Editing Mixing (process engineering) (section)

===Solid suspension===
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 associated [[eddy diffusion]] 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 [[boundary layer]], 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.<ref>{{cite web |url=http://www.bakker.org/cfm/webdoc4.htm |title=Stirred Vessels |publisher=Bakker.org |date=1998-04-10 |access-date=2017-06-23 |url-status=live |archive-url=https://web.archive.org/web/20170814175734/http://www.bakker.org/cfm/webdoc4.htm |archive-date=14 August 2017 |df=dmy-all }}</ref>[[File:Rsd - Copie.jpg|thumb|Solid volume fraction in a mixing tank <ref name=":0" />]]

The degree of homogeneity of a solid-liquid suspension can be described by the RSD ([[Relative standard deviation|Relative Standard Deviation]] 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,<ref>{{cite journal|last=Tamburini|first=A.|date=2012|title= CFD Predictions of Sufficient Suspension Conditions in Solid-Liquid Agitated Tanks |journal= International Journal of Nonlinear Sciences and Numerical Simulation |volume=13|issue=6|pages=427–443 |doi=10.1515/ijnsns-2012-0027|s2cid=125170997}}</ref> although this is case-dependent. The RSD can be obtained by experimental measurements 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 [[computational fluid dynamics]] software or by using [[correlation]]s 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 to use but are less accurate and don't cover any possible designs. The most popular correlation is the ‘just suspended speed’ correlation published by Zwietering (1958).<ref>{{cite journal|last=Zwietering|first=T.N.|date=1958|title= Suspending of solid particles in liquid by agitators |journal= Chemical Engineering Science |volume=8|issue=3–4|pages=244–253|doi=10.1016/0009-2509(58)85031-9|bibcode=1958ChEnS...8..244Z }}</ref> 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 ‘bad’ 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).<ref>{{Cite journal |last=Mersmann |first=A. |date=1998 |title=Theoretical prediction of the minimum stirrer speed in mechanically agitated suspensions |journal=Chem. Eng. Process. |volume=37|issue=6 |pages=503–510 |doi=10.1016/S0255-2701(98)00057-9 }}</ref> For ‘good’ quality suspensions, some examples of useful correlations can be found in the publications of Barresi (1987),<ref>{{cite journal|last=Barresi|first=A.|date=1987|title= Solid dispersion in an agitated vessel |journal= Chemical Engineering Science |volume=42}}</ref> Magelli (1991),<ref>{{cite journal|last=Magelli|first=F.|date=1991|title= Solids Concentration Distribution in Slurry Reactors Stirred with Multiple Axial Impeller|journal= Chem. Eng. Process. |volume=29|pages=27–32|doi=10.1016/0255-2701(91)87003-L}}</ref> Cekinski (2010) <ref>{{cite journal|last=Cekinski|first=E.|date=2010|title= A new approach to characterize suspensions in stirred vessels based on computational fluid dynamics |journal= Brazilian Journal of Chemical Engineering |volume=27|issue=2|pages=265–273|doi=10.1590/S0104-66322010000200005|doi-access=free}}</ref> or Macqueron (2017).<ref name=":0" /> [[Machine learning]] can also be used to build models way more accurate than "classical" correlations.<ref name=":0">{{Cite journal |last=Macqueron |first=Corentin |date=2017 |title=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 |url=https://www.researchgate.net/publication/318532121 |journal=Récents Progrès en Génie des Procédés |publisher=SFGP - Société Française de Génie des Procédés |volume=110 |isbn=978-2-910239-85-5 |issn=1775-335X}}</ref><ref>{{cite journal|last=Macqueron|first=C.|date=2018|title= Solid-Liquid Mixing in Stirred Vessels: Numerical Simulation, Experimental Validation and Suspension Quality Prediction Using Multivariate Regression and Machine Learning |journal= ResearchGate |doi=10.13140/RG.2.2.11074.84164/1}}</ref>