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. 2022 Sep 17;14(18):3880. doi: 10.3390/polym14183880
V arbitrary volume of suspension, [m3]
Vf volume of fluid part in arbitrary volume V, [m3]
Vp volume of dry particles in arbitrary volume V, [m3]
VM volume of mud in arbitrary volume V, [m3]
Vs =Vp+VM volume of solid phase in arbitrary volume V, [m3]
mf mass of fluid in arbitrary volume V, [kg]
mp mass of dry particles in arbitrary volume V, [kg]
mM mass of mud in arbitrary volume V, [kg]
ms =mp+mM mass of solid phase in arbitrary volume V, [kg]
m =mf+mp+mM mass of arbitrary suspension volume V, [kg]
c =mpm mass concentration of particles, dimensionless
ρ¯f fluid density, kgm3
ρ¯p density of dry particles, kgm3
ρ¯M mud density, kgm3
ϕf volume fraction of fluid, dimensionless
ϕp volume fraction of dry particles, dimensionless
ϕM volume fraction of mud, dimensionless
ϕs =ϕp+ϕM volume fraction of solid phase, dimensionless
ρf =ϕfρ¯f partial fluid density, kgm3
ρp =ϕpρ¯p partial particle density, kgm3
ρM =ϕMρ¯M partial mud density, kgm3
ρs =ρp+ρM partial density of solid phase, kgm3
ρ =ρf+ρp+ρM total density kgm3
ρ¯s =ρsϕs, density of the solid phase, kgm3
R0 =ρ¯sρ¯f, ratio of densities, dimensionless
g gravitational acceleration, 980cms2
p pressure, [Pa]
vf velocity of fluid phase, ms
vs velocity of solid phase, ms
u =vsvf difference of velocities, ms
v =ϕfvf+ϕsvs mean volume velocity, ms
v˜ =(1c)vf+cvs mean mass velocity, ms
Tf viscous part of stress tensor of fluid phase, [Pa]
Ts viscous part of stress tensor of solid phase, [Pa]
D rate of strain tensor, [s1]
Dd deviatoric part of D, [s1]
I          identity matrix, dimensionless