Plate-and-frame filter press hydraulics: the filtrate flow through the cake predominantly follows which flow regime?

Introduction / Context:
In pressure filtration of slurries using plate-and-frame presses, flow through the porous cake is typically slow and highly resistive. Identifying the flow regime informs the correct use of Darcy’s law.

Concept / Approach:
Darcy’s law assumes creeping (laminar) flow through a porous medium. Filtration velocities are small and pore Reynolds numbers are well below the transition threshold, so inertial effects are negligible and turbulence does not occur inside the cake.

Step-by-Step Solution:
Model cake as porous medium.Apply Darcy’s law: ΔP = μ * (α M/A) * v.Conclude laminar regime dominates inside the cake.

Why Other Options Are Wrong:
Turbulent: pore scales and velocities are too small.Plug flow: refers to reactor axial profiles, not porous-medium microflow.

Final Answer:
Laminar flow