Theories & Factors influencing filtration

Theories of Filtration

1) Poiseuille's Equation:

• Poiseuille's equation describes the laminar flow of a fluid through a cylindrical pipe, often applied to describe the flow through the pores of a filter medium.

• Where:

  • Q = flow rate

  • r = radius of the pore

  • ΔP = pressure drop across the filter

  • η = viscosity of the fluid

  • L = length of the pore

2) Darcy's Equation:

• Darcy's equation describes the flow of a fluid through a porous medium, useful for understanding filtration through filter cakes and media.

• Where:

  • Q = flow rate

  • k = permeability of the medium

  • A = cross-sectional area

  • ΔP = pressure drop across the medium

  • η = viscosity of the fluid

  • L = thickness of the medium

3) Carman-Kozeny Equation:

• The Carman-Kozeny equation is an extension of Darcy's law that takes into account the characteristics of the filter cake, such as particle size and porosity.

• Where:

  • ΔP = pressure drop

  • L = thickness of the filter cake

  • η = viscosity of the fluid

  • ϵ = porosity of the cake

  • dp = diameter of the particles

  • v = superficial velocity of the fluid

Factors Influencing Filtration

1. Particle Size and Distribution: Larger particles are generally easier to filter, while a wide size distribution can complicate the process.

2. Filter Medium Properties: Pore size, surface area, and material of the filter medium affect the efficiency and type of filtration.

3. Flow Rate: Higher flow rates can lead to lower filtration efficiency as particles may pass through the filter medium.

4. Viscosity of the Fluid: Higher viscosity fluids are harder to filter.

5. Temperature: Temperature can affect fluid viscosity and the properties of the filter medium.

6. Pressure Drop: The difference in pressure across the filter medium influences the filtration rate.

7. Solid Concentration: Higher solid concentrations can lead to faster clogging of the filter medium.