974:, where most of the resistance to mass transfer occurs. Axial-flow impellers are preferred for solid suspension because solid suspension needs momentum rather than shear, although radial-flow impellers can be used in a tank with baffles, which converts some of the rotational motion into vertical motion. When the solid is denser than the liquid (and therefore collects at the bottom of the tank), the impeller is rotated so that the fluid is pushed downwards; when the solid is less dense than the liquid (and therefore floats on top), the impeller is rotated so that the fluid is pushed upwards (though this is relatively rare). The equipment preferred for solid suspension produces large volumetric flows but not necessarily high shear; high flow-number turbine impellers, such as hydrofoils, are typically used. Multiple turbines mounted on the same shaft can reduce power draw.
999:
to use but are less accurate and don't cover any possible designs. The most popular correlation is the âjust suspended speedâ correlation published by
Zwietering (1958). It's an easy to use correlation but it is not meant for homogeneous suspension. It only provides a crude estimate of the stirring speed for âbadâ quality suspensions (partial suspensions) where no particle remains at the bottom for more than 1 or 2 seconds. Another equivalent correlation is the correlation from Mersmann (1998). For âgoodâ quality suspensions, some examples of useful correlations can be found in the publications of Barresi (1987), Magelli (1991), Cekinski (2010) or Macqueron (2017).
886:
882:
experience gained with these different machines, engineering knowledge has been developed to construct reliable equipment and to predict scale-up and mixing behavior. Nowadays the same mixing technologies are used for many more applications: to improve product quality, to coat particles, to fuse materials, to wet, to disperse in liquid, to agglomerate, to alter functional material properties, etc. This wide range of applications of mixing equipment requires a high level of knowledge, long time experience and extended test facilities to come to the optimal selection of equipment and processes.
2141:
1125:
2277:
2269:
1061:, or diffuses slowly into the liquid. Mixing in a tank is also useful when a (relatively) slow chemical reaction is occurring in the liquid phase, and so the concentration difference in the thin layer near the bubble is close to that of the bulk. This reduces the driving force for mass transfer. If there is a (relatively) fast chemical reaction in the liquid phase, it is sometimes advantageous to disperse but not recirculate the gas bubbles, ensuring that they are in
2261:
2293:
2245:
2285:
718:
1913:
2253:
978:
2237:
2482:-shaped blades encased in segments of cylindrical housings. These intersect so as to leave a ridge between the blades. The blades may be cored for circulation of heating or cooling. Its invention resulted in major labor and capital savings in the tire industry, doing away with the initial step of roller-milling rubber. It is also used for reinforcing fillers in a resin system.
842:. Often minor liquid additions are made to the dry blend to modify the product formulation. Blending times using dry ingredients are often short (15â30 minutes) but are somewhat dependent upon the varying percentages of each component, and the difference in the bulk densities of each. Ribbon, paddle, tumble and vertical blenders are available. Many products including
2015:
mixture come out the discharge of the machine. Many industries have converted to continuous mixing for many reasons. Some of those are ease of cleaning, lower energy consumption, smaller footprint, versatility, control, and many others. Continuous mixers, such as the twin-screw
Continuous Processor, also have the ability to handle very high viscosities.
2014:
In addition to performing typical batch mixing operations, some mixing can be done continuously. Using a machine like the
Continuous Processor, one or more dry ingredients and one or more liquid ingredients can be accurately and consistently metered into the machine and see a continuous, homogeneous
1086:
Gasâsolid mixing may be conducted to transport powders or small particulate solids from one place to another, or to mix gaseous reactants with solid catalyst particles. In either case, the turbulent eddies of the gas must provide enough force to suspend the solid particles, which otherwise sink under
1056:
is used for this purpose, with the packing acting as a motionless mixer and the air pump providing the driving force. When a tank and impeller are used, the objective is typically to ensure that the gas bubbles remain in contact with the liquid for as long as possible. This is especially important if
998:
built on theoretical developments, experimental measurements and/or computational fluid dynamics data. Computational fluid dynamics calculations are quite accurate and can accommodate virtually any tank and agitator designs, but they require expertise and long computation time. Correlations are easy
2152:
are useful for dispersing gases into liquids, but are not very helpful for dispersing settled solids into liquid. Newer turbines have largely supplanted the
Rushton turbine for gasâliquid mixing, such as the Smith turbine and Bakker turbine. The power number is an empirical measure of the amount of
989:
of the solid volume fraction field in the mixing tank). A perfect suspension would have a RSD of 0% but in practice, a RSD inferior or equal to 20% can be sufficient for the suspension to be considered homogeneous, although this is case-dependent. The RSD can be obtained by experimental measurements
881:
Blending powders is one of the oldest unit-operations in the solids handling industries. For many decades powder blending has been used just to homogenize bulk materials. Many different machines have been designed to handle materials with various bulk solids properties. On the basis of the practical
758:
Mixing of liquids occurs frequently in process engineering. The nature of liquids to blend determines the equipment used. Single-phase blending tends to involve low-shear, high-flow mixers to cause liquid engulfment, while multi-phase mixing generally requires the use of high-shear, low-flow mixers
1971:
area between the two fluids is maximized. Beyond just interfacing the two liquids people also made twisting channels to force the two fluids to mix. These included multilayered devices where the fluids would corkscrew, looped devices where the fluids would flow around obstructions and wavy devices
1481:
is the viscosity of the fluid. Note that the mixer power is strongly dependent upon the rotational speed and impeller diameter, and linearly dependent upon either the density or viscosity of the fluid, depending on which flow regime is present. In the transitional regime, flow near the impeller is
1071:
have been traditionally used to disperse gases into liquids, but newer options, such as the Smith turbine and Bakker turbine are becoming more prevalent. One of the issues is that as the gas flow increases, more and more of the gas accumulates in the low pressure zones behind the impeller blades,
936:
When materials are cohesive, which is the case with e.g. fine particles and also with wet material, convective mixing is no longer sufficient to obtain a randomly ordered mixture. The relative strong inter-particle forces form lumps, which are not broken up by the mild transportation forces in the
929:
In powder two different dimensions in the mixing process can be determined: convective mixing and intensive mixing. In the case of convective mixing material in the mixer is transported from one location to another. This type of mixing leads to a less ordered state inside the mixer, the components
893:
Solid-solid mixing can be performed either in batch mixers, which is the simpler form of mixing, or in certain cases in continuous dry-mix, more complex but which provide interesting advantages in terms of segregation, capacity and validation. One example of a solidâsolid mixing process is mulling
2161:
There are two main types of close-clearance mixers: anchors and helical ribbons. Anchor mixers induce solid-body rotation and do not promote vertical mixing, but helical ribbons do. Close clearance mixers are used in the laminar regime, because the viscosity of the fluid overwhelms the inertial
1937:
from powders), and liquidâliquid blending. Another peculiarity of laboratory mixing is that the mixer rests on the bottom of the vessel instead of being suspended near the center. Furthermore, the vessels used for laboratory mixing are typically more widely varied than those used for industrial
1027:
on the outside but dry on the inside. These types of materials are not easily mixed into liquid with the types of mixers preferred for solid suspension because the agglomerate particles must be subjected to intense shear to be broken up. In some ways, deagglomeration of solids is similar to the
795:
in each other occurs frequently in engineering (and in everyday life). An everyday example would be the addition of milk or cream to tea or coffee. Since both liquids are water-based, they dissolve easily in one another. The momentum of the liquid being added is sometimes enough to cause enough
965:
Suspension of solids into a liquid is done to improve the rate of mass transfer between the solid and the liquid. Examples include dissolving a solid reactant into a solvent, or suspending catalyst particles in liquid to improve the flow of reactants and products to and from the particles. The
945:
Liquidâsolid mixing is typically done to suspend coarse free-flowing solids, or to break up lumps of fine agglomerated solids. An example of the former is the mixing granulated sugar into water; an example of the latter is the mixing of flour or powdered milk into water. In the first case, the
1928:
in the fluid being mixed. This is acceptable on a small scale, since the vessels are small and mixing therefore occurs rapidly (short blend time). A variety of stir bar configurations exist, but because of the small size and (typically) low viscosity of the fluid, it is possible to use one
1120:
liquid with the bubble plume. This draws liquid upwards inside the plume, and causes liquid to fall outside the plume. If the viscosity of the liquid is too high to allow for this (or if the solid particles are too heavy), an impeller may be needed to keep the solid particles suspended.
1170:
Many of the equations used for determining the output of mixers are empirically derived, or contain empirically derived constants. Since mixers operate in the turbulent regime, many of the equations are approximations that are considered acceptable for most engineering purposes.
1116:); or in fermentation, where solid microbes and the gases they require must be well-distributed in a liquid medium. The type of mixer used depends upon the properties of the phases. In some cases, the mixing power is provided by the gas itself as it moves up through the liquid,
749:
The type of operation and equipment used during mixing depends on the state of materials being mixed (liquid, semi-solid, or solid) and the miscibility of the materials being processed. In this context, the act of mixing may be synonymous with stirring-, or kneading-processes.
1966:
is the dominant mechanism whereby two different fluids come together. Diffusion is a relatively slow process. Hence a number of researchers had to devise ways to get the two fluids to mix. This involved Y junctions, T junctions, three-way intersections and designs where the
990:
or by calculations. Measurements can be performed at full scale but this is generally unpractical, so it is common to perform measurements at small scale and use a "scale-up" criterion to extrapolate the RSD from small to full scale. Calculations can be performed using a
930:
that must be mixed are distributed over the other components. With progressing time the mixture becomes more randomly ordered. After a certain mixing time the ultimate random state is reached. Usually this type of mixing is applied for free-flowing and coarse materials.
2153:
torque needed to drive different impellers in the same fluid at constant power per unit volume; impellers with higher power numbers require more torque but operate at lower speed than impellers with lower power numbers, which operate at lower torque but higher speeds.
2304:
Ribbon blenders are very common in process industries for performing dry-mixing operations. The mixing is performed thanks to 2 helix (ribbon) welded on the shafts. Both helix move the product in opposite directions thus achieving the mixing (see picture of ribbon
1723:
2162:
forces of the flow and prevents the fluid leaving the impeller from entraining the fluid next to it. Helical ribbon mixers are typically rotated to push material at the wall downwards, which helps circulate the fluid and refresh the surface at the wall.
1998:
At an industrial scale, efficient mixing can be difficult to achieve. A great deal of engineering effort goes into designing and improving mixing processes. Mixing at industrial scale is done in batches (dynamic mixing), inline or with help of
2435:) under atmospheric or vacuum conditions. Capacities range from 0.5 US pints (0.24 L; 0.42 imp pt) through 750 US gallons (2,800 L; 620 imp gal). Many options including jacketing for heating or cooling,
1601:
946:
particles can be lifted into suspension (and separated from one another) by bulk motion of the fluid; in the second, the mixer itself (or the high shear field near it) must destabilize the lumps and cause them to disintegrate.
1111:
Multiphase mixing occurs when solids, liquids and gases are combined in one step. This may occur as part of a catalytic chemical process, in which liquid and gaseous reagents must be combined with a solid catalyst (such as
1144:
Rotational Speed, "N" is usually measured in revolutions per minute (RPM) or revolutions per second (RPS). This variable refers to the rotational speed of the impeller as this number can differ along points of the drive
1800:
675:
Mixing is performed to allow heat and/or mass transfer to occur between one or more streams, components or phases. Modern industrial processing almost always involves some form of mixing. Some classes of
2852:
Macqueron, C. (2018). "Solid-Liquid Mixing in
Stirred Vessels: Numerical Simulation, Experimental Validation and Suspension Quality Prediction Using Multivariate Regression and Machine Learning".
1958:
When scaled down to the microscale, fluid mixing behaves radically different. This is typically at sizes from a couple (2 or 3) millimeters down to the nanometer range. At this size range normal
937:
convective mixer. To decrease the lump size additional forces are necessary; i.e. more energy intensive mixing is required. These additional forces can either be impact forces or shear forces.
2184:
and therefore require comparatively little torque to spin at high speed. High shear dispersers are used for forming emulsions (or suspensions) of immiscible liquids and solid deagglomeration.
2637:"Suspension diphasique liquide-solide en cuve agitée : une corrélation de prédiction de la qualité du mélange sur la base de simulations numériques validées sur mesures expérimentales"
1608:
1924:
or by simple hand-shaking. Sometimes mixing in laboratory vessels is more thorough and occurs faster than is possible industrially. Magnetic stir bars are radial-flow mixers that induce
82:
2011:
are used to reduce speed and increase torque. Some applications require the use of multi-shaft mixers, in which a combination of mixer types are used to completely blend the product.
1852:
1903:
1285:
1343:
1512:
3287:
Nagy B; et al. (2017). "In-line Raman spectroscopic monitoring and feedback control of a continuous twin-screw pharmaceutical powder blending and tableting process".
1222:
3039:
933:
Possible threats during macro mixing is the de-mixing of the components, since differences in size, shape or density of the different particles can lead to segregation.
1174:
When a mixing impeller rotates in the fluid, it generates a combination of flow and shear. The impeller generated flow can be calculated with the following equation:
1459:
1392:
1372:
1479:
878:-and-speed combinations and optional features such as sanitary finishes, vacuum construction, special valves and cover openings are offered by most manufacturers.
1432:
1412:
1072:
which reduces the power drawn by the mixer (and therefore its effectiveness). Newer designs, such as the GDX impeller, have nearly eliminated this problem.
804:
of both liquids is relatively low. If necessary, a spoon or paddle could be used to complete the mixing process. Blending in a more viscous liquid, such as
1519:
3129:
949:
One example of a solidâliquid mixing process in industry is concrete mixing, where cement, sand, small stones or gravel and water are commingled to a
2176:
High shear dispersers create intense shear near the impeller but relatively little flow in the bulk of the vessel. Such devices typically resemble
970:
increases the rate of mass transfer within the bulk of the fluid, and the convection of material away from the particles decreases the size of the
3265:
2918:
2879:
631:
1023:
or form lumps during transportation and storage. Starchy materials or those that form gels when exposed to solvent can form lumps that are
2936:
1730:
1972:
where the channel would constrict and flare out. Additionally channels with features on the walls like notches or groves were tried.
3193:
1148:
Tank
Diameter, "T" The inside diameter of a cylindrical vessel. Most mixing vessels receiving industrial mixers will be cylindrical.
3348:
3409:
3035:
2912:
2652:
1226:
Flow numbers for impellers have been published in the North
American Mixing Forum sponsored Handbook of Industrial Mixing.
2575:"Powder Mixing - Design - problem solving - Ribbon blender, Paddle mixer, Drum blender, Froude Number - PowderProcess.net"
3013:
1987:. At high Peclet numbers (> 1), advection dominates. At low Peclet numbers (< 1), diffusion dominates.
2582:
3358:
1929:
configuration for nearly all mixing tasks. The cylindrical stir bar can be used for suspension of solids, as seen in
1718:{\displaystyle {\theta _{95}}={\frac {34596}{P_{o}{1 \over 3}N^{2}D^{2}}}({\frac {\mu }{\rho }})({\frac {T}{D}})^{2}}
624:
3194:"Emulsification using a "Sonolator" liquid whistle: A new correlation for droplet size from pilot-scale experiments"
3103:
2538:
2216:
which pass fluid at high pressure through an orifice and subsequently over a blade. This subjects the fluid to high
2198:
Static mixers are used when a mixing tank would be too large, too slow, or too expensive to use in a given process.
2608:
1141:
Impeller
Diameter, "D" is measured for industrial mixers as the maximum diameter swept around the axis of rotation.
3384:
2792:
Magelli, F. (1991). "Solids
Concentration Distribution in Slurry Reactors Stirred with Multiple Axial Impeller".
2746:
Mersmann, A. (1998). "Theoretical prediction of the minimum stirrer speed in mechanically agitated suspensions".
38:
2522:
3125:
3077:
597:
1808:
1091:. The size and shape of the particles is an important consideration, since different particles have different
3438:
2959:
1859:
885:
839:
657:
298:
135:
2676:
Tamburini, A. (2012). "CFD Predictions of
Sufficient Suspension Conditions in Solid-Liquid Agitated Tanks".
2521:
Ullmann, Fritz (2005). Ullmann's Chemical Engineering and Plant Design, Volumes 1â2. John Wiley & Sons.
1234:
683:
With the right equipment, it is possible to mix a solid, liquid or gas into another solid, liquid or gas. A
2560:
1292:
991:
617:
224:
1117:
986:
293:
202:
85:
3448:
3443:
3261:
2902:
2875:
2821:"A new approach to characterize suspensions in stirred vessels based on computational fluid dynamics"
2446:, and at the same time on a common axis, thereby providing complete mixing in a very short timeframe.
209:
3061:
2007:
that operate at standard speeds of 1800 or 1500 RPM, which is typically much faster than necessary.
1488:
3433:
504:
499:
288:
281:
114:
1179:
3322:
1029:
950:
843:
687:
fermenter may require the mixing of microbes, gases and liquid medium for optimal yield; organic
567:
562:
231:
2932:
119:
542:
160:
3396:
921:
that are metallic parts for automobile, machine building, construction or other industries.
3208:
3164:
2971:
2720:
2331:
1437:
1377:
1350:
906:
730:
380:
197:
177:
165:
109:
1464:
1229:
The power required to rotate an impeller can be calculated using the following equations:
1032:
is usually not a problem. An everyday example of this type of mixing is the production of
8:
2478:
and plastics. The original design dates back to 1916. The mixer consists of two rotating
2180:
blades and are rotated at high speed. Because of their shape, they have a relatively low
1100:
668:
of the water in a swimming pool to homogenize the water temperature, and the stirring of
661:
645:
582:
430:
323:
29:
3212:
3168:
2975:
2724:
1099:. A common unit operation the process industry uses to separate gases and solids is the
703:
organic phase; production of pharmaceutical tablets requires blending of solid powders.
2987:
2693:
2471:
2467:
1975:
One way to know if mixing is happening due to advection or diffusion is by finding the
1968:
1947:
1417:
1397:
870:
are manufactured in these designs. Dry blenders range in capacity from half-cubic-foot
851:
707:
602:
236:
192:
187:
2759:
3406:
3354:
3304:
3153:"Determination of the flow field inside a Sonolator liquid whistle using PIV and CFD"
2983:
2908:
2805:
2732:
2697:
2658:
2648:
2636:
2474:. Internal batch mixers such as the Banbury mixer are used for mixing or compounding
2276:
1596:{\displaystyle {\theta _{95}}={\frac {5.40}{P_{o}^{1 \over 3}N}}({\frac {T}{D}})^{2}}
910:
895:
711:
219:
170:
2991:
2861:
2837:
2820:
2140:
985:
The degree of homogeneity of a solid-liquid suspension can be described by the RSD (
3296:
3216:
3172:
2979:
2857:
2832:
2801:
2755:
2728:
2685:
2463:
2443:
2221:
2181:
2171:
1939:
1921:
1092:
1012:
1000:
835:
677:
557:
532:
445:
420:
415:
370:
3300:
2900:
1161:
Impeller Pumping Capacity, "Q" The resulting fluid motion from impeller rotation.
1003:
can also be used to build models way more accurate than "classical" correlations.
3413:
3262:"Powder Mixer - Ribbon blender - Design calculation and key operation parameters"
2711:
Zwietering, T.N. (1958). "Suspending of solid particles in liquid by agitators".
2397:
2348:
2149:
2053:
1156:
1068:
809:
768:
722:
547:
471:
435:
385:
316:
305:
250:
152:
1124:
3239:
Investigation of Fluid Dynamics and Emulsification in Sonolator Liquid Whistles
2225:
2207:
2004:
1943:
1374:
is the (dimensionless) power number, which is a function of impeller geometry;
1152:
971:
967:
734:
653:
552:
410:
375:
276:
182:
3221:
3177:
3152:
3427:
3005:
2689:
2662:
2523:
http://app.knovel.com/hotlink/toc/id:kpUCEPDV02/ullmanns-chemical-engineering
2494:
1976:
1934:
1113:
1053:
1049:
1045:
696:
592:
425:
1485:
The time required to blend a fluid to within 5% of the final concentration,
812:
per unit volume to achieve the same homogeneity in the same amount of time.
3418:
3308:
2574:
2432:
2268:
2213:
2193:
2177:
2000:
1081:
1016:
918:
821:
771:
of the flow. Turbulent or transitional mixing is frequently conducted with
760:
738:
577:
572:
537:
269:
3099:
2534:
2499:
2413:
2148:
Different types of impellers are used for different tasks; for instance,
1020:
995:
838:
which are typically used to blend multiple dry components until they are
700:
692:
587:
490:
16:
Process of mechanically stirring a heterogeneous mixture to homogenize it
2604:
2380:
2217:
1925:
875:
871:
855:
797:
509:
405:
3401:
2260:
1990:
Peclet number = (flow velocity Ă mixing path) / diffusion coefficient
1962:
does not happen unless it is forced by a hydraulic pressure gradient.
2901:
Edward L. Paul; Victor Atiemo-Obeng; Suzanne M. Kresta, eds. (2003).
2292:
2244:
2023:
A selection of turbine geometries and power numbers are shown below.
1984:
1980:
1963:
1959:
1930:
1062:
1033:
899:
867:
801:
764:
688:
481:
476:
310:
3073:
2678:
International Journal of Nonlinear Sciences and Numerical Simulation
2284:
779:; laminar mixing is conducted with helical ribbon or anchor mixers.
3192:
Ryan, David; Baker, Michael; Kowalski, Adam; Simmons, Mark (2018).
2428:
2409:
2393:
1912:
1795:{\displaystyle {\theta _{95}}={\frac {896*10^{3}K_{p}^{-1.69}}{N}}}
863:
788:
776:
460:
365:
345:
331:
3237:
717:
3062:
http://www.dairynetwork.com/product.mvc/Continuous-Processor-0002
2421:
2417:
2252:
2008:
1096:
1088:
1024:
859:
792:
772:
684:
669:
214:
2561:"Batch and continuous solids mixing comparison - Powder Mixing"
2479:
2475:
2436:
2236:
1058:
914:
355:
2773:
Barresi, A. (1987). "Solid dispersion in an agitated vessel".
1103:, which slows the gas and causes the particles to settle out.
1052:, gas is used to remove volatiles from a liquid. Typically, a
977:
2459:
2405:
874:
models to 500-cubic-foot production units. A wide variety of
805:
259:
2144:
Axial flow impeller (left) and radial flow impeller (right).
1137:
For liquid mixing, the nomenclature is rather standardized:
2401:
1151:
Power, "P" Is the energy input into a system usually by an
1095:, and particles made of different materials have different
954:
902:
847:
665:
1933:, deagglomeration (useful for preparation of microbiology
889:
Machine for incorporating liquids and finely ground solids
1414:
is the rotational speed, typically rotations per second;
1028:
blending of immiscible liquids, except for the fact that
395:
3191:
1482:
turbulent and so the turbulent power equation is used.
3036:"High Viscosity Mixers: Dual and Triple Shaft Mixers"
1862:
1811:
1733:
1611:
1522:
1514:, can be calculated with the following correlations:
1491:
1467:
1440:
1420:
1400:
1380:
1353:
1295:
1237:
1182:
41:
3402:
Visualizations of fluid dynamics in mixing processes
3397:
Wiki on equipment for mixing bulk solids and powders
3151:Ryan, David; Simmons, Mark; Baker, Michael (2017).
2904:
Handbook of Industrial Mixing: Science and Practice
2439:
or pressure, vari speed drives, etc. are available.
913:and reusable mass, applied for molding and pouring
2958:Nguyen, Nam-Trung; Wu, Zhigang (1 February 2005).
2647:. SFGP - Société Française de Génie des Procédés.
1897:
1846:
1794:
1717:
1595:
1506:
1473:
1453:
1426:
1406:
1386:
1366:
1337:
1279:
1216:
76:
3407:A textbook chapter on mixing in the food industry
2957:
2392:is a device used to mix round products including
3425:
3419:Information on Solids mixing - powderprocess.net
3150:
1946:may be used in addition to the more cylindrical
660:physical system with the intent to make it more
2296:Double shaft mixer for high-viscosity materials
1044:Liquids and gases are typically mixed to allow
767:or transitional flow regimes, depending on the
3385:Dry Blender Selection Criteria Technical Paper
2964:Journal of Micromechanics and Microengineering
2027:Selected Turbine Geometries and Power Numbers
1993:
1805:The Transitional/Turbulent boundary occurs at
1920:At a laboratory scale, mixing is achieved by
672:batter to eliminate lumps (deagglomeration).
625:
3126:"A Practical Guide to High Speed Dispersion"
1856:The Laminar/Transitional boundary occurs at
1128:Schematic drawing of a fluidized bed reactor
710:. A classical example of segregation is the
77:{\displaystyle J=-D{\frac {d\varphi }{dx}}}
2710:
1953:
905:, fine coal dust and water are mixed to a
632:
618:
3220:
3176:
2851:
2836:
2825:Brazilian Journal of Chemical Engineering
2675:
2634:
2517:
2515:
2156:
1165:
2894:
2818:
2745:
2291:
2283:
2275:
2267:
2259:
2251:
2243:
2235:
2165:
2139:
1911:
1847:{\displaystyle P_{o}^{1 \over 3}Re=6404}
1123:
1065:and can transfer mass more efficiently.
1006:
976:
884:
782:
744:
721:Schematics of an agitated vessel with a
716:
2791:
2772:
2470:. The "Banbury" trademark is owned by
2280:Industrial High shear Mixer/Granulator.
1898:{\displaystyle P_{o}^{1 \over 3}Re=186}
1048:to occur. For instance, in the case of
1015:pigments, and materials that have been
981:Solid volume fraction in a mixing tank
753:
3426:
3286:
2921:from the original on 21 November 2012.
2585:from the original on 28 September 2017
2512:
1280:{\displaystyle P=P_{o}\rho N^{3}D^{5}}
1036:from liquid milk and solid ice cream.
940:
3268:from the original on 16 February 2018
3242:(EngD.). University of Birmingham, UK
2641:Récents ProgrÚs en Génie des Procédés
1338:{\displaystyle P=K_{p}\mu N^{2}D^{3}}
1132:
957:, used in the construction industry.
826:
733:is highly abstract, and is a part of
3346:
3235:
2630:
2628:
2626:
2442:The blades each rotate on their own
2228:, deagglomeration and disinfection.
1907:
1106:
1039:
924:
759:to create droplets of one liquid in
3128:. Hockmeyer.com. 18 December 2012.
3106:from the original on 14 August 2017
3080:from the original on 14 August 2017
3016:from the original on 2 January 2018
3006:"Microfluidic Mixing - Redbud Labs"
2611:from the original on 14 August 2017
2427:This mixer is ideal for mixing and
1461:is the laminar power constant; and
1075:
1057:the gas is expensive, such as pure
960:
13:
3378:
2201:
14:
3460:
3390:
3347:Leab, Daniel J. (26 April 1985).
3132:from the original on 10 June 2017
2939:from the original on 11 June 2017
2882:from the original on 11 June 2017
2623:
2541:from the original on 26 June 2017
2003:. Moving mixers are powered with
1434:is the diameter of the impeller;
815:
3353:. University of Illinois Press.
3076:. Bakker.org. 16 December 1998.
3042:from the original on 3 July 2017
2933:"Power Number (Np) for turbines"
2431:viscous pastes (up to 6 million
2187:
656:that involves manipulation of a
3340:
3315:
3280:
3254:
3229:
3185:
3144:
3118:
3092:
3066:
3054:
3028:
2998:
2951:
2925:
2868:
2845:
2838:10.1590/S0104-66322010000200005
2812:
2785:
2766:
2272:Industrial Double Cone Blender.
691:requires concentrated (liquid)
2739:
2704:
2669:
2597:
2567:
2553:
2527:
2212:Liquid whistles are a kind of
1706:
1692:
1689:
1676:
1584:
1570:
1507:{\displaystyle {\theta _{95}}}
1:
3301:10.1016/j.ijpharm.2017.07.041
3102:. Bakker.org. 10 April 1998.
2862:10.13140/RG.2.2.11074.84164/1
2760:10.1016/S0255-2701(98)00057-9
2607:. Bakker.org. 10 April 1998.
2537:. Bakker.org. 10 April 1998.
2505:
2313:Twin-Screw Continuous Blender
1394:is the density of the fluid;
3201:Chemical Engineering Science
3157:Chemical Engineering Science
2806:10.1016/0255-2701(91)87003-L
2775:Chemical Engineering Science
2733:10.1016/0009-2509(58)85031-9
2713:Chemical Engineering Science
2635:Macqueron, Corentin (2017).
2535:"Various Mixing Experiments"
1217:{\displaystyle Q=Fl*N*D^{3}}
992:computational fluid dynamics
664:. Familiar examples include
7:
3074:"Asymmetric Blade Impeller"
2488:
2374:Hot/Cold mixing combination
2220:stresses and may result in
2018:
1994:Industrial mixing equipment
1011:Very fine powders, such as
987:Relative Standard Deviation
787:Mixing of liquids that are
10:
3465:
2984:10.1088/0960-1317/15/2/R01
2466:mixer, named for inventor
2264:Industrial Ribbon Blender.
2205:
2191:
2169:
1079:
819:
800:to mix the two, since the
706:The opposite of mixing is
3370:– via Google Books.
3222:10.1016/j.ces.2018.06.004
3178:10.1016/j.ces.2017.01.035
3100:"Helical Ribbon Impeller"
2339:Double & Triple Shaft
2134:
3350:The Labor History Reader
2690:10.1515/ijnsns-2012-0027
2248:Industrial Paddle Mixer.
2231:
136:ClausiusâDuhem (entropy)
86:Fick's laws of diffusion
3412:3 February 2019 at the
3327:www.accessmylibrary.com
3060:"Continuous Processor"
2345:High Shear Rotor Stator
2240:Industrial Paddle Mixer
1954:Mixing in microfluidics
808:, requires more mixing
294:NavierâStokes equations
232:Material failure theory
2960:"Micromixersâa review"
2297:
2289:
2281:
2273:
2265:
2257:
2249:
2241:
2157:Close-clearance mixers
2145:
2042:Blade angle (degrees)
1938:mixing; for instance,
1917:
1899:
1848:
1796:
1725:(Transitional region)
1719:
1597:
1508:
1475:
1455:
1428:
1408:
1388:
1368:
1339:
1281:
1218:
1166:Constitutive equations
1129:
982:
890:
726:
78:
2819:Cekinski, E. (2010).
2579:www.powderprocess.net
2295:
2287:
2279:
2271:
2263:
2256:Industrial V Blender.
2255:
2247:
2239:
2166:High shear dispersers
2143:
2075:Pitched blade turbine
1979:. It is the ratio of
1915:
1900:
1849:
1797:
1720:
1598:
1509:
1476:
1456:
1454:{\displaystyle K_{p}}
1429:
1409:
1389:
1387:{\displaystyle \rho }
1369:
1367:{\displaystyle P_{o}}
1340:
1282:
1219:
1127:
1007:Solid deagglomeration
994:software or by using
980:
888:
783:Single-phase blending
745:Mixing classification
731:mathematics of mixing
720:
289:Bernoulli's principle
282:Archimedes' principle
79:
3439:Industrial machinery
3323:"AML - support.gale"
3236:Ryan, David (2015).
2876:"Turbine principles"
2332:High Viscosity Mixer
2316:Continuous Processor
1860:
1809:
1731:
1609:
1520:
1489:
1474:{\displaystyle \mu }
1465:
1438:
1418:
1398:
1378:
1351:
1293:
1235:
1180:
754:Liquidâliquid mixing
381:Cohesion (chemistry)
203:Infinitesimal strain
39:
3213:2018ChEnS.189..369R
3169:2017ChEnS.163..123R
2976:2005JMiMi..15R...1N
2725:1958ChEnS...8..244Z
2325:Double Cone Blender
2029:
1926:solid body rotation
1882:
1831:
1785:
1603:(Turbulent regime)
1563:
1287:(Turbulent regime)
941:Liquidâsolid mixing
737:, itself a part of
699:to be mixed with a
646:process engineering
299:Poiseuille equation
30:Continuum mechanics
24:Part of a series on
2794:Chem. Eng. Process
2748:Chem. Eng. Process
2472:Farrel Corporation
2468:Fernley H. Banbury
2319:Cone Screw Blender
2298:
2290:
2282:
2274:
2266:
2258:
2250:
2242:
2146:
2026:
1918:
1916:A magnetic stirrer
1895:
1863:
1844:
1812:
1792:
1768:
1715:
1593:
1544:
1504:
1471:
1451:
1424:
1404:
1384:
1364:
1335:
1277:
1214:
1133:Basic nomenclature
1130:
983:
898:sand, where sand,
891:
827:Solidâsolid mixing
727:
505:Magnetorheological
500:Electrorheological
237:Fracture mechanics
74:
3449:Rotating machines
3444:Plastics industry
3038:. Hockmeyer.com.
2914:978-0-471-26919-9
2654:978-2-910239-85-5
2605:"Stirred Vessels"
2353:Dispersion Mixers
2138:
2137:
2045:Number of blades
1940:Erlenmeyer flasks
1922:magnetic stirrers
1908:Laboratory mixing
1880:
1829:
1802:(Laminar regime)
1790:
1703:
1687:
1674:
1651:
1581:
1568:
1561:
1427:{\displaystyle D}
1407:{\displaystyle N}
1345:(Laminar regime)
1107:Multiphase mixing
1093:drag coefficients
1040:Liquidâgas mixing
925:Mixing mechanisms
712:brazil nut effect
680:are also mixers.
678:chemical reactors
642:
641:
517:
516:
451:
450:
220:Contact mechanics
143:
142:
72:
3456:
3372:
3371:
3369:
3367:
3344:
3338:
3337:
3335:
3333:
3319:
3313:
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3284:
3278:
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3227:
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3141:
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3070:
3064:
3058:
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3023:
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3002:
2996:
2995:
2955:
2949:
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2922:
2898:
2892:
2891:
2889:
2887:
2872:
2866:
2865:
2849:
2843:
2842:
2840:
2816:
2810:
2809:
2789:
2783:
2782:
2770:
2764:
2763:
2743:
2737:
2736:
2719:(3â4): 244â253.
2708:
2702:
2701:
2673:
2667:
2666:
2632:
2621:
2620:
2618:
2616:
2601:
2595:
2594:
2592:
2590:
2571:
2565:
2564:
2557:
2551:
2550:
2548:
2546:
2531:
2525:
2519:
2385:Planetary mixer
2371:Horizontal Mixer
2336:Counter-rotating
2328:Double Planetary
2182:drag coefficient
2172:high-shear mixer
2150:Rushton turbines
2115:Marine Propeller
2030:
2025:
1904:
1902:
1901:
1896:
1881:
1873:
1871:
1853:
1851:
1850:
1845:
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1801:
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1275:
1266:
1265:
1253:
1252:
1223:
1221:
1220:
1215:
1213:
1212:
1076:Gasâsolid mixing
1069:Rushton turbines
1013:titanium dioxide
1001:Machine learning
961:Solid suspension
917:metal to obtain
836:industrial mixer
634:
627:
620:
466:
465:
431:Gay-Lussac's law
421:Combined gas law
371:Capillary action
256:
255:
99:
98:
83:
81:
80:
75:
73:
71:
63:
55:
21:
20:
3464:
3463:
3459:
3458:
3457:
3455:
3454:
3453:
3434:Unit operations
3424:
3423:
3414:Wayback Machine
3393:
3381:
3379:Further reading
3376:
3375:
3365:
3363:
3361:
3345:
3341:
3331:
3329:
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3033:
3029:
3019:
3017:
3004:
3003:
2999:
2956:
2952:
2942:
2940:
2935:. Cercell.com.
2931:
2930:
2926:
2915:
2899:
2895:
2885:
2883:
2878:. Cercell.com.
2874:
2873:
2869:
2850:
2846:
2817:
2813:
2790:
2786:
2771:
2767:
2744:
2740:
2709:
2705:
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2670:
2655:
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2624:
2614:
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2602:
2598:
2588:
2586:
2573:
2572:
2568:
2559:
2558:
2554:
2544:
2542:
2533:
2532:
2528:
2520:
2513:
2508:
2491:
2398:pharmaceuticals
2390:planetary mixer
2349:Impinging mixer
2301:Ribbon Blender
2234:
2210:
2204:
2202:Liquid whistles
2196:
2190:
2174:
2168:
2159:
2054:Rushton turbine
2048:Blade geometry
2039:Flow direction
2028:
2021:
2005:electric motors
1996:
1956:
1944:Florence flasks
1910:
1872:
1867:
1861:
1858:
1857:
1821:
1816:
1810:
1807:
1806:
1777:
1772:
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1248:
1244:
1236:
1233:
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1208:
1204:
1181:
1178:
1177:
1168:
1157:pneumatic motor
1135:
1109:
1084:
1078:
1042:
1009:
963:
953:self-hardening
943:
927:
844:pharmaceuticals
829:
824:
818:
785:
769:Reynolds number
756:
747:
723:Rushton turbine
638:
609:
608:
607:
527:
519:
518:
472:Viscoelasticity
463:
453:
452:
440:
390:
386:Surface tension
350:
253:
251:Fluid mechanics
243:
242:
241:
155:
153:Solid mechanics
145:
144:
96:
88:
64:
56:
54:
40:
37:
36:
17:
12:
11:
5:
3462:
3452:
3451:
3446:
3441:
3436:
3422:
3421:
3416:
3404:
3399:
3392:
3391:External links
3389:
3388:
3387:
3380:
3377:
3374:
3373:
3359:
3339:
3314:
3295:(1â2): 21â29.
3279:
3253:
3228:
3184:
3143:
3117:
3091:
3065:
3053:
3027:
3010:redbudlabs.com
2997:
2950:
2924:
2913:
2893:
2867:
2844:
2831:(2): 265â273.
2811:
2784:
2765:
2754:(6): 503â510.
2738:
2703:
2684:(6): 427â443.
2668:
2653:
2622:
2596:
2566:
2552:
2526:
2510:
2509:
2507:
2504:
2503:
2502:
2497:
2490:
2487:
2486:
2485:
2484:
2483:
2451:Banbury mixer
2449:
2448:
2447:
2440:
2425:
2383:
2378:
2377:Vertical mixer
2375:
2372:
2369:
2368:Intermix mixer
2366:
2363:
2360:
2357:
2354:
2351:
2346:
2343:
2340:
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2334:
2329:
2326:
2323:
2320:
2317:
2314:
2311:
2308:
2307:
2306:
2233:
2230:
2226:emulsification
2208:Liquid Whistle
2206:Main article:
2203:
2200:
2192:Main article:
2189:
2186:
2170:Main article:
2167:
2164:
2158:
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1153:electric motor
1149:
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1134:
1131:
1108:
1105:
1080:Main article:
1077:
1074:
1041:
1038:
1008:
1005:
972:boundary layer
968:eddy diffusion
962:
959:
942:
939:
926:
923:
834:are a type of
828:
825:
820:Main article:
817:
816:Gasâgas mixing
814:
784:
781:
755:
752:
746:
743:
735:ergodic theory
697:sulfuric acids
654:unit operation
644:In industrial
640:
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376:Chromatography
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104:
103:
97:
94:
93:
90:
89:
84:
70:
67:
62:
59:
53:
50:
47:
44:
33:
32:
26:
25:
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9:
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3:
2:
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3447:
3445:
3442:
3440:
3437:
3435:
3432:
3431:
3429:
3420:
3417:
3415:
3411:
3408:
3405:
3403:
3400:
3398:
3395:
3394:
3386:
3383:
3382:
3362:
3360:9780252011986
3356:
3352:
3351:
3343:
3328:
3324:
3318:
3310:
3306:
3302:
3298:
3294:
3290:
3289:Int. J. Pharm
3283:
3267:
3263:
3257:
3241:
3240:
3232:
3223:
3218:
3214:
3210:
3206:
3202:
3195:
3188:
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3170:
3166:
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3154:
3147:
3131:
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3101:
3095:
3079:
3075:
3069:
3063:
3057:
3041:
3037:
3031:
3015:
3011:
3007:
3001:
2993:
2989:
2985:
2981:
2977:
2973:
2970:(2): R1âR16.
2969:
2965:
2961:
2954:
2938:
2934:
2928:
2920:
2916:
2910:
2906:
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2897:
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2877:
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2863:
2859:
2855:
2848:
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2830:
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2803:
2799:
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2788:
2780:
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2769:
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2726:
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2718:
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2580:
2576:
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2562:
2556:
2540:
2536:
2530:
2524:
2518:
2516:
2511:
2501:
2498:
2496:
2495:Mixing paddle
2493:
2492:
2481:
2477:
2473:
2469:
2465:
2461:
2457:
2456:Banbury mixer
2453:
2452:
2450:
2445:
2441:
2438:
2434:
2430:
2426:
2423:
2419:
2415:
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2399:
2395:
2391:
2387:
2386:
2384:
2382:
2379:
2376:
2373:
2370:
2367:
2365:Drum Blenders
2364:
2362:Mobile Mixers
2361:
2358:
2355:
2352:
2350:
2347:
2344:
2341:
2338:
2335:
2333:
2330:
2327:
2324:
2322:Screw Blender
2321:
2318:
2315:
2312:
2309:
2303:
2302:
2300:
2299:
2294:
2286:
2278:
2270:
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2254:
2246:
2238:
2229:
2227:
2223:
2219:
2215:
2209:
2199:
2195:
2188:Static mixers
2185:
2183:
2179:
2173:
2163:
2154:
2151:
2142:
2133:
2129:
2126:
2123:
2120:
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2113:
2109:
2106:
2103:
2100:
2097:
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2069:
2066:
2063:
2060:
2057:
2055:
2052:
2051:
2047:
2044:
2041:
2038:
2036:Power number
2035:
2032:
2031:
2024:
2016:
2012:
2010:
2006:
2002:
2001:static mixers
1991:
1988:
1986:
1982:
1978:
1977:Peclet number
1973:
1970:
1965:
1961:
1951:
1949:
1945:
1941:
1936:
1935:growth medium
1932:
1927:
1923:
1914:
1905:
1892:
1889:
1886:
1883:
1877:
1874:
1868:
1864:
1854:
1841:
1838:
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1823:
1817:
1813:
1803:
1787:
1781:
1778:
1773:
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1736:
1726:
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1483:
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1140:
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1126:
1122:
1119:
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1114:hydrogenation
1104:
1102:
1098:
1094:
1090:
1087:the force of
1083:
1073:
1070:
1066:
1064:
1060:
1055:
1054:packed column
1051:
1050:air stripping
1047:
1046:mass transfer
1037:
1035:
1031:
1026:
1022:
1018:
1014:
1004:
1002:
997:
993:
988:
979:
975:
973:
969:
958:
956:
952:
947:
938:
934:
931:
922:
920:
919:sand castings
916:
912:
908:
904:
901:
897:
887:
883:
879:
877:
873:
869:
865:
861:
857:
853:
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845:
841:
837:
833:
823:
813:
811:
807:
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794:
790:
780:
778:
774:
770:
766:
762:
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742:
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736:
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724:
719:
715:
713:
709:
704:
702:
698:
694:
690:
686:
681:
679:
673:
671:
667:
663:
659:
658:heterogeneous
655:
651:
647:
635:
630:
628:
623:
621:
616:
615:
613:
612:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
534:
531:
530:
523:
522:
511:
508:
506:
503:
501:
498:
497:
496:
495:
492:
489:
488:
483:
480:
478:
475:
473:
470:
469:
468:
467:
462:
457:
456:
447:
444:
443:
437:
434:
432:
429:
427:
424:
422:
419:
417:
416:Charles's law
414:
412:
409:
407:
404:
403:
401:
400:
397:
394:
393:
387:
384:
382:
379:
377:
374:
372:
369:
367:
364:
363:
361:
360:
357:
354:
353:
347:
344:
340:
337:
333:
330:
325:
324:non-Newtonian
322:
318:
314:
313:
312:
309:
307:
304:
300:
297:
295:
292:
290:
287:
283:
280:
278:
275:
271:
268:
267:
265:
264:
261:
258:
257:
252:
247:
246:
238:
235:
233:
230:
226:
223:
222:
221:
218:
216:
213:
211:
210:Compatibility
208:
204:
201:
199:
198:Finite strain
196:
195:
194:
191:
189:
186:
184:
181:
179:
176:
172:
169:
168:
167:
164:
162:
159:
158:
154:
149:
148:
137:
134:
133:
132:
131:
127:
126:
121:
118:
116:
113:
111:
108:
107:
106:
105:
102:Conservations
101:
100:
92:
91:
87:
68:
65:
60:
57:
51:
48:
45:
42:
35:
34:
31:
28:
27:
23:
22:
19:
3364:. Retrieved
3349:
3342:
3330:. Retrieved
3326:
3317:
3292:
3288:
3282:
3270:. Retrieved
3256:
3244:. Retrieved
3238:
3231:
3204:
3200:
3187:
3160:
3156:
3146:
3134:. Retrieved
3120:
3108:. Retrieved
3094:
3082:. Retrieved
3068:
3056:
3044:. Retrieved
3030:
3018:. Retrieved
3009:
3000:
2967:
2963:
2953:
2941:. Retrieved
2927:
2903:
2896:
2884:. Retrieved
2870:
2854:ResearchGate
2853:
2847:
2828:
2824:
2814:
2797:
2793:
2787:
2778:
2774:
2768:
2751:
2747:
2741:
2716:
2712:
2706:
2681:
2677:
2671:
2644:
2640:
2613:. Retrieved
2599:
2587:. Retrieved
2578:
2569:
2555:
2543:. Retrieved
2529:
2500:Dry blending
2462:of internal
2455:
2389:
2342:Vacuum Mixer
2288:Drum-Blender
2214:static mixer
2211:
2197:
2194:static mixer
2178:circular saw
2175:
2160:
2147:
2022:
2013:
1997:
1989:
1974:
1957:
1919:
1855:
1804:
1727:
1605:
1516:
1484:
1347:
1289:
1231:
1228:
1225:
1176:
1173:
1169:
1136:
1110:
1085:
1082:Fluidization
1067:
1043:
1010:
996:correlations
984:
964:
948:
944:
935:
932:
928:
892:
880:
832:Dry blenders
831:
830:
822:Gas blending
791:or at least
786:
757:
748:
739:chaos theory
728:
705:
682:
674:
649:
643:
491:Smart fluids
436:Graham's law
342:
338:
335:
320:
306:Pascal's law
302:
285:
273:
128:Inequalities
18:
3272:16 February
3246:1 September
3207:: 369â379.
3163:: 123â136.
2414:electronics
2404:(including
1969:interfacial
1030:coalescence
1021:agglomerate
1017:spray dried
966:associated
951:homogeneous
856:fertilizers
840:homogeneous
725:and baffles
708:segregation
701:hydrophobic
662:homogeneous
510:Ferrofluids
411:Boyle's law
183:Hooke's law
161:Deformation
3428:Categories
2506:References
2433:centipoise
2381:Turbomixer
1118:entraining
1034:milkshakes
876:horsepower
872:laboratory
798:turbulence
563:Gay-Lussac
526:Scientists
426:Fick's law
406:Atmosphere
225:frictional
178:Plasticity
166:Elasticity
2907:. Wiley.
2800:: 27â32.
2698:125170997
2663:1775-335X
2410:chemicals
2394:adhesives
2359:Jet Mixer
2310:V Blender
2305:blender).
2218:turbulent
2095:Hydrofoil
2009:Gearboxes
1985:diffusion
1981:advection
1964:Diffusion
1960:advection
1931:iodometry
1779:−
1756:∗
1737:θ
1685:ρ
1682:μ
1615:θ
1526:θ
1495:θ
1469:μ
1382:ρ
1313:μ
1255:ρ
1202:∗
1196:∗
1097:densities
1063:plug flow
900:bentonite
868:cosmetics
852:chemicals
802:viscosity
777:impellers
765:turbulent
689:nitration
603:Truesdell
533:Bernoulli
482:Rheometer
477:Rheometry
317:Newtonian
311:Viscosity
61:φ
49:−
3410:Archived
3366:26 April
3332:26 April
3309:28723408
3266:Archived
3130:Archived
3104:Archived
3078:Archived
3040:Archived
3020:26 April
3014:Archived
2992:16772224
2937:Archived
2919:Archived
2880:Archived
2609:Archived
2589:26 April
2583:Archived
2539:Archived
2489:See also
2429:kneading
2422:pigments
2418:plastics
2019:Turbines
911:moldable
894:foundry
864:pigments
860:plastics
789:miscible
773:turbines
461:Rheology
366:Adhesion
346:Pressure
332:Buoyancy
277:Dynamics
115:Momentum
3209:Bibcode
3165:Bibcode
3136:23 June
3110:23 June
3084:23 June
3046:23 June
2972:Bibcode
2943:23 June
2886:23 June
2721:Bibcode
2615:23 June
2545:23 June
2130:Curved
2110:Curved
1101:cyclone
1089:gravity
907:plastic
896:molding
793:soluble
761:laminar
685:biofuel
670:pancake
666:pumping
548:Charles
356:Liquids
270:Statics
215:Bending
3357:
3307:
2990:
2911:
2696:
2661:
2651:
2480:spiral
2476:rubber
2437:vacuum
2356:Paddle
2222:mixing
2061:Radial
1948:beaker
1145:train.
1059:oxygen
1025:wetted
915:molten
866:, and
693:nitric
650:mixing
598:Stokes
593:Pascal
583:Navier
578:Newton
568:Graham
543:Cauchy
446:Plasma
341:
339:Mixing
334:
319:
301:
284:
272:
260:Fluids
193:Strain
188:Stress
171:linear
120:Energy
3197:(PDF)
2988:S2CID
2694:S2CID
2464:batch
2460:brand
2458:is a
2406:dough
2402:foods
2232:Other
2121:Axial
2104:45â60
2101:Axial
2090:Flat
2084:45â60
2081:Axial
2070:Flat
2033:Name
1942:, or
1630:34596
1155:or a
848:foods
810:power
806:honey
652:is a
573:Hooke
553:Euler
538:Boyle
396:Gases
3368:2018
3355:ISBN
3334:2018
3305:PMID
3274:2018
3248:2015
3138:2017
3112:2017
3086:2017
3048:2017
3022:2018
2945:2017
2909:ISBN
2888:2017
2659:ISSN
2649:ISBN
2617:2017
2591:2018
2547:2017
2454:The
2444:axes
2420:and
1842:6404
1782:1.69
1541:5.40
1019:may
955:mass
903:clay
729:The
695:and
588:Noll
558:Fick
110:Mass
95:Laws
3297:doi
3293:530
3217:doi
3205:189
3173:doi
3161:163
2980:doi
2858:doi
2833:doi
2802:doi
2756:doi
2729:doi
2686:doi
2645:110
2408:),
2124:N/A
2118:0.2
2107:3â6
2098:0.3
2087:3â6
2078:1.3
2058:4.6
1983:to
1893:186
1753:896
775:or
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3303:.
3291:.
3264:.
3215:.
3203:.
3199:.
3171:.
3159:.
3155:.
3012:.
3008:.
2986:.
2978:.
2968:15
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2962:.
2917:.
2856:.
2829:27
2827:.
2823:.
2798:29
2796:.
2779:42
2777:.
2752:37
2750:.
2727:.
2715:.
2692:.
2682:13
2680:.
2657:.
2643:.
2639:.
2625:^
2581:.
2577:.
2514:^
2416:,
2412:,
2400:,
2396:,
2388:A
2224:,
1950:.
1760:10
1741:95
1619:95
1530:95
1499:95
909:,
862:,
858:,
854:,
850:,
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714:.
648:,
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3299::
3276:.
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3088:.
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2994:.
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2804::
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1711:2
1707:)
1701:D
1698:T
1693:(
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1536:=
1447:p
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1308:p
1304:K
1300:=
1297:P
1273:5
1269:D
1263:3
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1242:=
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1210:3
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1199:N
1193:l
1190:F
1187:=
1184:Q
633:e
626:t
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343:·
336:·
326:)
321:·
315:(
303:·
286:·
274:·
69:x
66:d
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46:=
43:J
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