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Critical review of different aspects of liquid-solid mixing operations

  • Prakash Mishra and Farhad Ein-Mozaffari EMAIL logo
Published/Copyright: January 11, 2019
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Abstract

Mechanically stirred slurry tanks are utilized in several industries to perform various unit operations such as crystallization, adsorption, ion-exchange, suspensions polymerization, dispersion of solid particles, leaching and dissolution, and activated sludge processes. The major goal of this review paper is to critically and thoroughly analyse the different aspects of previous research works reported in the literature in the field of liquid-solid mixing. This paper sheds light on the advantages and limitations of various particle concentration measurement methods employed to assess the suspension quality and the extent of solid suspensions in slurry reactors. Attempts are being made to identify and compare various mathematical models and methods to quantify particle dispersion and distribution in slurry reactors. It has been shown that various factors such as geometric configurations, agitation conditions, and physical characteristics of liquid and solid have pronounced influence on local suspension quality and power consumption. Computational fluid dynamics (CFD) modeling can be extremely useful in assessing the suspension of solid particles in slurry tanks. A critical review of different scale-up procedures employed for solid suspension and distribution in liquid-solid systems is presented as well. The findings of this review paper can be useful for future research works in liquid-solid mixing.

Award Identifier / Grant number: RGPIN-2014-03957

Funding statement: The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (Funder Id: 10.13039/501100000038, grant number: RGPIN-2014-03957) is gratefully acknowledged.

Nomenclature

A

constant [Eq. (3)], dimensionless

a

constant [Eq. (11)], dimensionless

Ar

Archimedes number, dimensionless

A

constant [Eq. (12)], dimensionless

Bo

particle concentration percent, dimensionless

b

constant [Eq. (11)], dimensionless

C

impeller clearance, m

CD

drag coefficient, dimensionless

CDo

drag coefficient at stagnant medium, dimensionless

CH

cloud height, m

Cp

constant [Eq. (29)], dimensionless

Cv

solid volume fraction, dimensionless

D

impeller (stirrer) diameter, m

De.p

solid dispersion coefficient, dimensionless

DL

impeller diameter in large-scale vessel, m

Dr

relative impeller diameter, dimensionless

Ds

impeller diameter in small-scale vessel, m

dp

solid particle diameter, μm

Fr*

constant modified Froude number, dimensionless

g

gravitational acceleration, m/s2

h

slurry height, m

K

constant [Eq. (25)], dimensionless

Ksl

solid-liquid exchange coefficient, dimensionless

k

kinetic energy due to turbulence, m2s2

MIo

overall mixing index [Eq. (21), (24)], dimensionless

MIr

radial mixing index [Eq. (20), (23)], dimensionless

MIz

mixing index [Eq. (19), (22)], dimensionless

N

impeller (stirrer) speed, s−1

Njs

just suspended agitation speed, s−1

NRSD

stirrer speed at relative standard deviation, s−1

NL

stirrer speed of large-scale vessel, s−1

Np

power number, dimensionless

Nps

power number for slurry, dimensionless

Nr

relative impeller speed, dimensionless

NS

stirrer speed of small-scale vessel, s−1

m

mixing time, dimensionless

n

number of pixels on selected plane

np

power-law index, dimensionless

ns

number of sampling positions, dimensionless

P

power, W

p

total number of pixels

Pe

Peclet number, dimensionless

Pe*

modified Peclet number, dimensionless

Po

power number, dimensionless

Rep

particle Reynolds number, dimensionless

q

number of sensor planes

r

number of rings

S

Zwietering constant, dimensionless

T

mixing tank diameter, m

Uto

terminal velocity at stagnant medium, m/s

Utt

terminal velocity at turbulent medium, m/s

Vt

terminal settling velocity, m/s

vs

solid-phase velocity vector, m/s

vl

liquid-phase velocity vector, m/s

X

mass ratio, dimensionless

Xq¯

average solid volume fraction in plane q, dimensionless

Xr¯

average solid volume fraction in ring r, dimensionless

Xr,q

average solid volume fraction in ring r and plane q, dimensionless

Xr,q¯

total average of all Xr,q values, dimensionless

Xv

solid volume fraction, dimensionless

Xvb

particle bed volumetric concentration, dimensionless

Xv¯

average solid volume fraction, dimensionless

x

amplification exponent, dimensionless

Z

slurry height, m

z

constant [Eq. (13)], dimensionless

Greek letters
α

constant [Eq. (4)], dimensionless

αi

local particle concentration, dimensionless

αavg

average solid volume fraction, dimensionless

αp

particle phase volume fraction, dimensionless

αl

liquid phase volume fraction, dimensionless

β

constant [Eq. (4)], dimensionless

θ

constant [Eq. (11)], dimensionless

θm

mixing time, s

μl

liquid viscosity, N s/m2

υ

kinematic viscosity of the fluid, m2/s

ε

dissipation rate of turbulence, m2/s3

λ

Kolmogoroff length scale, m

ηr,γ

constant-shear-rate relative viscosity, dimensionless

ρl

fluid density, kg/m3

ρs

density of solid particle, kg/m3

ρsl

density of slurry, kg/m3

Δρ

difference in density between solid and liquid phase, kg/m3

ϕ

particle volume fraction, dimensionless

ϕm

maximum particle volume fraction, dimensionless

σ̅

mean conductivity value over whole selected volume, mS/cm

σk

conductivity in each pixel, mS/cm

σl

conductivity of the continuous (liquid) phase, mS/cm

σ̅i

average conductivity on the selected plane, mS/cm

σmc

conductivity of the slurry, mS/cm

ω

angular velocity, rad/s

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Received: 2018-03-29
Accepted: 2018-10-08
Published Online: 2019-01-11
Published in Print: 2020-07-28

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