230:
1222:
1220:
1218:
1215:
1214:
1192:
1188:
1179:
1175:
1166:
1162:
1149:
1141:
1139:
1137:
1134:
1133:
1123:
1119:
999:magnesium oxide
975:Calcium oxalate
957:Calcium sulfate
921:reverse osmosis
906:
881:
876:
864:
858:
853:
848:
839:
835:
830:
825:
818:
806:
805:
800:
795:
787:
782:
774:
769:
767:
766:
764:
761:
760:
741:, leading to a
700:crystallization
664:
599:crystallization
591:
556:Manmade refuse;
507:
360:
310:
148:
137:
131:
128:
85:
83:
73:
61:
50:
43:
28:
23:
22:
15:
12:
11:
5:
4340:
4330:
4329:
4324:
4319:
4314:
4309:
4304:
4290:
4289:
4285:
4278:
4277:External links
4275:
4273:
4272:
4260:
4240:
4221:
4212:
4194:
4174:
4165:
4146:
4136:
4092:
4083:
4074:
4054:
4040:
4029:
3988:
3979:
3936:
3925:(4): 392–406.
3909:
3898:(2): 121–143.
3882:
3847:
3820:
3811:
3791:
3779:
3759:
3740:
3721:
3718:(Google books)
3699:
3687:
3635:
3633:
3630:
3628:
3627:
3622:
3617:
3612:
3607:
3601:
3599:
3596:
3535:(for example,
3529:etidronic acid
3527:(for example,
3517:octadecylamine
3515:(for example,
3507:(for example,
3401:debris filters
3381:
3378:
3292:
3289:
3285:
3284:
3272:
3266:
3261:
3257:
3253:
3249:
3245:
3242:
3238:
3232:
3228:
3224:
3221:
3218:
3215:
3212:
3197:
3193:
3189:
3182:
3178:
3175:
3174:
3162:
3157:
3151:
3148:
3145:
3141:
3137:
3134:
3130:
3123:
3116:
3112:
3105:
3100:
3096:
3092:
3088:
3081:
3076:
3071:
3067:
3061:
3057:
3050:
3047:
3044:
3041:
3038:
3023:
3020:
3019:
3015:
3012:
3008:
3005:
3001:
2998:
2994:
2991:
2988:
2984:
2981:
2980:t is time (s);
2978:
2971:
2970:
2957:
2952:
2949:
2946:
2941:
2937:
2933:
2928:
2924:
2920:
2917:
2914:
2911:
2906:
2902:
2896:
2892:
2888:
2885:
2880:
2876:
2870:
2866:
2862:
2858:
2855:
2851:
2845:
2841:
2837:
2833:
2832:
2829:
2826:
2823:
2818:
2814:
2808:
2804:
2800:
2797:
2792:
2788:
2782:
2778:
2774:
2770:
2767:
2763:
2759:
2756:
2752:
2751:
2749:
2717:
2716:
2701:
2690:
2687:
2684:
2681:
2678:
2655:thermophoresis
2639:
2632:
2616:
2613:
2612:
2611:
2608:sawtooth curve
2604:Seesaw fouling
2601:
2595:
2585:
2571:
2568:Linear fouling
2565:
2559:
2545:
2542:
2477:
2474:
2453:
2450:
2444:
2441:
2378:Main article:
2375:
2372:
2366:
2363:
2344:polymerization
2335:
2332:
2323:
2320:
2304:
2303:
2293:
2250:zeta potential
2242:
2241:
2227:
2223:
2200:
2196:
2185:
2171:
2167:
2163:
2158:
2154:
2150:
2145:
2141:
2130:
2115:
2112:
2107:
2104:
2087:
2086:
2073:
2069:
2062:
2058:
2053:
2047:
2044:
2039:
2036:
2023:
2010:
2007:
2002:
1994:
1990:
1986:
1981:
1974:
1970:
1966:
1960:
1955:
1950:
1946:
1931:
1930:
1917:
1913:
1906:
1902:
1897:
1891:
1888:
1883:
1880:
1847:
1825:
1821:
1798:
1794:
1782:
1781:
1768:
1764:
1760:
1757:
1752:
1748:
1724:
1691:
1688:
1687:
1686:
1674:
1671:
1666:
1662:
1658:
1653:
1649:
1626:
1622:
1618:
1613:
1609:
1605:
1600:
1596:
1585:
1567:
1563:
1559:
1554:
1550:
1539:
1525:
1521:
1510:
1496:
1492:
1481:
1467:
1463:
1452:
1440:
1430:
1418:
1404:
1403:
1388:
1384:
1379:
1373:
1369:
1365:
1360:
1356:
1352:
1347:
1343:
1339:
1333:
1330:
1325:
1322:
1308:
1293:
1289:
1284:
1278:
1274:
1270:
1265:
1261:
1257:
1251:
1247:
1242:
1236:
1233:
1228:
1225:
1211:
1200:
1195:
1191:
1187:
1182:
1178:
1174:
1169:
1165:
1161:
1155:
1152:
1147:
1144:
1126:
1125:
1121:
1117:
1114:nickel ferrite
1110:
1107:hydroxyapatite
1103:
1088:
1070:
1048:
1006:
988:
981:Barium sulfate
978:
972:
954:
925:ionic strength
904:
901:
900:
879:
871:
867:
856:
847:
842:
833:
824:
815:
809:
798:
793:
785:
777:
735:degasification
676:heat exchanger
663:
660:
659:
658:
655:
645:
642:
639:
628:
618:
590:
587:
586:
585:
575:
569:
563:
560:
557:
553:
552:
550:
535:cooling towers
506:
503:
502:
501:
490:
487:
472:
466:
460:
457:orifice plates
450:
447:
440:
431:
424:
418:
415:
409:
402:
398:
391:Heat exchanger
359:
356:
334:), fouling of
332:marine fouling
312:
311:
309:
308:
301:
294:
286:
283:
282:
281:
280:
275:
270:
265:
260:
255:
250:
245:
240:
235:
230:
225:
220:
215:
210:
205:
200:
192:
191:
159:Heat exchanger
150:
149:
64:
62:
55:
26:
9:
6:
4:
3:
2:
4339:
4328:
4325:
4323:
4320:
4318:
4315:
4313:
4310:
4308:
4305:
4303:
4300:
4299:
4297:
4288:
4286:
4284:
4281:
4280:
4270:
4264:
4257:
4253:
4250:
4244:
4238:
4234:
4231:
4225:
4216:
4210:
4206:
4203:
4198:
4192:
4188:
4185:
4178:
4169:
4162:(5): 258–262.
4161:
4157:
4150:
4140:
4132:
4131:1721.1/107916
4128:
4123:
4118:
4114:
4110:
4103:
4096:
4087:
4078:
4071:
4067:
4064:
4058:
4051:
4044:
4038:
4033:
4025:
4021:
4016:
4011:
4007:
4003:
3999:
3992:
3983:
3975:
3971:
3967:
3963:
3959:
3955:
3951:
3947:
3940:
3932:
3928:
3924:
3920:
3913:
3905:
3901:
3897:
3893:
3886:
3878:
3874:
3870:
3866:
3862:
3858:
3851:
3843:
3839:
3835:
3831:
3824:
3815:
3809:
3805:
3802:
3795:
3786:
3784:
3777:
3773:
3770:
3763:
3757:
3753:
3750:
3744:
3738:
3734:
3731:
3725:
3719:
3716:
3715:90-5809-242-9
3712:
3706:
3704:
3697:
3691:
3683:
3679:
3674:
3669:
3664:
3659:
3655:
3651:
3647:
3640:
3636:
3626:
3625:Tube cleaning
3623:
3621:
3618:
3616:
3613:
3611:
3608:
3606:
3603:
3602:
3595:
3593:
3589:
3585:
3581:
3577:
3571:
3569:
3565:
3561:
3557:
3551:
3548:
3544:
3542:
3538:
3534:
3530:
3526:
3522:
3518:
3514:
3510:
3506:
3502:
3498:
3497:are applied.
3496:
3495:bottom paints
3492:
3488:
3484:
3480:
3476:
3472:
3468:
3464:
3461:
3457:
3452:
3450:
3446:
3442:
3438:
3434:
3430:
3426:
3422:
3418:
3414:
3410:
3406:
3402:
3398:
3394:
3391:
3387:
3377:
3375:
3370:
3366:
3361:
3357:
3356:nuclear power
3353:
3352:steam turbine
3349:
3348:power station
3345:
3340:
3338:
3334:
3330:
3326:
3322:
3318:
3314:
3309:
3307:
3297:
3288:
3270:
3264:
3259:
3255:
3251:
3247:
3243:
3240:
3236:
3230:
3226:
3222:
3216:
3210:
3203:
3202:
3201:
3186:
3160:
3155:
3149:
3146:
3143:
3139:
3135:
3132:
3128:
3121:
3114:
3110:
3103:
3098:
3094:
3090:
3086:
3079:
3074:
3069:
3065:
3059:
3055:
3048:
3042:
3036:
3029:
3028:
3027:
3013:
3006:
2999:
2992:
2989:
2982:
2979:
2976:
2975:
2974:
2947:
2939:
2935:
2931:
2926:
2922:
2918:
2912:
2904:
2900:
2894:
2890:
2886:
2883:
2878:
2874:
2868:
2864:
2860:
2856:
2853:
2849:
2843:
2839:
2835:
2824:
2816:
2812:
2806:
2802:
2798:
2795:
2790:
2786:
2780:
2776:
2772:
2768:
2765:
2761:
2757:
2754:
2747:
2738:
2737:
2736:
2733:
2730:
2727:
2724:
2721:
2714:
2710:
2706:
2702:
2699:
2695:
2691:
2688:
2685:
2682:
2679:
2676:
2672:
2668:
2667:sedimentation
2664:
2660:
2656:
2652:
2648:
2644:
2640:
2637:
2633:
2630:
2629:
2628:
2621:
2609:
2605:
2602:
2599:
2596:
2593:
2589:
2586:
2583:
2579:
2575:
2572:
2569:
2566:
2563:
2560:
2557:
2556:
2552:
2551:
2550:
2541:
2537:
2535:
2534:hot corrosion
2530:
2526:
2522:
2518:
2514:
2510:
2506:
2501:
2499:
2495:
2489:
2487:
2482:
2473:
2471:
2467:
2463:
2459:
2449:
2440:
2438:
2437:Zebra mussels
2434:
2432:
2428:
2424:
2418:
2416:
2411:
2409:
2405:
2401:
2395:
2394:zebra mussels
2391:
2386:
2381:
2371:
2362:
2359:
2357:
2353:
2349:
2345:
2341:
2331:
2329:
2319:
2317:
2313:
2309:
2301:
2297:
2296:Sedimentation
2294:
2291:
2287:
2283:
2282:lepidocrocite
2279:
2275:
2271:
2268:
2267:
2266:
2263:
2260:
2257:
2255:
2251:
2247:
2225:
2221:
2198:
2194:
2186:
2169:
2165:
2161:
2156:
2152:
2148:
2143:
2139:
2131:
2113:
2110:
2105:
2102:
2092:
2091:
2090:
2071:
2067:
2060:
2056:
2051:
2045:
2042:
2037:
2034:
2024:
2008:
2005:
2000:
1992:
1988:
1984:
1979:
1972:
1968:
1964:
1958:
1953:
1948:
1944:
1936:
1935:
1934:
1915:
1911:
1904:
1900:
1895:
1889:
1886:
1881:
1878:
1868:
1867:
1866:
1863:
1861:
1845:
1823:
1819:
1796:
1792:
1766:
1762:
1758:
1755:
1750:
1746:
1738:
1737:
1736:
1722:
1714:
1710:
1706:
1701:
1697:
1672:
1669:
1664:
1660:
1656:
1651:
1647:
1624:
1620:
1616:
1611:
1607:
1603:
1598:
1594:
1586:
1583:
1565:
1561:
1557:
1552:
1548:
1540:
1523:
1519:
1511:
1494:
1490:
1482:
1465:
1461:
1453:
1438:
1431:
1416:
1409:
1408:
1407:
1386:
1382:
1371:
1367:
1363:
1358:
1354:
1345:
1341:
1337:
1331:
1328:
1323:
1320:
1309:
1291:
1287:
1276:
1272:
1268:
1263:
1259:
1249:
1245:
1240:
1234:
1231:
1226:
1223:
1212:
1193:
1189:
1185:
1180:
1176:
1167:
1163:
1159:
1153:
1150:
1145:
1142:
1131:
1130:
1129:
1115:
1112:Magnetite or
1111:
1108:
1104:
1101:
1097:
1093:
1089:
1086:
1082:
1078:
1074:
1071:
1068:
1064:
1060:
1056:
1052:
1049:
1046:
1042:
1038:
1034:
1030:
1026:
1022:
1018:
1014:
1010:
1007:
1004:
1000:
996:
992:
989:
986:
982:
979:
976:
973:
970:
966:
962:
958:
955:
952:
948:
944:
940:
937:
936:
935:
932:
930:
926:
922:
916:
913:
908:
759:
758:
757:
755:
751:
746:
744:
743:precipitation
740:
736:
732:
727:
725:
721:
717:
713:
709:
705:
701:
692:
684:
677:
672:
668:
656:
653:
649:
646:
643:
640:
637:
633:
629:
626:
622:
619:
616:
612:
608:
604:
600:
596:
595:
594:
589:Micro fouling
583:
579:
576:
573:
570:
567:
564:
561:
558:
555:
554:
551:
548:
547:
546:
544:
540:
536:
532:
528:
524:
520:
516:
512:
505:Macro fouling
499:
495:
491:
488:
485:
481:
477:
473:
470:
467:
464:
461:
458:
454:
453:Venturi tubes
451:
448:
445:
441:
439:
438:muzzleloaders
435:
432:
429:
425:
422:
419:
416:
413:
410:
407:
403:
399:
396:
392:
389:
388:
387:
381:
376:
369:
364:
355:
351:
349:
345:
341:
340:cooling water
337:
336:heat-transfer
333:
328:
324:
322:
318:
307:
302:
300:
295:
293:
288:
287:
285:
284:
279:
276:
274:
271:
269:
268:Thermal shock
266:
264:
261:
259:
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
219:
216:
214:
211:
209:
206:
204:
201:
199:
196:
195:
194:
193:
189:
188:
182:
178:
175:
171:
164:
160:
156:
146:
143:
135:
132:November 2008
124:
121:
117:
114:
110:
107:
103:
100:
96:
93: –
92:
88:
87:Find sources:
81:
77:
71:
70:
65:This article
63:
59:
54:
53:
48:
41:
37:
33:
19:
4263:
4243:
4224:
4215:
4197:
4177:
4168:
4159:
4155:
4149:
4139:
4112:
4108:
4095:
4086:
4077:
4057:
4043:
4032:
4005:
4001:
3991:
3982:
3949:
3945:
3939:
3922:
3918:
3912:
3895:
3891:
3885:
3863:(1): 81–97.
3860:
3856:
3850:
3833:
3829:
3823:
3814:
3794:
3762:
3743:
3724:
3690:
3653:
3649:
3639:
3572:
3552:
3545:
3499:
3453:
3437:ethanolamine
3411:technology (
3383:
3369:capital cost
3360:desalination
3341:
3310:
3302:
3286:
3187:
3176:
3021:
2972:
2734:
2731:
2728:
2725:
2718:
2709:erosion wear
2671:Magnus force
2626:
2603:
2597:
2587:
2573:
2567:
2561:
2553:
2547:
2538:
2529:permeability
2502:
2490:
2483:
2479:
2455:
2448:components.
2446:
2435:
2419:
2412:
2398:
2368:
2360:
2337:
2325:
2305:
2264:
2261:
2258:
2243:
2088:
1932:
1864:
1862:conditions.
1783:
1705:flocculation
1693:
1405:
1132:Transport:
1127:
1105:Phosphates (
1037:cristobalite
1027:, amorphous
933:
917:
909:
902:
747:
728:
697:
636:carbon steel
592:
508:
482:– decreased
385:
352:
329:
325:
316:
315:
222:
138:
129:
119:
112:
105:
98:
86:
74:Please help
69:verification
66:
31:
18:Lead fouling
4115:: 381–390.
3177:where λ = λ
2713:exfoliation
2698:cementation
2663:Stefan flow
2466:Opportunity
2356:carbonizing
2352:asphaltenes
2298:fouling by
1709:coagulation
965:hemihydrate
731:evaporation
621:Particulate
613:from water
519:water pumps
463:Pitot tubes
426:Electrical
163:power plant
161:in a steam
4296:Categories
4269:(abstract)
4230:(abstract)
4063:(abstract)
4008:: 137008.
3656:: 132583.
3632:References
3513:polyamines
3433:morpholine
3397:filtration
3393:technology
3374:root cause
3365:compressor
3329:ecological
2720:Deposition
2400:Biofouling
2390:canal lock
2380:Biofouling
2374:Biofouling
2312:flue gases
1310:Overall:
1081:cancrinite
1013:serpentine
912:solubility
739:saturation
720:hard water
712:hydroxides
648:Biofouling
611:hydroxides
498:senescence
469:Spark plug
321:biofouling
183:(cut open)
181:biofouling
102:newspapers
4024:249223220
3682:240007081
3460:inorganic
3445:hydrazine
3313:corrosion
3256:λ
3252:−
3244:−
3231:∗
3147:λ
3144:−
3136:−
3122:λ
3111:λ
3095:λ
3080:λ
3075:ρ
2932:⋅
2923:λ
2919:−
2891:λ
2887:−
2884:ρ
2803:λ
2799:−
2796:ρ
2643:molecular
2636:advection
2592:asymptote
2328:substrate
2286:maghemite
2274:magnetite
2006:−
1700:colloidal
1451:- time, s
1364:−
1269:−
1186:−
1045:xonotlite
1041:pectolite
1025:gehlenite
1009:Silicates
1003:periclase
961:anhydrite
947:aragonite
866:↑
841:↓
823:⟶
724:limescale
716:solutions
702:of solid
671:Limescale
654:and algae
632:corrosion
625:colloidal
615:solutions
601:of solid
480:oil wells
401:blockage;
380:corrosion
203:Corrosion
174:Condenser
91:"Fouling"
4252:Archived
4233:Archived
4205:Archived
4187:Archived
4066:Archived
3974:32303762
3966:24731003
3836:: 1522.
3804:Archived
3772:Archived
3752:Archived
3733:Archived
3598:See also
3592:abrasive
3556:Blowdown
3491:ammonium
3483:biocides
3471:cleavers
3463:chlorine
3456:biocides
3409:membrane
3333:biocides
3325:fretting
2705:spalling
2703:Deposit
2525:Porosity
2509:waviness
2340:catalyst
2308:aerosols
2290:goethite
2278:hematite
1100:tenorite
1085:noselite
1077:analcite
1067:corundum
1063:diaspore
1059:gibbsite
1055:boehmite
1021:gyrolite
951:vaterite
929:flashing
652:bacteria
638:surfaces
549:Examples
545:damage.
543:fretting
412:Turbines
348:calculus
278:Yielding
228:Fracture
198:Buckling
4307:Filters
4302:Fouling
3865:Bibcode
3521:helamin
3467:bromide
3429:ammonia
3321:fatigue
3192:, and λ
2973:where:
2578:tangent
2517:pitting
2410:(MIC).
2404:diatoms
2348:olefins
2089:where:
1406:where:
1096:cuprite
995:brucite
943:calcite
811:aqueous
572:Mussels
434:Firearm
370:scaling
317:Fouling
223:Fouling
218:Fatigue
116:scholar
47:fowling
4144:12171.
4022:
3972:
3964:
3713:
3680:
3568:Teflon
3531:), or
3487:methyl
3479:oxygen
2462:Spirit
1784:where
1092:copper
1033:quartz
1029:silica
1017:acmite
985:barite
969:gypsum
710:, and
708:oxides
609:, and
607:oxides
582:trunks
578:Leaves
527:rivers
515:refuse
511:coarse
382:traces
344:plaque
238:Impact
118:
111:
104:
97:
89:
4184:(pdf)
4105:(PDF)
4050:(pdf)
4020:S2CID
3970:S2CID
3801:(pdf)
3769:(pdf)
3749:(pdf)
3730:(pdf)
3696:(pdf)
3678:S2CID
3576:acids
3475:ozone
3419:) or
3390:water
2711:, or
2456:NASA
1116:(NiFe
714:from
704:salts
603:salts
566:Algae
531:lakes
494:aging
213:Creep
123:JSTOR
109:books
3962:PMID
3711:ISBN
3578:and
3509:EDTA
3477:and
3465:and
3337:fuel
2527:and
2464:and
2425:(or
2300:silt
2213:and
1811:and
1696:crud
828:CaCO
478:and
406:drag
273:Wear
177:tube
95:news
32:foul
4127:hdl
4117:doi
4113:528
4010:doi
4006:446
3954:doi
3927:doi
3900:doi
3873:doi
3838:doi
3668:hdl
3658:doi
3654:430
3439:or
3323:),
3306:GDP
3181:+ λ
2645:or
2536:).
1715:",
1707:or
997:);
919:in
780:HCO
733:or
529:or
523:sea
346:or
78:by
4298::
4158:.
4125:.
4111:.
4107:.
4018:.
4004:.
4000:.
3968:.
3960:.
3950:55
3948:.
3923:14
3921:.
3896:12
3894:.
3871:.
3861:72
3859:.
3834:69
3832:.
3782:^
3702:^
3676:.
3666:.
3652:.
3648:.
3543:.
3519:,
3473:,
3451:.
3435:,
3431:,
3425:pH
3415:,
3407:,
3344:MW
3185:.
2707:,
2669:,
2661:,
2657:,
2653:,
2638:);
2519:,
2515:,
2318:.
2292:);
2288:,
2284:,
2280:,
2276:,
1735::
1580:-
1109:);
1102:);
1098:,
1094:,
1087:);
1083:,
1079:,
1069:);
1065:,
1061:,
1057:,
1047:);
1043:,
1039:,
1035:,
1031:,
1023:,
1019:,
1015:,
1005:);
987:);
971:);
967:,
963:,
953:);
945:,
851:CO
771:Ca
726:.
706:,
605:,
525:,
455:,
4247:"
4160:4
4133:.
4129::
4119::
4072:.
4052:.
4048:(
4026:.
4012::
3976:.
3956::
3933:.
3929::
3906:.
3902::
3879:.
3875::
3867::
3844:.
3840::
3684:.
3670::
3660::
3271:)
3265:t
3260:r
3248:e
3241:1
3237:(
3227:m
3223:=
3220:)
3217:t
3214:(
3211:m
3198:c
3194:c
3190:r
3183:c
3179:r
3161:)
3156:)
3150:t
3140:e
3133:1
3129:(
3115:r
3104:+
3099:c
3091:t
3087:(
3070:m
3066:C
3060:d
3056:k
3049:=
3046:)
3043:t
3040:(
3037:m
3024:r
3016:c
3014:λ
3009:r
3007:m
3002:r
3000:λ
2995:m
2993:C
2985:d
2983:k
2951:)
2948:t
2945:(
2940:r
2936:m
2927:c
2916:)
2913:t
2910:(
2905:r
2901:m
2895:r
2879:m
2875:C
2869:d
2865:k
2861:=
2857:t
2854:d
2850:/
2844:r
2840:m
2836:d
2828:)
2825:t
2822:(
2817:r
2813:m
2807:r
2791:m
2787:C
2781:d
2777:k
2773:=
2769:t
2766:d
2762:/
2758:m
2755:d
2748:{
2715:.
2492:"
2460:(
2272:(
2226:b
2222:C
2199:i
2195:C
2170:d
2166:k
2162:,
2157:t
2153:k
2149:,
2144:a
2140:k
2114:t
2111:d
2106:m
2103:d
2072:b
2068:C
2061:d
2057:k
2052:=
2046:t
2043:d
2038:m
2035:d
2009:1
2001:)
1993:t
1989:k
1985:1
1980:+
1973:a
1969:k
1965:1
1959:(
1954:=
1949:d
1945:k
1916:i
1912:C
1905:a
1901:k
1896:=
1890:t
1887:d
1882:m
1879:d
1846:P
1824:t
1820:k
1797:d
1793:k
1767:t
1763:k
1759:P
1756:=
1751:d
1747:k
1723:P
1685:)
1673:1
1670:=
1665:2
1661:n
1657:=
1652:1
1648:n
1625:d
1621:k
1617:,
1612:r
1608:k
1604:,
1599:t
1595:k
1566:2
1562:n
1558:,
1553:1
1549:n
1524:e
1520:C
1495:i
1491:C
1466:b
1462:C
1439:t
1417:m
1387:2
1383:n
1378:)
1372:e
1368:C
1359:b
1355:C
1351:(
1346:d
1342:k
1338:=
1332:t
1329:d
1324:m
1321:d
1292:1
1288:n
1283:)
1277:e
1273:C
1264:i
1260:C
1256:(
1250:r
1246:k
1241:=
1235:t
1232:d
1227:m
1224:d
1199:)
1194:i
1190:C
1181:b
1177:C
1173:(
1168:t
1164:k
1160:=
1154:t
1151:d
1146:m
1143:d
1122:4
1120:O
1118:2
1075:(
1053:(
1011:(
1001:(
993:(
983:(
959:(
941:(
905:2
886:O
878:2
874:H
870:+
855:2
846:+
832:3
814:)
808:(
797:2
792:)
784:3
776:(
678:.
584:.
574:;
568:;
500:.
496:/
305:e
298:t
291:v
145:)
139:(
134:)
130:(
120:·
113:·
106:·
99:·
72:.
49:.
42:.
20:)
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