Theories & Factors influencing filtration

Theories & Factors influencing filtration

• Factors influencing filtration revolve around separating solid particles from liquid or gas using a porous medium

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.
• $Q = \frac{\pi r^4 \Delta P}{8 \eta L}$
• 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

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.

$Q = \frac{kA \Delta P}{\eta L}$

• 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

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.
• $
  \frac{\Delta P}{L} = \frac{180 \, \eta \, (1 – \varepsilon)^2}{d_p^2 \, \varepsilon^3} \cdot v
  $
• Where:
  • ΔP = pressure drop
  • L = thickness of the filter cake
  • η = viscosity of the fluid
  • ϵ = porosity of the cake
  • d_p​ = 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.

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