2319:. 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.
2599:. 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").
680:
2553:- 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.
2374:
2470:
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).
656:
47:
364:
2609:
672:
3571:, 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
3285:
352:
159:
144:
3392:. 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,
3185:. 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
2589:- 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.
3559:) 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.
526:, 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
904:
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.
2957:
2409:
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
342:
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
907:
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
3360:
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
2711:
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.
2469:
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.
2358:
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
315:
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
3542:
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
2436:
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
312:, 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.
4221:
903:
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
4193:
3161:
3538:
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.
3543:
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.
3562:
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
2520:
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
3787:
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.
4090:
389:
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
4132:
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
4218:
2528:
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.
4190:
2500:), 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.,
3351:
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
1691:
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
887:
2730:
3528:, 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
2565:- 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
4036:
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
1700:. 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 "
4170:
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.
2010:
3292:
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
2583:). 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.
3021:
2595:- 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
2537:
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:
2480:
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
3593:
4079:
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.
2547:- 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.
662:
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
2721: [ rate of accumulation of unconsolidated deposit ] = [ rate of deposition ] - [ rate of re-entrainment of unconsolidated deposit ] - [ rate of consolidation of unconsolidated deposit ]
3755:
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
1295:
3271:
1390:
3717:
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.
1198:
4208:
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.
683:
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.
2073:
1917:
3879:
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".
2675:
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;
707:. 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
4070:
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.
3721:
3297:. 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.
2715:
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:
2171:
1626:
3492:
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:
2116:
4175:
3792:
1672:
3933:
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".
1768:
2724:
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):
2327:
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
1567:
3807:"Modeling PWR Fuel Corrosion Product Deposition and Growth Processes (5)", Technical Report 1009734, Electric Power Research Institute, Palo Alto, California, USA, 2004.
2359:
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.
386:, decreases heat flux, increases temperature on the hot side, decreases temperature on the cold side, induces under-deposit corrosion, increases use of cooling water;
3308:), increased pressure drop, flow blockages, flow redistribution inside components, flow instabilities, induced vibrations (possibly leading to other problems, e.g.,
3683:"Marine fouling and its prevention"; prepared for Bureau of Ships, Navy Dept, Woods Hole Oceanographic Institution, United States, Navy Dept. Bureau of Ship, 1952.
2402:
Bacteria can form biofilms or slimes. Thus the organisms can aggregate on surfaces using colloidal hydrogels of water and extracellular polymeric substances (EPS) (
2227:
2200:
1825:
1798:
1525:
1496:
1467:
751:
2952:{\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}}}
3740:
4217:"Dispersants for Tube Fouling Control: Volume 2: Short-Term Trial at ANO-2", Report 1003144, Electric Power Research Institute, Palo Alto, California, USA, 2001
3547:
capability is always incorporated into steam generators or evaporators to control the accumulation of non-volatile impurities that cause or aggravate fouling.
1845:
1722:
1438:
1416:
2473:
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
438:
Injection/spray nozzles (e.g., a nozzle spraying a fuel into a furnace) – incorrect amount injected, malformed jet, component inefficiency, component failure;
3373:
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
2335:
occurs in cooling water for the chemical industry which has a minor content of hydrocarbons. Systems in petroleum processing are prone to polymerization of
2579:- Here, the fouling rate decreases with time, until it finally reaches zero. At this point, the deposit thickness remains constant with time (a horizontal
2350:
Fouling through an ionic reaction with an evolution of an inorganic solid is commonly classified as precipitation fouling (not chemical reaction fouling).
4256:
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
3906:
Changani, S.D.; Belmar-Beiny, M.T.; Fryer, P.J. (May 1997). "Engineering and chemical factors associated with fouling and cleaning in milk processing".
2248:
Particles larger than those of colloidal dimensions may also foul e.g., by sedimentation ("sedimentation fouling") or straining in small-size openings.
892:
The calcium carbonate that forms through this reaction precipitates. Due to the temperature dependence of the reaction, and increasing volatility of CO
292:
4050:"Steam Generator Thermal Performance Degradation Case Studies", Report TR-110018, Electric Power Research Institute, Palo Alto, California, USA, 1998
1628:- kinetic rate constants for the transport, the surface reaction, and the overall deposition reaction, respectively; with the dimension of m/s (when
3189:=0. In the absence of consolidation, the asymptotic fouling is always anticipated by this older model and the fouling progress can be described as:
4161:
H. Mueller-Steinhagen and A.P. Watkinson, "Fouling of Heat Exchanger--New Approaches to Solve Old Problem", Heat Transfer Engineering, 26(2), 2005.
3505:
1928:
3156:{\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)}
923:
The following lists some of the industrially common phases of precipitation fouling deposits observed in practice to form from aqueous solutions:
2395:, plants, and animals on surfaces, such as ships and submarine hulls, or piping and reservoirs with untreated water. This can be accompanied by
3347:
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
2251:
With time, the resulting surface deposit may harden through processes collectively known as "deposit consolidation" or, colloquially, "aging".
2457:) experienced (presumably) abiotic fouling of solar panels by dust particles from the Martian atmosphere. Some of the deposits subsequently
3817:
Ruckenstein, Eli; Prieve, Dennis C. (1973). "Rate of deposition of Brownian particles under the action of London and double-layer forces".
3760:
3718:
3633:
Løge, Isaac A.; Bentzon, Jakob R.; Klingaa, Christopher G.; Walther, Jens H.; Anabaraonye, Benaiah U.; Fosbøl, Philip L. (February 2022).
2241:. A maximum fouling rate is usually observed when the fouling particles and the substrate exhibit opposite electrical charge, or near the
4054:
2718: [ rate of deposit accumulation ] = [ rate of deposition ] - [ rate of re-entrainment of unconsolidated deposit ]
4240:
3328:
input to compensate for the reduced output caused by fouling, and an increased use of cooling water in once-through cooling systems.
481:
Living organisms – deposition of excess minerals (e.g., calcium, iron, copper) in tissues is (sometimes controversially) linked to
1205:
4091:"Theoretical framework for predicting inorganic fouling in membrane distillation and experimental validation with calcium sulfate"
1854:
An alternative to using the sticking probability is to use a kinetic attachment rate constant, assuming the first order reaction:
4172:
3789:
3195:
1302:
3576:
3316:, premature failure of electrical heating elements, and a large number of other often unanticipated problems. In addition, the
285:
4257:
3698:
Siobhán Francesca E. Boerlage, "Scaling and Particulate Fouling in Membrane Filtration Systems", Taylor & Francis; 2001,
2669:
Induction period, i.e., a near-nil fouling rate at the initial period of fouling (observed only for some fouling mechanisms);
2638:, but may also occur by inertial coasting/impaction, particle interception by the surface (for particles with finite sizes),
2672:
Foulant crystallisation on the surface (or attachment of the colloidal particle, or chemical reaction, or bacterial growth);
2418:), which produce sulfide and often cause corrosion of ferrous metals (and other alloys). Sulfide-oxidizing bacteria (e.g.,
2347:
of organic matter. The food industry, for example milk processing, also experiences fouling problems by chemical reactions.
319:
Fouling phenomena are common and diverse, ranging from fouling of ship hulls, natural surfaces in the marine environment (
308:
is the accumulation of unwanted material on solid surfaces. The fouling materials can consist of either living organisms (
1124:
4271:
3361:
in lost revenue in a typical power plant), and the cost of actually doing this maintenance. Finally, fouling is often a
1687:") or in gas progresses by a mechanism different than precipitation fouling. This process is usually most important for
896:
with increasing temperature, the scaling is higher at the hotter outlet of the heat exchanger than at the cooler inlet.
3737:
2299:
is also of industrial significance. The particles can be either solid or liquid. The common examples can be fouling by
633:
Solidification fouling - when components of the flowing fluid with a high-melting point freeze onto a subcooled surface
4276:
111:
3703:
278:
130:
83:
2016:
1860:
916:. Similarly, precipitation fouling can occur because of solubility changes induced by other factors, e.g., liquid
4191:
Herve BODINEAU and Thierry SOLLIER, "Tube support plate clogging up of French steam generators", Eurosafe webpage
3608:
2569:
to the fouling curve at zero deposit loading or zero time) and the fouling rate after a long period of time (an
4300:
90:
68:
3844:
Bowen, Bruce D; Epstein, Norman (October 1979). "Fine particle deposition in smooth parallel-plate channels".
1922:
and then the transport and attachment kinetic coefficients are combined as two processes occurring in series:
3412:. The generation of the corrosion products in the water piping systems is often minimized by controlling the
3177:
This model reproduces either linear, falling, or asymptotic fouling, depending on the relative values of k, λ
2316:
630:
Chemical reaction fouling, for example, decomposition or polymerization of organic matter on heating surfaces
4305:
2304:
2237:
phenomenon, this fouling mechanism can be very sensitive to factors that affect colloidal stability, e.g.,
412:– increases pressure drop, increases energy expenditure, reduces flux, membrane failure (in severe cases);
3489:
2630:
Foulant transport from the bulk of the process fluid to the fouling surface. This transport is often by
2482:
2229:
are the concentration of the particle foulant at the interface and in the bulk fluid, respectively; kg m.
241:
97:
3572:
3356:-operated coolers is also easily in the two-digit area. In addition to the operational costs, also the
3000:
is the mass loading of the removable (i.e., unconsolidated) fraction of the surface deposit (kg/m); and
2123:
1578:
231:
4038:
2084:
4310:
3598:
2509:
2486:
2411:
1039:
731:
527:
432:
246:
162:
2739:
2612:
Schematics of the fouling process consisting of simultaneous foulant deposition and deposit removal.
679:
79:
4315:
3535:
3474:. One of the most important unoxidizable biocides is a mixture of chloromethyl-isothiazolinone and
2415:
1631:
64:
3778:
T.R. Bott, "Fouling of Heat Exchangers (Chemical Engineering Monographs)", Elsevier Science, 1995.
2496:
is of primary concern, it is important to note non-uniformity of deposit thickness (e.g., deposit
1730:
2501:
2303:, or fouling of air-cooled components by dust in air. The mechanisms are discussed in article on
1532:
472:
251:
57:
3757:
1573:
for the crystallization reaction and the overall deposition process, respectively, dimensionless
375:
Examples of components that may be subject to fouling and the corresponding effects of fouling:
3320:
costs should be (but typically are not) considered. The ecological costs arise from the use of
3294:
2708:
2446:
2422:), on the other hand, can produce sulfuric acid, and can be involved in corrosion of concrete.
2378:
882:{\displaystyle {\ce {\mathsf {{Ca(HCO3)2}_{(aqueous)}->{CaCO3(v)}+{CO2}\!{\uparrow }+H2O}}}}
221:
2966:
m is the mass loading of the deposit (consolidated and unconsolidated) on the surface (kg/m);
2686:
2663:
1847:
for colloidal particles is a function of both the surface chemistry, geometry, and the local
912:
systems can occur due to differential solubility of barium sulfate in solutions of different
530:. They may also create flow blockages, redistribute the flow inside the components, or cause
24:
4051:
3975:
Hong Lu, "Composite Fouling of Heat Exchanger Surfaces", Nova Science Books, New York, 2007.
3706:
2428:
serve as an example of larger animals that have caused widespread fouling in North America.
3853:
2242:
2205:
2178:
1803:
1776:
1701:
1503:
1474:
1445:
704:
603:
4237:
3987:"Growth mechanisms of composite fouling: The impact of substrates on detachment processes"
2477:
can be of particular interest when the impact of fouling on pressure drop is of interest.
8:
4247:", Public Works Technical Bulletin 420-49-34, U.S. Army Corps of Engineers, 15 June 2001.
4089:
Warsinger, David M.; Tow, Emily W.; Swaminathan, Jaichander; Lienhard V, John H. (2017).
3603:
3437:
3409:
3405:
3397:
3362:
2396:
2373:
1827:
are the kinetic rate constants for deposition and transport, respectively. The value of
979:
738:
464:
266:
236:
201:
3857:
3365:
of serious degradation problems that may limit the life of components or entire plants.
4008:
3958:
3666:
3309:
3276:
where m is the maximum (asymptotic) mass loading of the deposit on the surface (kg/m).
1830:
1707:
1423:
1401:
383:
316:
also have meanings outside of this scope; therefore, they should be used with caution.
226:
206:
4143:
Kern, D.O.; Seaton, R.E. (1959). "A theoretical analysis of thermal surface fouling".
3919:
3684:
2689:, which account for deposit losing its porosity and becoming more tenacious with time;
920:, liquid degassing, redox potential changes, or mixing of incompatible fluid streams.
646:
Composite fouling, whereby fouling involves more than one foulant or fouling mechanism
4012:
3950:
3865:
3699:
3670:
3548:
3529:
3305:
2701:
2570:
2505:
2493:
2474:
2454:
2419:
2234:
1570:
1527:- equilibrium concentration of the substance at the conditions of the interface, kg/m
927:
917:
742:
356:
336:
320:
196:
165:
104:
3962:
2391:
or biological fouling is the undesirable accumulation of micro-organisms, algae and
1117:
The deposition rate by precipitation is often described by the following equations:
4295:
4290:
4115:
4105:
3998:
3942:
3915:
3888:
3861:
3826:
3656:
3646:
3635:"Scale attachment and detachment: The role of hydrodynamics and surface morphology"
3552:
3525:
3429:
2682:
2647:
2543:
1001:
953:
692:
591:
502:
matter of either biological or inorganic origin, for example industrially produced
409:
28:
4244:
4225:
4197:
4179:
4110:
4058:
3946:
3796:
3764:
3744:
3725:
3521:
3513:
3493:
3401:
3393:
2639:
2254:
The common particulate fouling deposits formed from aqueous suspensions include:
1848:
1061:
987:
963:
945:
909:
727:
688:
587:
475:
with time; plugging; in some cases complete stoppage of flow in a matter of days;
416:
3985:
Løge, Isaac A.; Anabaraonye, Benaiah U.; Fosbøl, Philip Loldrup (October 2022).
3594:
International Convention on the Control of Harmful Anti-fouling Systems on Ships
343:
the one that is usually more difficult to prevent and therefore more important.
3661:
3544:
3517:
3389:
3353:
2643:
2635:
2458:
2403:
2332:
2238:
1102:
1095:
969:
913:
723:
664:
570:
394:
379:
324:
147:
4003:
3986:
3651:
3634:
2620:
Generation or ingress of the species that causes fouling ("foulant sourcing");
2410:
in closed systems when sufficient nutrients are present. Examples may include
419:– increases temperature of the element, increases corrosion, reduces lifespan;
4284:
3613:
3478:-isothiazolinone. Also applied are dibrom nitrilopropionamide and quaternary
3459:
3374:
3344:
3340:
3336:
2655:
2596:
2522:
2344:
2284:
2270:
2005:{\displaystyle k_{d}=\left({\frac {1}{k_{a}}}+{\frac {1}{k_{t}}}\right)^{-1}}
523:
445:
332:
328:
256:
4025:
3892:
3575:
alternative. In some heat-transfer applications, mechanical mitigation with
3954:
3483:
3425:
3357:
3348:
2659:
2450:
2425:
2382:
1693:
1025:
624:
441:
426:
2406:, lipids, nucleic acids, etc.). The biofilm structure is usually complex.
4119:
3830:
3580:
2651:
1697:
719:
609:
151:
506:. Such matter enters into the cooling water circuit through the cooling
3421:
3385:
3381:
3317:
2693:
2517:
2388:
2368:
2340:
2258:
1069:
900:
708:
636:
507:
486:
457:
451:
309:
169:
2678:
Deposit dissolution (or re-entrainment of loosely attached particles);
2623:
Foulant transport with the stream of the process fluid (most often by
551:
Tools and other "foreign objects" accidentally left after maintenance;
3501:
3448:
3433:
3432:), control of oxygen dissolved in water (for example, by addition of
3301:
2631:
2624:
2580:
2274:
2262:
1688:
1033:
1029:
1013:
991:
949:
935:
712:
700:
659:
620:
613:
599:
368:
191:
2616:
Fouling of a system can be modelled as consisting of several steps:
655:
454:
in airplanes – inaccurate or incorrect indication of airplane speed;
339:
on teeth or deposits on solar panels on Mars, among other examples.
46:
3479:
3451:
3313:
3279:
3011:
This system of equations can be integrated (taking that m = 0 and m
2513:
2497:
2328:
2300:
2278:
2266:
1088:
1073:
1065:
1055:
1051:
1047:
1043:
1009:
1005:
997:
939:
640:
531:
468:
363:
216:
186:
19:
This article is about fouling in engineering. For uses of the term
2608:
2559:- The fouling rate can be steady with time. This is a common case.
2461:. This illustrates the universal nature of the fouling phenomena.
4088:
3568:
3509:
3471:
3455:
3444:
3417:
3321:
2566:
2392:
2296:
1084:
983:
931:
671:
422:
400:
35:
3583:
cleaning methods are available for many specific applications.
3475:
3467:
3284:
2336:
2315:
Corrosion deposits are created in-situ by the corrosion of the
1469:- concentration of the substance in the bulk of the fluid, kg/m
1080:
1021:
1017:
973:
957:
560:
503:
499:
3736:"Spark Plug Faces", brochure "Bosch Spark Plugs 0307", Part 1
3443:
For water systems at relatively low temperatures, the applied
741:- always prevailing in natural water - and the poorly soluble
3932:
3463:
3378:
1684:
1290:{\displaystyle {\frac {dm}{dt}}={k_{r}}(C_{i}-C_{e})^{n_{1}}}
696:
595:
554:
515:
482:
3331:
For example, "normal" fouling at a conventionally fired 500
478:
Teeth – promotes tooth or gum disease, decreases aesthetics;
435:– axial offset anomaly, may need to de-rate the power plant;
351:
158:
143:
3878:
3564:
3556:
3497:
3332:
3325:
3266:{\displaystyle m(t)=m^{*}\left(1-e^{-\lambda _{r}t}\right)}
2945:
2697:
2288:
1385:{\displaystyle {\frac {dm}{dt}}=k_{d}(C_{b}-C_{e})^{n_{2}}}
737:
As an example, the equilibrium between the readily soluble
566:
519:
261:
425:
barrels - increases chamber pressure; hampers loading for
3905:
3632:
3300:
The losses initially result from impaired heat transfer,
871:
848:
825:
808:
790:
777:
511:
2343:, waxes, etc.). High tube wall temperatures may lead to
406:
Solar panels – decreases the electrical power generated;
3819:
Journal of the Chemical Society, Faraday Transactions 2
3413:
2685:
or differential solubility in temperature gradient) or
1498:- concentration of the substance at the interface, kg/m
802:
796:
780:
764:
403:– reduces efficiency, increases probability of failure;
3288:
Cost relations between the individual types of fouling
3984:
3881:
Comprehensive Reviews in Food Science and Food Safety
3198:
3024:
2733:
2208:
2181:
2126:
2087:
2019:
1931:
1863:
1833:
1806:
1779:
1733:
1710:
1634:
1581:
1535:
1506:
1477:
1448:
1426:
1404:
1305:
1208:
1127:
754:
612:
fouling, i.e., accumulation of particles, typically
3416:
of the process fluid (typically alkalinization with
3324:
for the avoidance of biofouling, from the increased
2681:
Deposit consolidation on the surface (e.g., through
1418:- mass of the material (per unit surface area), kg/m
582:
As to micro fouling, distinctions are made between:
2173:
are the kinetic rate constants for deposition, m/s,
2118:
is the rate of the deposition by particles, kg m s,
1193:{\displaystyle {\frac {dm}{dt}}=k_{t}(C_{b}-C_{i})}
448:– inaccurate or incorrect measurement of flow rate;
71:. Unsourced material may be challenged and removed.
16:
Accumulation of unwanted material on solid surfaces
4082:
3265:
3155:
2951:
2221:
2194:
2165:
2110:
2067:
2004:
1911:
1839:
1819:
1792:
1762:
1716:
1666:
1620:
1561:
1519:
1490:
1461:
1432:
1410:
1384:
1289:
1192:
881:
745:, the following chemical equation may be written:
3816:
852:
4282:
3280:Economic and environmental importance of fouling
2986:- mass fraction of foulant in the fluid (kg/kg);
2532:
346:
3935:Critical Reviews in Food Science and Nutrition
397:, increases fuel usage, reduces maximum speed;
2291:and other relatively coarse suspended matter.
2068:{\displaystyle {\frac {dm}{dt}}={k_{d}}C_{b}}
1912:{\displaystyle {\frac {dm}{dt}}={k_{a}}C_{i}}
286:
3843:
3512:, and other "film-forming" amines), organic
3377:and other major industrial installations of
2464:
2322:
726:, the concentration of salts may exceed the
606:(e.g., calcium carbonate or calcium sulfate)
327:components through ingredients contained in
718:Through changes in temperature, or solvent
619:Corrosion fouling, i.e., in-situ growth of
4142:
2993:is the re-entrainment rate constant (1/s);
1683:Fouling by particles suspended in water ("
687:Scaling or precipitation fouling involves
293:
279:
4109:
4002:
3694:
3692:
3660:
3650:
3384:, macro fouling is avoided by way of pre-
3007:is the consolidation rate constant (1/s).
2353:
938:usually at t > ~50 °C, or rarely
874:
862:
839:
816:
799:
768:
759:
131:Learn how and when to remove this message
3846:Journal of Colloid and Interface Science
3304:damage (in particular under-deposit and
3283:
2607:
2372:
678:
670:
654:
650:
362:
350:
157:
142:
27:. For fouling on membrane surfaces, see
3577:dynamic scraped surface heat exchangers
3339:unit accounts for output losses of the
899:In general, the dependence of the salt
355:cross-section of a condenser tube with
4283:
3908:Experimental Thermal and Fluid Science
3774:
3772:
3689:
2976:is the deposition rate constant (m/s);
2397:microbiologically influenced corrosion
1678:
1113:) from extremely pure, low-iron water.
866:
858:
843:
834:
820:
785:
772:
548:Detached internal parts of components;
460:electrodes in cars – engine misfiring;
331:or gases, and even the development of
4026:Mars Pathfinder - Dust Settling (MAE)
3482:compounds. For underwater ship hulls
586:Scaling or precipitation fouling, as
2603:
2431:
2310:
623:deposits, for example, magnetite on
69:adding citations to reliable sources
40:
3769:
2654:(in condensation and evaporation),
367:cross-section of a brass tube with
13:
3500:), long-chain aliphatic amines or
3368:
2440:
2339:or deposition of heavy fractions (
2259:iron oxides and iron oxyhydroxides
14:
4327:
4265:
3579:is an option. Also ultrasonic or
2381:in Northern France, covered with
2166:{\displaystyle k_{a},k_{t},k_{d}}
1621:{\displaystyle k_{t},k_{r},k_{d}}
675:Extreme boiler pipe scale buildup
3555:, or of low surface energy like
3458:compounds, chlorine and bromide
3343:of 5 MW and more. In a 1,300 MW
2662:(acting on rotating particles),
2111:{\displaystyle {\frac {dm}{dt}}}
577:
493:
393:Ship hulls – creates additional
45:
4250:
4230:
4211:
4202:
4184:
4164:
4155:
4136:
4126:
4073:
4064:
4044:
4030:
4019:
3978:
3969:
3926:
3899:
3872:
3837:
3810:
3609:Steam generator (nuclear power)
569:, parts of plants up to entire
56:needs additional citations for
3801:
3781:
3749:
3730:
3711:
3677:
3626:
3447:may be classified as follows:
3208:
3202:
3034:
3028:
2979:ρ is the fluid density (kg/m);
2939:
2933:
2904:
2898:
2816:
2810:
2295:Fouling by particles from gas
1366:
1339:
1271:
1244:
1187:
1161:
854:
829:
811:
734:of solids (usually crystals).
1:
3920:10.1016/S0894-1777(96)00141-0
3620:
2533:Progress of fouling with time
2362:
2331:. For example, corrosion and
1667:{\displaystyle n_{1}=n_{2}=1}
347:Components subject to fouling
4145:British Chemical Engineering
4111:10.1016/j.memsci.2017.01.031
3991:Chemical Engineering Journal
3947:10.1080/10408398.2012.752343
3866:10.1016/0021-9797(79)90184-X
3639:Chemical Engineering Journal
1763:{\displaystyle k_{d}=Pk_{t}}
7:
4098:Journal of Membrane Science
3586:
3551:(for example, very smooth,
3490:Chemical fouling inhibitors
3015:= 0 at t = 0) to the form:
1562:{\displaystyle n_{1},n_{2}}
522:. In closed circuits, like
510:from sources like the open
498:Macro fouling is caused by
242:Metal-induced embrittlement
10:
4332:
4272:Crude Oil Fouling research
3573:environmentally friendlier
2366:
1202:Surface crystallisation:
1040:Aluminium oxide hydroxides
433:pressurized water reactors
232:Liquid metal embrittlement
33:
18:
4004:10.1016/j.cej.2022.137008
3652:10.1016/j.cej.2021.132583
3599:Oilfield scale inhibition
2510:stress corrosion cracking
2487:heat transfer coefficient
2485:"), or by development of
2465:Quantification of fouling
2459:spontaneously cleaned off
2412:sulfate-reducing bacteria
2323:Chemical reaction fouling
528:heat transfer coefficient
410:Reverse osmosis membranes
247:Stress corrosion cracking
154:, fouled by macro fouling
4238:Magnetic Water Treatment
3536:Magnetic water treatment
2636:turbulent-eddy diffusion
2512:, or localized wastage.
2416:sulfur-reducing bacteria
179:Mechanical failure modes
34:Not to be confused with
23:outside technology, see
3893:10.1111/1541-4337.12000
3470:cleavers, unoxidizable
3335:(net electrical power)
2666:, and other mechanisms.
2447:Mars Exploration Rovers
616:particles, on a surface
252:Sulfide stress cracking
3289:
3267:
3157:
2953:
2613:
2573:to the fouling curve).
2385:
2354:Solidification fouling
2223:
2196:
2167:
2112:
2069:
2006:
1913:
1841:
1821:
1794:
1764:
1718:
1668:
1622:
1563:
1521:
1492:
1463:
1434:
1412:
1386:
1291:
1194:
883:
684:
676:
668:
639:, like settlements of
372:
360:
222:Hydrogen embrittlement
173:
155:
4301:Hydraulic engineering
3287:
3268:
3158:
2954:
2664:thermoelectric effect
2611:
2376:
2224:
2222:{\displaystyle C_{b}}
2197:
2195:{\displaystyle C_{i}}
2168:
2113:
2070:
2007:
1914:
1842:
1822:
1820:{\displaystyle k_{t}}
1795:
1793:{\displaystyle k_{d}}
1765:
1719:
1669:
1623:
1564:
1522:
1520:{\displaystyle C_{e}}
1493:
1491:{\displaystyle C_{i}}
1464:
1462:{\displaystyle C_{b}}
1435:
1413:
1387:
1292:
1195:
884:
711:and often results in
682:
674:
658:
651:Precipitation fouling
366:
354:
161:
146:
25:Foul (disambiguation)
3831:10.1039/F29736901522
3549:Low-fouling surfaces
3438:corrosion inhibitors
3375:steam power stations
3196:
3022:
2731:
2587:Accelerating fouling
2502:intergranular attack
2492:If under-deposit or
2243:point of zero charge
2233:Being essentially a
2206:
2179:
2124:
2085:
2017:
1929:
1861:
1831:
1804:
1777:
1731:
1708:
1702:sticking probability
1632:
1579:
1533:
1504:
1475:
1446:
1424:
1402:
1303:
1206:
1125:
752:
473:petroleum production
465:petroleum reservoirs
65:improve this article
4306:Transport phenomena
3858:1979JCIS...72...81B
3662:20.500.11850/517338
3604:Particle deposition
3553:implanted with ions
3410:ion-exchange resins
3406:electrodeionization
2245:of either of them.
1679:Particulate fouling
980:Magnesium hydroxide
873:
850:
827:
810:
792:
779:
739:calcium bicarbonate
463:Production zone of
382:surfaces – reduces
237:Mechanical overload
4243:2011-12-15 at the
4224:2011-07-10 at the
4196:2011-07-26 at the
4178:2009-05-12 at the
4057:2011-07-10 at the
3795:2009-05-12 at the
3763:2010-05-30 at the
3743:2009-12-29 at the
3724:2006-09-17 at the
3436:), or addition of
3388:and cooling water
3290:
3263:
3153:
2949:
2944:
2614:
2577:Asymptotic fouling
2551:"Negative" fouling
2489:(W/mK) with time.
2483:fouling resistance
2386:
2305:aerosol deposition
2219:
2192:
2163:
2108:
2065:
2002:
1909:
1837:
1817:
1790:
1760:
1714:
1664:
1618:
1559:
1517:
1488:
1459:
1430:
1408:
1382:
1287:
1190:
966:(e.g., beerstone);
879:
861:
838:
815:
767:
762:
757:
685:
677:
669:
384:thermal efficiency
373:
361:
174:
156:
3941:(12): 1724–1743.
3569:complexing agents
3530:process chemicals
3306:crevice corrosion
3114:
3072:
2604:Fouling modelling
2571:oblique asymptote
2494:crevice corrosion
2475:surface roughness
2432:Composite fouling
2420:Acidithiobacillus
2311:Corrosion fouling
2235:surface chemistry
2106:
2038:
1986:
1966:
1882:
1840:{\displaystyle P}
1717:{\displaystyle P}
1571:order of reaction
1433:{\displaystyle t}
1411:{\displaystyle m}
1324:
1227:
1146:
1079:Copper (metallic
928:Calcium carbonate
876:
864:
841:
818:
801:
770:
761:
743:calcium carbonate
357:calcium carbonate
303:
302:
197:Corrosion fatigue
168:with residues of
141:
140:
133:
115:
4323:
4311:Water technology
4260:
4254:
4248:
4234:
4228:
4215:
4209:
4206:
4200:
4188:
4182:
4168:
4162:
4159:
4153:
4152:
4140:
4134:
4130:
4124:
4123:
4113:
4095:
4086:
4080:
4077:
4071:
4068:
4062:
4048:
4042:
4034:
4028:
4023:
4017:
4016:
4006:
3982:
3976:
3973:
3967:
3966:
3930:
3924:
3923:
3903:
3897:
3896:
3876:
3870:
3869:
3841:
3835:
3834:
3814:
3808:
3805:
3799:
3785:
3779:
3776:
3767:
3753:
3747:
3734:
3728:
3715:
3709:
3696:
3687:
3681:
3675:
3674:
3664:
3654:
3630:
3526:polyacrylic acid
3522:polyelectrolytes
3514:phosphonic acids
3494:chelating agents
3430:sodium phosphate
3272:
3270:
3269:
3264:
3262:
3258:
3257:
3256:
3252:
3251:
3223:
3222:
3162:
3160:
3159:
3154:
3152:
3148:
3147:
3143:
3142:
3141:
3115:
3113:
3108:
3107:
3106:
3096:
3091:
3090:
3073:
3071:
3066:
3062:
3061:
3052:
3051:
3041:
2958:
2956:
2955:
2950:
2948:
2947:
2932:
2931:
2919:
2918:
2897:
2896:
2887:
2886:
2871:
2870:
2861:
2860:
2848:
2841:
2836:
2835:
2809:
2808:
2799:
2798:
2783:
2782:
2773:
2772:
2760:
2753:
2683:Ostwald ripening
2648:diffusiophoresis
2544:Induction period
2377:A fragment of a
2228:
2226:
2225:
2220:
2218:
2217:
2201:
2199:
2198:
2193:
2191:
2190:
2172:
2170:
2169:
2164:
2162:
2161:
2149:
2148:
2136:
2135:
2117:
2115:
2114:
2109:
2107:
2105:
2097:
2089:
2074:
2072:
2071:
2066:
2064:
2063:
2054:
2053:
2052:
2039:
2037:
2029:
2021:
2011:
2009:
2008:
2003:
2001:
2000:
1992:
1988:
1987:
1985:
1984:
1972:
1967:
1965:
1964:
1952:
1941:
1940:
1918:
1916:
1915:
1910:
1908:
1907:
1898:
1897:
1896:
1883:
1881:
1873:
1865:
1846:
1844:
1843:
1838:
1826:
1824:
1823:
1818:
1816:
1815:
1799:
1797:
1796:
1791:
1789:
1788:
1769:
1767:
1766:
1761:
1759:
1758:
1743:
1742:
1723:
1721:
1720:
1715:
1673:
1671:
1670:
1665:
1657:
1656:
1644:
1643:
1627:
1625:
1624:
1619:
1617:
1616:
1604:
1603:
1591:
1590:
1568:
1566:
1565:
1560:
1558:
1557:
1545:
1544:
1526:
1524:
1523:
1518:
1516:
1515:
1497:
1495:
1494:
1489:
1487:
1486:
1468:
1466:
1465:
1460:
1458:
1457:
1439:
1437:
1436:
1431:
1417:
1415:
1414:
1409:
1391:
1389:
1388:
1383:
1381:
1380:
1379:
1378:
1364:
1363:
1351:
1350:
1338:
1337:
1325:
1323:
1315:
1307:
1296:
1294:
1293:
1288:
1286:
1285:
1284:
1283:
1269:
1268:
1256:
1255:
1243:
1242:
1241:
1228:
1226:
1218:
1210:
1199:
1197:
1196:
1191:
1186:
1185:
1173:
1172:
1160:
1159:
1147:
1145:
1137:
1129:
1062:Aluminosilicates
888:
886:
885:
880:
878:
877:
872:
869:
857:
851:
849:
846:
833:
832:
826:
823:
809:
806:
805:
793:
791:
788:
783:
778:
775:
431:Nuclear fuel in
417:heating elements
295:
288:
281:
176:
175:
136:
129:
125:
122:
116:
114:
73:
49:
41:
29:Membrane fouling
4331:
4330:
4326:
4325:
4324:
4322:
4321:
4320:
4316:Water treatment
4281:
4280:
4268:
4263:
4255:
4251:
4245:Wayback Machine
4235:
4231:
4226:Wayback Machine
4216:
4212:
4207:
4203:
4198:Wayback Machine
4189:
4185:
4180:Wayback Machine
4169:
4165:
4160:
4156:
4141:
4137:
4131:
4127:
4093:
4087:
4083:
4078:
4074:
4069:
4065:
4059:Wayback Machine
4049:
4045:
4035:
4031:
4024:
4020:
3983:
3979:
3974:
3970:
3931:
3927:
3904:
3900:
3877:
3873:
3842:
3838:
3815:
3811:
3806:
3802:
3797:Wayback Machine
3786:
3782:
3777:
3770:
3765:Wayback Machine
3754:
3750:
3745:Wayback Machine
3735:
3731:
3726:Wayback Machine
3716:
3712:
3697:
3690:
3682:
3678:
3631:
3627:
3623:
3618:
3589:
3402:reverse osmosis
3394:microfiltration
3371:
3369:Fouling control
3282:
3247:
3243:
3239:
3235:
3228:
3224:
3218:
3214:
3197:
3194:
3193:
3188:
3184:
3180:
3173:
3169:
3131:
3127:
3120:
3116:
3109:
3102:
3098:
3097:
3095:
3086:
3082:
3078:
3074:
3067:
3057:
3053:
3047:
3043:
3042:
3040:
3023:
3020:
3019:
3014:
3006:
2999:
2992:
2985:
2975:
2943:
2942:
2927:
2923:
2914:
2910:
2892:
2888:
2882:
2878:
2866:
2862:
2856:
2852:
2837:
2831:
2827:
2823:
2820:
2819:
2804:
2800:
2794:
2790:
2778:
2774:
2768:
2764:
2749:
2742:
2735:
2734:
2732:
2729:
2728:
2640:electrophoresis
2606:
2563:Falling fouling
2535:
2467:
2443:
2441:Fouling on Mars
2434:
2404:polysaccharides
2371:
2365:
2356:
2325:
2313:
2213:
2209:
2207:
2204:
2203:
2186:
2182:
2180:
2177:
2176:
2157:
2153:
2144:
2140:
2131:
2127:
2125:
2122:
2121:
2098:
2090:
2088:
2086:
2083:
2082:
2059:
2055:
2048:
2044:
2043:
2030:
2022:
2020:
2018:
2015:
2014:
1993:
1980:
1976:
1971:
1960:
1956:
1951:
1950:
1946:
1945:
1936:
1932:
1930:
1927:
1926:
1903:
1899:
1892:
1888:
1887:
1874:
1866:
1864:
1862:
1859:
1858:
1849:thermohydraulic
1832:
1829:
1828:
1811:
1807:
1805:
1802:
1801:
1784:
1780:
1778:
1775:
1774:
1754:
1750:
1738:
1734:
1732:
1729:
1728:
1709:
1706:
1705:
1681:
1652:
1648:
1639:
1635:
1633:
1630:
1629:
1612:
1608:
1599:
1595:
1586:
1582:
1580:
1577:
1576:
1553:
1549:
1540:
1536:
1534:
1531:
1530:
1511:
1507:
1505:
1502:
1501:
1482:
1478:
1476:
1473:
1472:
1453:
1449:
1447:
1444:
1443:
1425:
1422:
1421:
1403:
1400:
1399:
1374:
1370:
1369:
1365:
1359:
1355:
1346:
1342:
1333:
1329:
1316:
1308:
1306:
1304:
1301:
1300:
1279:
1275:
1274:
1270:
1264:
1260:
1251:
1247:
1237:
1233:
1232:
1219:
1211:
1209:
1207:
1204:
1203:
1181:
1177:
1168:
1164:
1155:
1151:
1138:
1130:
1128:
1126:
1123:
1122:
1112:
1108:
988:magnesium oxide
964:Calcium oxalate
946:Calcium sulfate
910:reverse osmosis
895:
870:
865:
853:
847:
842:
837:
828:
824:
819:
814:
807:
795:
794:
789:
784:
776:
771:
763:
758:
756:
755:
753:
750:
749:
730:, leading to a
689:crystallization
653:
588:crystallization
580:
545:Manmade refuse;
496:
349:
299:
137:
126:
120:
117:
74:
72:
62:
50:
39:
32:
17:
12:
11:
5:
4329:
4319:
4318:
4313:
4308:
4303:
4298:
4293:
4279:
4278:
4274:
4267:
4266:External links
4264:
4262:
4261:
4249:
4229:
4210:
4201:
4183:
4163:
4154:
4135:
4125:
4081:
4072:
4063:
4043:
4029:
4018:
3977:
3968:
3925:
3914:(4): 392–406.
3898:
3887:(2): 121–143.
3871:
3836:
3809:
3800:
3780:
3768:
3748:
3729:
3710:
3707:(Google books)
3688:
3676:
3624:
3622:
3619:
3617:
3616:
3611:
3606:
3601:
3596:
3590:
3588:
3585:
3524:(for example,
3518:etidronic acid
3516:(for example,
3506:octadecylamine
3504:(for example,
3496:(for example,
3390:debris filters
3370:
3367:
3281:
3278:
3274:
3273:
3261:
3255:
3250:
3246:
3242:
3238:
3234:
3231:
3227:
3221:
3217:
3213:
3210:
3207:
3204:
3201:
3186:
3182:
3178:
3171:
3167:
3164:
3163:
3151:
3146:
3140:
3137:
3134:
3130:
3126:
3123:
3119:
3112:
3105:
3101:
3094:
3089:
3085:
3081:
3077:
3070:
3065:
3060:
3056:
3050:
3046:
3039:
3036:
3033:
3030:
3027:
3012:
3009:
3008:
3004:
3001:
2997:
2994:
2990:
2987:
2983:
2980:
2977:
2973:
2970:
2969:t is time (s);
2967:
2960:
2959:
2946:
2941:
2938:
2935:
2930:
2926:
2922:
2917:
2913:
2909:
2906:
2903:
2900:
2895:
2891:
2885:
2881:
2877:
2874:
2869:
2865:
2859:
2855:
2851:
2847:
2844:
2840:
2834:
2830:
2826:
2822:
2821:
2818:
2815:
2812:
2807:
2803:
2797:
2793:
2789:
2786:
2781:
2777:
2771:
2767:
2763:
2759:
2756:
2752:
2748:
2745:
2741:
2740:
2738:
2706:
2705:
2690:
2679:
2676:
2673:
2670:
2667:
2644:thermophoresis
2628:
2621:
2605:
2602:
2601:
2600:
2597:sawtooth curve
2593:Seesaw fouling
2590:
2584:
2574:
2560:
2557:Linear fouling
2554:
2548:
2534:
2531:
2466:
2463:
2442:
2439:
2433:
2430:
2367:Main article:
2364:
2361:
2355:
2352:
2333:polymerization
2324:
2321:
2312:
2309:
2293:
2292:
2282:
2239:zeta potential
2231:
2230:
2216:
2212:
2189:
2185:
2174:
2160:
2156:
2152:
2147:
2143:
2139:
2134:
2130:
2119:
2104:
2101:
2096:
2093:
2076:
2075:
2062:
2058:
2051:
2047:
2042:
2036:
2033:
2028:
2025:
2012:
1999:
1996:
1991:
1983:
1979:
1975:
1970:
1963:
1959:
1955:
1949:
1944:
1939:
1935:
1920:
1919:
1906:
1902:
1895:
1891:
1886:
1880:
1877:
1872:
1869:
1836:
1814:
1810:
1787:
1783:
1771:
1770:
1757:
1753:
1749:
1746:
1741:
1737:
1713:
1680:
1677:
1676:
1675:
1663:
1660:
1655:
1651:
1647:
1642:
1638:
1615:
1611:
1607:
1602:
1598:
1594:
1589:
1585:
1574:
1556:
1552:
1548:
1543:
1539:
1528:
1514:
1510:
1499:
1485:
1481:
1470:
1456:
1452:
1441:
1429:
1419:
1407:
1393:
1392:
1377:
1373:
1368:
1362:
1358:
1354:
1349:
1345:
1341:
1336:
1332:
1328:
1322:
1319:
1314:
1311:
1297:
1282:
1278:
1273:
1267:
1263:
1259:
1254:
1250:
1246:
1240:
1236:
1231:
1225:
1222:
1217:
1214:
1200:
1189:
1184:
1180:
1176:
1171:
1167:
1163:
1158:
1154:
1150:
1144:
1141:
1136:
1133:
1115:
1114:
1110:
1106:
1103:nickel ferrite
1099:
1096:hydroxyapatite
1092:
1077:
1059:
1037:
995:
977:
970:Barium sulfate
967:
961:
943:
914:ionic strength
893:
890:
889:
868:
860:
856:
845:
836:
831:
822:
813:
804:
798:
787:
782:
774:
766:
724:degasification
665:heat exchanger
652:
649:
648:
647:
644:
634:
631:
628:
617:
607:
579:
576:
575:
574:
564:
558:
552:
549:
546:
542:
541:
539:
524:cooling towers
495:
492:
491:
490:
479:
476:
461:
455:
449:
446:orifice plates
439:
436:
429:
420:
413:
407:
404:
398:
391:
387:
380:Heat exchanger
348:
345:
323:), fouling of
321:marine fouling
301:
300:
298:
297:
290:
283:
275:
272:
271:
270:
269:
264:
259:
254:
249:
244:
239:
234:
229:
224:
219:
214:
209:
204:
199:
194:
189:
181:
180:
148:Heat exchanger
139:
138:
53:
51:
44:
15:
9:
6:
4:
3:
2:
4328:
4317:
4314:
4312:
4309:
4307:
4304:
4302:
4299:
4297:
4294:
4292:
4289:
4288:
4286:
4277:
4275:
4273:
4270:
4269:
4259:
4253:
4246:
4242:
4239:
4233:
4227:
4223:
4220:
4214:
4205:
4199:
4195:
4192:
4187:
4181:
4177:
4174:
4167:
4158:
4151:(5): 258–262.
4150:
4146:
4139:
4129:
4121:
4120:1721.1/107916
4117:
4112:
4107:
4103:
4099:
4092:
4085:
4076:
4067:
4060:
4056:
4053:
4047:
4040:
4033:
4027:
4022:
4014:
4010:
4005:
4000:
3996:
3992:
3988:
3981:
3972:
3964:
3960:
3956:
3952:
3948:
3944:
3940:
3936:
3929:
3921:
3917:
3913:
3909:
3902:
3894:
3890:
3886:
3882:
3875:
3867:
3863:
3859:
3855:
3851:
3847:
3840:
3832:
3828:
3824:
3820:
3813:
3804:
3798:
3794:
3791:
3784:
3775:
3773:
3766:
3762:
3759:
3752:
3746:
3742:
3739:
3733:
3727:
3723:
3720:
3714:
3708:
3705:
3704:90-5809-242-9
3701:
3695:
3693:
3686:
3680:
3672:
3668:
3663:
3658:
3653:
3648:
3644:
3640:
3636:
3629:
3625:
3615:
3614:Tube cleaning
3612:
3610:
3607:
3605:
3602:
3600:
3597:
3595:
3592:
3591:
3584:
3582:
3578:
3574:
3570:
3566:
3560:
3558:
3554:
3550:
3546:
3540:
3537:
3533:
3531:
3527:
3523:
3519:
3515:
3511:
3507:
3503:
3499:
3495:
3491:
3487:
3486:are applied.
3485:
3484:bottom paints
3481:
3477:
3473:
3469:
3465:
3461:
3457:
3453:
3450:
3446:
3441:
3439:
3435:
3431:
3427:
3423:
3419:
3415:
3411:
3407:
3403:
3399:
3395:
3391:
3387:
3383:
3380:
3376:
3366:
3364:
3359:
3355:
3350:
3346:
3345:nuclear power
3342:
3341:steam turbine
3338:
3337:power station
3334:
3329:
3327:
3323:
3319:
3315:
3311:
3307:
3303:
3298:
3296:
3286:
3277:
3259:
3253:
3248:
3244:
3240:
3236:
3232:
3229:
3225:
3219:
3215:
3211:
3205:
3199:
3192:
3191:
3190:
3175:
3149:
3144:
3138:
3135:
3132:
3128:
3124:
3121:
3117:
3110:
3103:
3099:
3092:
3087:
3083:
3079:
3075:
3068:
3063:
3058:
3054:
3048:
3044:
3037:
3031:
3025:
3018:
3017:
3016:
3002:
2995:
2988:
2981:
2978:
2971:
2968:
2965:
2964:
2963:
2936:
2928:
2924:
2920:
2915:
2911:
2907:
2901:
2893:
2889:
2883:
2879:
2875:
2872:
2867:
2863:
2857:
2853:
2849:
2845:
2842:
2838:
2832:
2828:
2824:
2813:
2805:
2801:
2795:
2791:
2787:
2784:
2779:
2775:
2769:
2765:
2761:
2757:
2754:
2750:
2746:
2743:
2736:
2727:
2726:
2725:
2722:
2719:
2716:
2713:
2710:
2703:
2699:
2695:
2691:
2688:
2684:
2680:
2677:
2674:
2671:
2668:
2665:
2661:
2657:
2656:sedimentation
2653:
2649:
2645:
2641:
2637:
2633:
2629:
2626:
2622:
2619:
2618:
2617:
2610:
2598:
2594:
2591:
2588:
2585:
2582:
2578:
2575:
2572:
2568:
2564:
2561:
2558:
2555:
2552:
2549:
2546:
2545:
2541:
2540:
2539:
2530:
2526:
2524:
2523:hot corrosion
2519:
2515:
2511:
2507:
2503:
2499:
2495:
2490:
2488:
2484:
2478:
2476:
2471:
2462:
2460:
2456:
2452:
2448:
2438:
2429:
2427:
2426:Zebra mussels
2423:
2421:
2417:
2413:
2407:
2405:
2400:
2398:
2394:
2390:
2384:
2383:zebra mussels
2380:
2375:
2370:
2360:
2351:
2348:
2346:
2342:
2338:
2334:
2330:
2320:
2318:
2308:
2306:
2302:
2298:
2290:
2286:
2285:Sedimentation
2283:
2280:
2276:
2272:
2271:lepidocrocite
2268:
2264:
2260:
2257:
2256:
2255:
2252:
2249:
2246:
2244:
2240:
2236:
2214:
2210:
2187:
2183:
2175:
2158:
2154:
2150:
2145:
2141:
2137:
2132:
2128:
2120:
2102:
2099:
2094:
2091:
2081:
2080:
2079:
2060:
2056:
2049:
2045:
2040:
2034:
2031:
2026:
2023:
2013:
1997:
1994:
1989:
1981:
1977:
1973:
1968:
1961:
1957:
1953:
1947:
1942:
1937:
1933:
1925:
1924:
1923:
1904:
1900:
1893:
1889:
1884:
1878:
1875:
1870:
1867:
1857:
1856:
1855:
1852:
1850:
1834:
1812:
1808:
1785:
1781:
1755:
1751:
1747:
1744:
1739:
1735:
1727:
1726:
1725:
1711:
1703:
1699:
1695:
1690:
1686:
1661:
1658:
1653:
1649:
1645:
1640:
1636:
1613:
1609:
1605:
1600:
1596:
1592:
1587:
1583:
1575:
1572:
1554:
1550:
1546:
1541:
1537:
1529:
1512:
1508:
1500:
1483:
1479:
1471:
1454:
1450:
1442:
1427:
1420:
1405:
1398:
1397:
1396:
1375:
1371:
1360:
1356:
1352:
1347:
1343:
1334:
1330:
1326:
1320:
1317:
1312:
1309:
1298:
1280:
1276:
1265:
1261:
1257:
1252:
1248:
1238:
1234:
1229:
1223:
1220:
1215:
1212:
1201:
1182:
1178:
1174:
1169:
1165:
1156:
1152:
1148:
1142:
1139:
1134:
1131:
1120:
1119:
1118:
1104:
1101:Magnetite or
1100:
1097:
1093:
1090:
1086:
1082:
1078:
1075:
1071:
1067:
1063:
1060:
1057:
1053:
1049:
1045:
1041:
1038:
1035:
1031:
1027:
1023:
1019:
1015:
1011:
1007:
1003:
999:
996:
993:
989:
985:
981:
978:
975:
971:
968:
965:
962:
959:
955:
951:
947:
944:
941:
937:
933:
929:
926:
925:
924:
921:
919:
915:
911:
905:
902:
897:
748:
747:
746:
744:
740:
735:
733:
732:precipitation
729:
725:
721:
716:
714:
710:
706:
702:
698:
694:
690:
681:
673:
666:
661:
657:
645:
642:
638:
635:
632:
629:
626:
622:
618:
615:
611:
608:
605:
601:
597:
593:
589:
585:
584:
583:
578:Micro fouling
572:
568:
565:
562:
559:
556:
553:
550:
547:
544:
543:
540:
537:
536:
535:
533:
529:
525:
521:
517:
513:
509:
505:
501:
494:Macro fouling
488:
484:
480:
477:
474:
470:
466:
462:
459:
456:
453:
450:
447:
443:
442:Venturi tubes
440:
437:
434:
430:
428:
427:muzzleloaders
424:
421:
418:
414:
411:
408:
405:
402:
399:
396:
392:
388:
385:
381:
378:
377:
376:
370:
365:
358:
353:
344:
340:
338:
334:
330:
329:cooling water
326:
325:heat-transfer
322:
317:
313:
311:
307:
296:
291:
289:
284:
282:
277:
276:
274:
273:
268:
265:
263:
260:
258:
257:Thermal shock
255:
253:
250:
248:
245:
243:
240:
238:
235:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
208:
205:
203:
200:
198:
195:
193:
190:
188:
185:
184:
183:
182:
178:
177:
171:
167:
164:
160:
153:
149:
145:
135:
132:
124:
121:November 2008
113:
110:
106:
103:
99:
96:
92:
89:
85:
82: –
81:
77:
76:Find sources:
70:
66:
60:
59:
54:This article
52:
48:
43:
42:
37:
30:
26:
22:
4252:
4232:
4213:
4204:
4186:
4166:
4157:
4148:
4144:
4138:
4128:
4101:
4097:
4084:
4075:
4066:
4046:
4032:
4021:
3994:
3990:
3980:
3971:
3938:
3934:
3928:
3911:
3907:
3901:
3884:
3880:
3874:
3852:(1): 81–97.
3849:
3845:
3839:
3822:
3818:
3812:
3803:
3783:
3751:
3732:
3713:
3679:
3642:
3638:
3628:
3561:
3541:
3534:
3488:
3442:
3426:ethanolamine
3400:technology (
3372:
3358:capital cost
3349:desalination
3330:
3299:
3291:
3275:
3176:
3165:
3010:
2961:
2723:
2720:
2717:
2714:
2707:
2698:erosion wear
2660:Magnus force
2615:
2592:
2586:
2576:
2562:
2556:
2550:
2542:
2536:
2527:
2518:permeability
2491:
2479:
2472:
2468:
2444:
2437:components.
2435:
2424:
2408:
2401:
2387:
2357:
2349:
2326:
2314:
2294:
2253:
2250:
2247:
2232:
2077:
1921:
1853:
1851:conditions.
1772:
1694:flocculation
1682:
1394:
1121:Transport:
1116:
1094:Phosphates (
1026:cristobalite
1016:, amorphous
922:
906:
898:
891:
736:
717:
686:
625:carbon steel
581:
497:
471:– decreased
374:
341:
318:
314:
305:
304:
211:
127:
118:
108:
101:
94:
87:
75:
63:Please help
58:verification
55:
20:
4104:: 381–390.
3166:where λ = λ
2702:exfoliation
2687:cementation
2652:Stefan flow
2455:Opportunity
2345:carbonizing
2341:asphaltenes
2287:fouling by
1698:coagulation
954:hemihydrate
720:evaporation
610:Particulate
602:from water
508:water pumps
452:Pitot tubes
415:Electrical
152:power plant
150:in a steam
4285:Categories
4258:(abstract)
4219:(abstract)
4052:(abstract)
3997:: 137008.
3645:: 132583.
3621:References
3502:polyamines
3422:morpholine
3386:filtration
3382:technology
3363:root cause
3354:compressor
3318:ecological
2709:Deposition
2389:Biofouling
2379:canal lock
2369:Biofouling
2363:Biofouling
2301:flue gases
1299:Overall:
1070:cancrinite
1002:serpentine
901:solubility
728:saturation
709:hard water
701:hydroxides
637:Biofouling
600:hydroxides
487:senescence
458:Spark plug
310:biofouling
172:(cut open)
170:biofouling
91:newspapers
4013:249223220
3671:240007081
3449:inorganic
3434:hydrazine
3302:corrosion
3245:λ
3241:−
3233:−
3220:∗
3136:λ
3133:−
3125:−
3111:λ
3100:λ
3084:λ
3069:λ
3064:ρ
2921:⋅
2912:λ
2908:−
2880:λ
2876:−
2873:ρ
2792:λ
2788:−
2785:ρ
2632:molecular
2625:advection
2581:asymptote
2317:substrate
2275:maghemite
2263:magnetite
1995:−
1689:colloidal
1440:- time, s
1353:−
1258:−
1175:−
1034:xonotlite
1030:pectolite
1014:gehlenite
998:Silicates
992:periclase
950:anhydrite
936:aragonite
855:↑
830:↓
812:⟶
713:limescale
705:solutions
691:of solid
660:Limescale
643:and algae
621:corrosion
614:colloidal
604:solutions
590:of solid
469:oil wells
390:blockage;
369:corrosion
192:Corrosion
163:Condenser
80:"Fouling"
4241:Archived
4222:Archived
4194:Archived
4176:Archived
4055:Archived
3963:32303762
3955:24731003
3825:: 1522.
3793:Archived
3761:Archived
3741:Archived
3722:Archived
3587:See also
3581:abrasive
3545:Blowdown
3480:ammonium
3472:biocides
3460:cleavers
3452:chlorine
3445:biocides
3398:membrane
3322:biocides
3314:fretting
2694:spalling
2692:Deposit
2514:Porosity
2498:waviness
2329:catalyst
2297:aerosols
2279:goethite
2267:hematite
1089:tenorite
1074:noselite
1066:analcite
1056:corundum
1052:diaspore
1048:gibbsite
1044:boehmite
1010:gyrolite
940:vaterite
918:flashing
641:bacteria
627:surfaces
538:Examples
534:damage.
532:fretting
401:Turbines
337:calculus
267:Yielding
217:Fracture
187:Buckling
4296:Filters
4291:Fouling
3854:Bibcode
3510:helamin
3456:bromide
3418:ammonia
3310:fatigue
3181:, and λ
2962:where:
2567:tangent
2506:pitting
2399:(MIC).
2393:diatoms
2337:olefins
2078:where:
1395:where:
1085:cuprite
984:brucite
932:calcite
800:aqueous
561:Mussels
423:Firearm
359:scaling
306:Fouling
212:Fouling
207:Fatigue
105:scholar
36:fowling
4133:12171.
4011:
3961:
3953:
3702:
3669:
3557:Teflon
3520:), or
3476:methyl
3468:oxygen
2451:Spirit
1773:where
1081:copper
1022:quartz
1018:silica
1006:acmite
974:barite
958:gypsum
699:, and
697:oxides
598:, and
596:oxides
571:trunks
567:Leaves
516:rivers
504:refuse
500:coarse
371:traces
333:plaque
227:Impact
107:
100:
93:
86:
78:
4173:(pdf)
4094:(PDF)
4039:(pdf)
4009:S2CID
3959:S2CID
3790:(pdf)
3758:(pdf)
3738:(pdf)
3719:(pdf)
3685:(pdf)
3667:S2CID
3565:acids
3464:ozone
3408:) or
3379:water
2700:, or
2445:NASA
1105:(NiFe
703:from
693:salts
592:salts
555:Algae
520:lakes
483:aging
202:Creep
112:JSTOR
98:books
3951:PMID
3700:ISBN
3567:and
3498:EDTA
3466:and
3454:and
3326:fuel
2516:and
2453:and
2414:(or
2289:silt
2202:and
1800:and
1685:crud
817:CaCO
467:and
395:drag
262:Wear
166:tube
84:news
21:foul
4116:hdl
4106:doi
4102:528
3999:doi
3995:446
3943:doi
3916:doi
3889:doi
3862:doi
3827:doi
3657:hdl
3647:doi
3643:430
3428:or
3312:),
3295:GDP
3170:+ λ
2634:or
2525:).
1704:",
1696:or
986:);
908:in
769:HCO
722:or
518:or
512:sea
335:or
67:by
4287::
4147:.
4114:.
4100:.
4096:.
4007:.
3993:.
3989:.
3957:.
3949:.
3939:55
3937:.
3912:14
3910:.
3885:12
3883:.
3860:.
3850:72
3848:.
3823:69
3821:.
3771:^
3691:^
3665:.
3655:.
3641:.
3637:.
3532:.
3508:,
3462:,
3440:.
3424:,
3420:,
3414:pH
3404:,
3396:,
3333:MW
3174:.
2696:,
2658:,
2650:,
2646:,
2642:,
2627:);
2508:,
2504:,
2307:.
2281:);
2277:,
2273:,
2269:,
2265:,
1724::
1569:-
1098:);
1091:);
1087:,
1083:,
1076:);
1072:,
1068:,
1058:);
1054:,
1050:,
1046:,
1036:);
1032:,
1028:,
1024:,
1020:,
1012:,
1008:,
1004:,
994:);
976:);
960:);
956:,
952:,
942:);
934:,
840:CO
760:Ca
715:.
695:,
594:,
514:,
444:,
4236:"
4149:4
4122:.
4118::
4108::
4061:.
4041:.
4037:(
4015:.
4001::
3965:.
3945::
3922:.
3918::
3895:.
3891::
3868:.
3864::
3856::
3833:.
3829::
3673:.
3659::
3649::
3260:)
3254:t
3249:r
3237:e
3230:1
3226:(
3216:m
3212:=
3209:)
3206:t
3203:(
3200:m
3187:c
3183:c
3179:r
3172:c
3168:r
3150:)
3145:)
3139:t
3129:e
3122:1
3118:(
3104:r
3093:+
3088:c
3080:t
3076:(
3059:m
3055:C
3049:d
3045:k
3038:=
3035:)
3032:t
3029:(
3026:m
3013:r
3005:c
3003:λ
2998:r
2996:m
2991:r
2989:λ
2984:m
2982:C
2974:d
2972:k
2940:)
2937:t
2934:(
2929:r
2925:m
2916:c
2905:)
2902:t
2899:(
2894:r
2890:m
2884:r
2868:m
2864:C
2858:d
2854:k
2850:=
2846:t
2843:d
2839:/
2833:r
2829:m
2825:d
2817:)
2814:t
2811:(
2806:r
2802:m
2796:r
2780:m
2776:C
2770:d
2766:k
2762:=
2758:t
2755:d
2751:/
2747:m
2744:d
2737:{
2704:.
2481:"
2449:(
2261:(
2215:b
2211:C
2188:i
2184:C
2159:d
2155:k
2151:,
2146:t
2142:k
2138:,
2133:a
2129:k
2103:t
2100:d
2095:m
2092:d
2061:b
2057:C
2050:d
2046:k
2041:=
2035:t
2032:d
2027:m
2024:d
1998:1
1990:)
1982:t
1978:k
1974:1
1969:+
1962:a
1958:k
1954:1
1948:(
1943:=
1938:d
1934:k
1905:i
1901:C
1894:a
1890:k
1885:=
1879:t
1876:d
1871:m
1868:d
1835:P
1813:t
1809:k
1786:d
1782:k
1756:t
1752:k
1748:P
1745:=
1740:d
1736:k
1712:P
1674:)
1662:1
1659:=
1654:2
1650:n
1646:=
1641:1
1637:n
1614:d
1610:k
1606:,
1601:r
1597:k
1593:,
1588:t
1584:k
1555:2
1551:n
1547:,
1542:1
1538:n
1513:e
1509:C
1484:i
1480:C
1455:b
1451:C
1428:t
1406:m
1376:2
1372:n
1367:)
1361:e
1357:C
1348:b
1344:C
1340:(
1335:d
1331:k
1327:=
1321:t
1318:d
1313:m
1310:d
1281:1
1277:n
1272:)
1266:e
1262:C
1253:i
1249:C
1245:(
1239:r
1235:k
1230:=
1224:t
1221:d
1216:m
1213:d
1188:)
1183:i
1179:C
1170:b
1166:C
1162:(
1157:t
1153:k
1149:=
1143:t
1140:d
1135:m
1132:d
1111:4
1109:O
1107:2
1064:(
1042:(
1000:(
990:(
982:(
972:(
948:(
930:(
894:2
875:O
867:2
863:H
859:+
844:2
835:+
821:3
803:)
797:(
786:2
781:)
773:3
765:(
667:.
573:.
563:;
557:;
489:.
485:/
294:e
287:t
280:v
134:)
128:(
123:)
119:(
109:·
102:·
95:·
88:·
61:.
38:.
31:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
