The name is absent

Chapter 3

If we assume that the water fraction in each layer does not change during
sedimentation, the sedimentation velocity within the emulsion can be obtained by
applying a mass balance across the sedimentation front. If there is negligible
sedimentation in the concentrated emulsion with volume fraction φ_max, the
sedimentation velocity of water droplets in emulsion above the front is given by:

‰_er = ^^max~^^e^∙                        (Iowerfront)             [3.40]

<P_e dt

In sample 3 (no solids, no PR₅, Figure 3.16) a sharp front moving upward
from the bottom is less evident. However, a front moving downward from the top
of sample 3 (though less clearly in sample 1 ) can be seen with nearly water-free
oil above and emulsion below (Figure 3.23). A similar mass balance yields:

⅛ =          =                     (upper front)             [3.41]

φ_e at dt

In these equations h is front position, v∣_0wer and v_upper are the sedimentation
velocity of water droplets in the emulsion, whose volume fraction φ_e is assumed
as 0.50. The average water fraction in the concentrated emulsion layer 0.75 can
be used as the φ_max value, and the average water fraction in the clean oil layer
φ_min is close to zero.

The predicted sedimentation velocity of the emulsion can be calculated with
the following equation, which is an empirical modification of Stokes Law:^{[19L [20]}

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