Question

The ................. law is useful in developing a relationship between the flux through membrane and the pressure differential across it.

• A. Hagen‐Poiseuille
• B. Boyl’s
• C. Rittenger’s
• D. Van’t Hoff

Hint:

Flux ($J$) = Permeability $\times$ Driving Force ($\Delta P$). The permeability constant is derived using the geometry of the Hagen-Poiseuille model.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the fundamental physical law that relates fluid flux (flow rate per unit area) to the pressure driving force in a membrane system.

Step 2: Detailed Explanation:

• Membrane filtration involves the flow of a liquid through a porous structure. The rate at which the liquid permeates the membrane is called the flux (\(J\)).

• For porous membranes (like MF and UF), the structure can be modeled as a collection of cylindrical capillaries.

• The Hagen-Poiseuille Law describes the laminar flow of an incompressible fluid through a long cylindrical pipe: \[ Q = \frac{\pi \cdot r^4 \cdot \Delta P}{8 \cdot \mu \cdot L} \] Where \(Q\) is flow rate, \(r\) is radius, \(\Delta P\) is pressure drop, \(\mu\) is viscosity, and \(L\) is length.

• Dividing the flow rate by the surface area of the membrane gives the flux (\(J\)). This provides the direct mathematical relationship: Flux is proportional to the pressure differential (\(\Delta P\)) and inversely proportional to the viscosity.

• Van’t Hoff’s law relates to osmotic pressure, which is more relevant to RO and NF but describes the pressure limit rather than the hydraulic flow relationship. Boyle’s law is for gases. Rittinger’s law is for size reduction.

• Therefore, Hagen-Poiseuille is the basis for describing flux through porous membrane media.

Step 3: Final Answer:
The Hagen-Poiseuille law relates membrane flux to pressure differential.