How to Calculate and Solve for Sedimentation of Concentrated Suspension | Rheology

The image above represents sedimentation of concentrated suspension.

To compute for sedimentation of concentrated suspension, five essential parameters are needed and these parameters are Change in Density between the Dispersed and Continuous Phase of the Suspension (ΔP), Acceleration due to Gravity (g), Particle Radius (a), Viscosity of Continuous Phase (η) and Solid Landing (φ).

The formula for calculating sedimentation of concentrated suspension:

v = 2ΔPga2 / (1 – φ)5 ± 0.25

Where:

v = Sedimentation of Concentrated Suspension
ΔP = Change in Density between the Dispersed and Continuous Phase of the Suspension
g = Acceleration due to Gravity
η = Viscosity of Continuous Phase
φ = Solid Landing

Let’s solve an example;
Find the sedimentation of concentrated suspension when the change in density between the dispersed and continuous phase of the suspension is 20, the acceleration due to gravity is 12, the particle radius is 32, the viscosity of continuous phase is 14 and the solid landing is 0.

This implies that;

ΔP = Change in Density between the Dispersed and Continuous Phase of the Suspension = 20
g = Acceleration due to Gravity = 12
a = Particle Radius = 32
η = Viscosity of Continuous Phase = 14
φ = Solid Landing = 0

v = 2ΔPga2 / (1 – φ)5 ± 0.25
v = 2 x 20 x 12 x 322 / 9 x 14 x (1 – 0)5 + 0.25
v = 2 x 20 x 12 x 1024 / 126 x (1)5.25
v = 491520 / 126 x 1
v = 3900.95 x 1
v = 3900.95

Therefore, the sedimentation of concentrated suspension is 3900.95.

How to Calculate and Solve for Sedimentation of Dilute Suspension | Rheology

The image above represents sedimentation of dilute suspension.

To compute for sedimentation of dilute suspension, four essential parameters are needed and these parameters are Change in Density between the Dispersed and Continuous Phase of the Suspension (ΔP), Acceleration due to Gravity (g), Particle Radius (a) and Viscosity of Continuous Phase (η).

The formula for calculating sedimentation of dilute suspension:

v = 2ΔPga2 /

Where:

v = Sedimentation of Dilute Suspension
ΔP = Change in Density between the Dispersed and Continuous Phase of the Suspension
g = Acceleration due to Gravity
η = Viscosity of Continuous Phase

Let’s solve an example;
Find the sedimentation of dilute suspension when the change in density between the dispersed and continuous phase of the suspension is 10, the acceleration due to gravity is 9.8, particle radius is 22 and the viscosity of continuous phase is 11.

This implies that;

ΔP = Change in Density between the Dispersed and Continuous Phase of the Suspension = 10
g = Acceleration due to Gravity = 9.8
a = Particle Radius = 22
η = Viscosity of Continuous Phase = 11

v = 2ΔPga2 /
v = 2 x 10 x 9.8 x 222 / 9 x 11
v = 2 x 10 x 9.8 x 484 / 99
v = 94864 / 99
v = 958.2

Therefore, the sedimentation of dilute suspension is 958.2.

How to Calculate and Solve for Relative Apparent Viscosity | Rheology

The image above represents relative apparent viscosity.

To compute for relative apparent viscosity, two essential parameters are needed and these parameters are Viscosity of Non-Newtonian Fluid (ηa) and Viscosity of Continuous Phase (ηc).

The formula for calculating relative apparent viscosity:

ηra = ηa / ηc

Where:

ηra = Relative Apparent Viscosity
ηa = Viscosity of Non-Newtonian Fluid
ηc = Viscosity of Continuous Phase

Let’s solve an example;
Find the relative apparent viscosity when the viscosity of non-newtonian fluids is 44 and the viscosity of continuous phase is 11.

This implies that;

ηa = Viscosity of Non-Newtonian Fluid = 44
ηc = Viscosity of Continuous Phase = 11

ηra = ηa / ηc
ηra = 44 / 11
ηra = 4

Therefore, the relative apparent viscosity is 4.

Calculating for Viscosity of Non-Newtonian Fluids when the Relative Apparent Viscosity and the Viscosity of Continuous Phase is Given.

ηa = ηra x ηc

Where;

ηa = Viscosity of Non-Newtonian Fluid
ηra = Relative Apparent Viscosity
ηc = Viscosity of Continuous Phase

Let’s solve an example;
Find the viscosity of non-newtonian fluid when the relative apparent viscosity is 16 and the viscosity of continuous phase is 8.

This implies that;

ηra = Relative Apparent Viscosity = 16
ηc = Viscosity of Continuous Phase = 8

ηa = ηra x ηc
ηa = 16 x 8
ηa = 128

Therefore, the viscosity of non-newtonian fluid is 128.