Gravitational Sedimentation of a Bidisperse Emulsion in an Electric Field

Gravitational Sedimentation of a Bidisperse Emulsion in an Electric Field 

Substituting into (13.44) the expression (13.16) for collision cross section G and introducing dimensionless variables t = 0.024eEQWt/n/2g, k = R2/R1, we obtain 

At T CO, the ratio W2/W — 0, and the characteristic time Xa during which large drops pick out small ones, decreases with the increase of ko. It means that the smaller the size difference between the two kinds of drops, the faster the drops of kind 1 will pick out drops of kind 2. 

Consider now a bidisperse emulsion, distributed uniformly in a layer between parallel horizontal planes z = 0 and z = H at the initial moment. The vertical z-axis is directed parallel to gravity. The initial volume concentrations of drops are small (Wio 1 and W20 1), so the hindered character of sedimentation can be neglected. After a certain time, all large drops of kind 1 will settle. We can select a column of a unit cross section in the emulsion volume and ask how many small drops will remain inside this column. A similar problem is of interest in laboratory studies on how the electric field affects the emulsion sedimentation rate. 

Denote by C2 (z) the volume concentration of drops of kind 2 that will remain in the cross-sectional layer at height z after the large drops that were initially in the layer above z pass through the layer z. The sedimentation rate of small drops is much lower than that of large ones, therefore for simplicity s sake, we can assume that there is no settling of small drops. Then after the sedimentation of large drops in the layer 0 z H is completed, the ratio of the volume of remaining drops to the total initial volume of drops will be equal to 

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