Cake filtration is a process where solids are separated from a fluid by passing the mixture through a filter medium, upon which the solids deposit to form a 'cake'. The process is governed by Darcy's Law, adapted for filtration.

The fundamental equation for constant pressure filtration relates the time of filtration (t) to the volume of filtrate collected (V):

This is a linear relationship where:

• t / V is the specific filtration time.
• V is the cumulative filtrate volume.
• Kₚ is the specific cake constant, representing resistance due to the cake itself.
• B is the filter medium constant, representing the initial resistance of the filter cloth/medium.

These constants are defined by the following formulas:

Where:

• t = Filtration Time (s)
• V = Filtrate Volume (m³)
• ΔP = Pressure Drop (Pa)
• μ = Filtrate Viscosity (Pa·s)
• A = Filter Area (m²)
• α = Specific Cake Resistance (m/kg)
• c = Mass of solids per volume of filtrate (kg/m³)
• Rₘ = Filter Medium Resistance (m⁻¹)