Centrifugal filtration principle: in a rotating basket or disc centrifuge used for filtration, which physical quantity actually provides the driving force for liquid flow through the cake and medium?

Introduction / Context:
Centrifuges accelerate phase separation by imposing very high body forces. In filtration mode, liquid is driven through the porous cake and filter medium by a pressure difference generated by rotation. Understanding the exact driving force helps in scaling and troubleshooting.

Given Data / Assumptions:

• Centrifugal acceleration a = ω^2 * r.
• Pressure head ΔP produced in the liquid column scales with density * a * radial height.
• Cake structure modulates resistance but does not create the driving force.

Concept / Approach:
Rotational speed contributes to acceleration, but the effective driver is the centrifugal pressure gradient. Darcy-type relations still apply: filtrate flow ∝ ΔP / resistance. Thus, ΔP is the centrifugal pressure exerted by the rotating liquid mass.

Step-by-Step Solution:
Relate speed to acceleration and then to pressure: ΔP = ρ * ω^2 * (r_out^2 − r_in^2) / 2 for a rotating liquid layer.Recognize that cake porosity reduces resistance but does not provide ΔP.Select “centrifugal pressure” as the correct driving force.

Verification / Alternative check:
Scale-up equations for basket and peeler centrifuges explicitly feature centrifugal pressure terms rather than speed alone.

Why Other Options Are Wrong:
Rotational speed alone: speed creates acceleration; only the resulting pressure drives flow.Narrow diameter: geometry may affect ΔP via radius, but diameter itself is not the driving force.Porous cake: beneficial for permeability, not the source of ΔP.

Common Pitfalls:
Confusing operating variable (rpm) with the thermodynamic driving force (pressure). Proper analysis must track the full chain rpm → acceleration → pressure difference → flow.

Final Answer:
Centrifugal pressure exerted by the liquid