Download e-book for iPad: Surface and Interfacial Tension: Measurement, Theory, and by Stanley Hartland

Nonfiction 6

By Stanley Hartland

ISBN-10: 0824750349

ISBN-13: 9780824750343

This edited quantity deals whole assurance of the newest theoretical, experimental, and computer-based information as summarized via prime foreign researchers. It promotes complete figuring out of the actual phenomena and mechanisms at paintings in floor and interfacial tensions and gradients, their direct influence on interface form and flow, and their importance to varied functions. Assessing tools for the actual dimension of floor rigidity, interfacial stress, and get in touch with angles, floor and Interfacial rigidity provides sleek simulations of complicated interfacial motions, similar to bubble movement in drinks, and authoritatively illuminates bubble nucleation and detachment.

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14 shows the right-hand sides of Eqs. 00826. The curves AB (Eq. (124)) and BC (Eq. (123)) show the lower limit of e0, below which foam collapse occurs, and curves DB (Eq. (122)) and BE (Eq. (121)) represent the upper limit for e0, beyond which the continuous phase separates. Point B corresponds to L0 = Lmax. At this point, there is no phase Copyright n 2004 by Marcel Dekker, Inc. All Rights Reserved. FIG. 14 A generalized phase diagram. separation and at equilibrium, e = eb at the bottom and e = ec at the top.

Bcs  qL À eD þ qL c s À ð2nF CAF Þ   Bz z1 V z1 ð68Þ Ã 1 dz1 Â ðnp ap l þ nF AF xF Þcs þ 2nF CAF jz1 ¼ V dt Using Eq.   Bcs  e 1þe cs þ þ qL eD ð2nF CAF Þ  ¼ 0  Bz z1 1Àe Ve z1 ð69Þ The other boundary condition is obtained from the fact that at the foam/ liquid interface, the concentration is that of the original foaming solution (cs0): cs jz2 ¼ cs0 ð70Þ The basic conservation equations for the continuous-phase liquid and the surfactant have now been formulated. However, several additional details are required to specify the system completely.

1 À eb 1 1 À eb e0 > P tanÀ1 À tanÀ1 þ for L0 < Lmax eb eb P " e0 > P tanÀ1 sffiffiffiffiffiffiffiffiffiffiffiffiffi! rffiffiffiffiffiffiffiffiffiffiffiffiffi# 1 À ec 1 À eb for L0 > Lmax À tanÀ1 ec eb ð121Þ ð122Þ Dispersed phase gas separates when: sffiffiffiffiffiffiffiffiffiffiffiffiffi! # 1 À ec 1 À ec 1 À1 À1 for L0 < Lmax e0 < P tan À tan À ec ec P ð123Þ sffiffiffiffiffiffiffiffiffiffiffiffiffi! "sffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffi r ffiffiffiffiffiffiffiffiffiffiffiffiffi  # 1 À ec 1 À eb 1 À ec 1 À eb À1 À1 e0 < 1 À P À þ tan À tan ec eb ec eb for L0 > Lmax ð124Þ It can be seen from Eqs. (121)–(124) that for a given e0, the occurrence of phase separation is determined entirely by the value of P.

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Surface and Interfacial Tension: Measurement, Theory, and Applications (Surfactant Science) by Stanley Hartland

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