Interfacial Film Model

The filtering media of the WaterWall® process is preferentially wetted by the continuous water phase, therefore supporting a liquid-liquid interfacial film acting as a barrier against the passage of the dispersed oily phase: this mechanism is similar to the principle of liquid-liquid separation by porous membranes, but no external pressure gradient is imposed across the filter, and no micro-scale capillaries are present.

This fact is clearly demonstrated by the high flow rate of the water that passes through the two phase filtering media.

As a matter of fact, the flow rate in the system under review does not follow the basic law of the capillary flow.

This can be explained with the onset of an additional liquid-liquid interfacial tension originating from the molecular and/or electrostatic mutual interaction between water/filtering media and oil. This additional interface tension must be function of the interfacial tension existing between the non-miscible liquids(oil and water), and of the radius of the oil droplet moving towards the interfacial film. The resulting expression is:
where the constant C has the dimensions of the inverse of a length and it is characteristic for every type of media; its value is determined experimentally.

An oil droplet reaching the surface of the two phase media will therefore pass through it if the force due to the additional interfacial tension is less than the force necessary to revert the droplet momentum. The pressure force exerted by the droplet on the layer surface, due to its dynamic pressure, is
where is the largest between the droplet radius and the mean distance between fibres in the two phase filtering media, to account for entrainment of smaller droplets and for different density of fibres in the filtering layer.

The surface tension force resulting from (1) is
The incident oil droplet is therefore rejected by the filter surface if the condition is satisfied.

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