By Henry Hazlitt

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The terms inside the parentheses represent the driving forces due to gravity (qg) and the gradient of Plateau border suction B/Bz(r/rp). , when the liquid fraction (and hence rp) is smaller at the top). Leonard and Lemlich [21] were the ﬁrst to consider the eﬀects of surface viscosity on drainage in a Plateau border channel. However, Eq. (36), which diﬀers from their equation only by a constant factor, has been used more frequently because Desai and Kumar have provided a very simple equation for cv.

Between z = 0 and z = z1), a mass balance for the bubbling gas can be written as: Z d GA ¼ dt z2 Að1 À eÞdz þ A z1 dz1 dt ð125Þ In Eq.

Each is discussed separately. (a) Case 1: Separation of the Continuous Phase. Let us deﬁne a critical volume: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ! rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ r 1 À eb KUgR0 L0 1 À eb À1 À1 Vc u tan þ ð107Þ À tan eb r eb KUgR0 A comparison with Eq. (98) indicates that Vc is the volume of the continuous phase per unit cross-section in an equilibrated foam when z1e = 0 and z2e = L0 (see Fig. 10). Thus, if e0L0 = Vc, the continuous phase will redistribute itself until an equilibrium is established with eAz¼z2 ¼ eb.