Membrane separation of liquid-like droplets

Liquid (like) droplets may be separated from the continuous phase in which they are dispersed by employing a membrane. Because droplets are deformable, the separation is not simply based on size; droplets may deform sufficiently to enter pores that are much smaller than the droplets themselves. Such a deformation requires a certain critical pressure drop, Δpc. Assuming the geometry of the droplet is determined by a natural tendency for a minimum surface area, Δpc can be shown to depend on the surface tension γ, the contact angle θ, and the ratio a of the radii of droplet and pore, rd and rp, respectively. When 100% retention is required, Δpc should not be exceeded and, hence, this pressure drop corresponds to the highest attainable (critical) flux Nc. An almost linear increase is predicted for Δpc with a. Despite the monotone increase of Δpc, the critical flux Nc shows a maximum at a≈−2/cos(θ). Hence, on the basis of a and θ an optimal membrane selection can be made. In the absence of affinity (θ=π), the pore radius should be approximately two times larger then the initial droplet radius. When affinity is not negligible, the pore radius required to maintain complete retention increases rapidly, i.e., the maximum critical flux decreases and is observed at larger a. The largest change in maximum attainable Nc with the contact angle is observed at θ=0.75 π.