Multiple Particle Systems: Settling of a Suspension

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What is used to model the multiple particle system in a suspension of particles in a fluid?

Effective viscosity and average suspension density (correct)

Drag coefficient

Stokes' law

Fluid particle interaction

What does 'e' represent in the context of the suspension of particles in a fluid?

Fluid particle interaction

Voidage or volume fraction occupied by the fluid (correct)

Drag coefficient

Stokes' law

What is the drag coefficient for a single particle in the Stokes' law region?

R0/rave Urel

24me

24/Rep (correct)

(24me)/(Rep Urel rave)

What does 'Urel' represent in the context of the suspension of particles in a fluid?

Relative velocity of the particle to the fluid Signup and view all the answers

What is used to calculate the effective average suspension density for a suspension of particles in a fluid?

(erf + (1 - e)rp) Signup and view all the answers

Which law becomes modified when effective viscosity and average density are used to model a suspension of particles in a fluid?

Stokes' Law Signup and view all the answers

In hindered settling under gravity, what is the relative velocity between the particles and the fluid?

$UrelT - UT ef(e)$ Signup and view all the answers

What is the expression for the hindered settling velocity of particles relative to the vessel wall in batch settling?

$UT / (e^2*f(e))$ Signup and view all the answers

What does the effective viscosity function, f(e), represent for uniform spheres forming a suspension of solid volume fraction less than 0.1?

A function of the solid volume fraction Signup and view all the answers

What does Ufs represent in the context of a suspension of particles in a fluid?

Superficial fluid velocity Signup and view all the answers

What are the actual velocities of the fluid and the particles, Uf and Up, given by?

$Ufs * e$ and $Ups * (1 - e)$ Signup and view all the answers

What is the flow area occupied by the particles, Ap, in terms of the vessel cross-sectional area A and the solid volume fraction e?

$(1 - e)A$ Signup and view all the answers

What does UrelT represent in the context of a particle in a suspension?

$UT * ef(e)$ Signup and view all the answers

What is the expression for the terminal falling velocity for a particle in a suspension, UrelT, when considering average density, effective viscosity, particle density, gravitational acceleration, and solid volume fraction?

$(rp - rf)x^2gef(e)/(18m) Signup and view all the answers

What is the relation between flow area occupied by the fluid, Af, and vessel cross-sectional area A?

$eA$ Signup and view all the answers

What is the expression for UrelT when comparing it with UT using effective viscosity function ef(e)?

$UrelT = UT*ef(e)$ Signup and view all the answers

What is the effective viscosity of the suspension equal to?

The fluid viscosity modified by a function of the fluid volume fraction Signup and view all the answers

What does the average suspension density (rave) represent?

The voidage or volume fraction occupied by the fluid Signup and view all the answers

What does the drag coefficient (CD) represent in the context of a single particle in the Stokes' law region?

The relative velocity of the particle to the fluid Signup and view all the answers

What is used to calculate the effective average suspension density for a suspension of particles in a fluid?

Effective viscosity function f(e) Signup and view all the answers

What is the relation between CD, R0, and rave when using effective viscosity and average density to model a suspension of particles in a fluid?

$CD = R0/rave$ Signup and view all the answers

What does the voidage or volume fraction occupied by the fluid represent in the context of a suspension of particles in a fluid?

The relative velocity of the particle to the fluid Signup and view all the answers

What does the term UrelT represent in the context of a particle in a suspension?

The particle settling velocity in the presence of other particles Signup and view all the answers

What is the relation between flow area occupied by the fluid, Af, and vessel cross-sectional area A?

$Af = eA$ Signup and view all the answers

What is used to calculate the effective average suspension density for a suspension of particles in a fluid?

Effective viscosity function Signup and view all the answers

What is the drag coefficient for a single particle in the Stokes' law region?

$3.4$ Signup and view all the answers

What does 'Ufs' represent in the context of a suspension of particles in a fluid?

Superficial fluid velocity Signup and view all the answers

What does 'e' represent in the context of the suspension of particles in a fluid?

Solid volume fraction Signup and view all the answers

What are the actual velocities of the fluid and the particles, Uf and Up, given by?

$Uf = Ufs/e$, $Up = Ups/(1 - e)$ Signup and view all the answers

Which law becomes modified when effective viscosity and average density are used to model a suspension of particles in a fluid?

Stokes' law Signup and view all the answers

What does 'Up' represent in the context of batch settling?

Superficial particle velocity Signup and view all the answers

What is used to model the multiple particle system in a suspension of particles in a fluid?

Superficial velocities of the fluid and the particles Signup and view all the answers

Multiple Particle Systems: Settling of a Suspension

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Questions and Answers

What is used to model the multiple particle system in a suspension of particles in a fluid?

What does 'e' represent in the context of the suspension of particles in a fluid?

What is the drag coefficient for a single particle in the Stokes' law region?

What does 'Urel' represent in the context of the suspension of particles in a fluid?

What is used to calculate the effective average suspension density for a suspension of particles in a fluid?

Which law becomes modified when effective viscosity and average density are used to model a suspension of particles in a fluid?

In hindered settling under gravity, what is the relative velocity between the particles and the fluid?

What is the expression for the hindered settling velocity of particles relative to the vessel wall in batch settling?

What does the effective viscosity function, f(e), represent for uniform spheres forming a suspension of solid volume fraction less than 0.1?

What does Ufs represent in the context of a suspension of particles in a fluid?

What are the actual velocities of the fluid and the particles, Uf and Up, given by?

What is the flow area occupied by the particles, Ap, in terms of the vessel cross-sectional area A and the solid volume fraction e?

What does UrelT represent in the context of a particle in a suspension?

What is the expression for the terminal falling velocity for a particle in a suspension, UrelT, when considering average density, effective viscosity, particle density, gravitational acceleration, and solid volume fraction?

What is the relation between flow area occupied by the fluid, Af, and vessel cross-sectional area A?

What is the expression for UrelT when comparing it with UT using effective viscosity function ef(e)?

What is the effective viscosity of the suspension equal to?

What does the average suspension density (rave) represent?

What does the drag coefficient (CD) represent in the context of a single particle in the Stokes' law region?

What is used to calculate the effective average suspension density for a suspension of particles in a fluid?

What is the relation between CD, R0, and rave when using effective viscosity and average density to model a suspension of particles in a fluid?

What does the voidage or volume fraction occupied by the fluid represent in the context of a suspension of particles in a fluid?

What does the term UrelT represent in the context of a particle in a suspension?

What is the relation between flow area occupied by the fluid, Af, and vessel cross-sectional area A?

What is used to calculate the effective average suspension density for a suspension of particles in a fluid?

What is the drag coefficient for a single particle in the Stokes' law region?

What does 'Ufs' represent in the context of a suspension of particles in a fluid?

What does 'e' represent in the context of the suspension of particles in a fluid?

What are the actual velocities of the fluid and the particles, Uf and Up, given by?

Which law becomes modified when effective viscosity and average density are used to model a suspension of particles in a fluid?

What does 'Up' represent in the context of batch settling?

What is used to model the multiple particle system in a suspension of particles in a fluid?

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