The behavior of suspensions and macromolecular solutions in crossflow microfiltration

https://hal.archives-ouvertes.fr/hal-00201119/document

Critical and sustainable fluxes: Theory, experiments and applications

Spacer characterization and pressure drop modelling in spacer-filled channels for ultrafiltration

A novel theory is developed for concentration polarization of non-interacting particles in crossflow-filtration systems. This theory reveals that the extent of concentration polarization, as well as the behaviour of the permeate flux, are characterized by an important dimensionless filtration number (NF= 4πa3pΔP/3kT). There is a critical value of the filtration number for a given suspension and operational conditions. When the filtration number is smaller than the critical value, a polarization layer exists directly over the membrane surface and the wall particle concentration is determined by the pressure and temperature. At higher filtration numbers, a cake layer of retained particles forms between the polarization layer and the membrane surface. Mathematical models are constructed for both cases and analytical solutions for the permeate flux are derived. An increase in permeate flux with increasing pressure is predicted for all operational conditions.

Theory of concentration polarization in crossflow filtration

KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel

The Navier‐Stokes equations have been solved to obtain a complete description of the fluid flow in a channel having a rectangular cross section and two equally porous walls. The scope has been limited to two‐dimensional incompressible steady‐state laminar flow.The solution of the flow equations leads to detailed expressions for the dependence of the velocity components and the pressure on position coordinates, channel dimensions, and fluid properties.

Laminar Flow in Channels with Porous Walls

When certain restrictions are applied to the radial component of flow it is possible to obtain an exact solution to the Navier‐Stokes equations describing the steady‐state flow of an incompressible fluid in an annulus having porous walls. The effects of such restricted radial flows on the characteristics of the flow field have been examined.

Laminar Flow in an Annulus with Porous Walls

Concerning Laminar Flow in Channels with Porous Walls

Free Molecule Flow in an Annulus

The free molecule flow through a long tube rotating about its axis is investigated. For a given density difference across the tube ends the mass flow through the rotating tube is less than that through a stationary tube. For low rotation speed the decrease in mass flow is proportional to the square of the angular velocity while for high speed the mass flow is proportional to the reciprocal of the square of the angular velocity. Radial molecular density and molecular flux distributions are also obtained.

Abraham S. Berman

Papers

Laminar Flow in Channels with Porous Walls

Laminar Flow in an Annulus with Porous Walls

Concerning Laminar Flow in Channels with Porous Walls

Free Molecule Flow in an Annulus

Free Molecule Flow Through a Long Rotating Tube