Expansion rate, dynamic behavior

Many surfactant solutions show dynamic surface tension behavior. That is, some time is required to establish the equilibrium surface tension. If the surface area of the solution is suddenly increased or decreased (locally), then the adsorbed surfactant layer at the interface would require some time to restore its equilibrium surface concentration by diffusion of surfactant from or to the bulk liquid. In the meantime, the original adsorbed surfactant layer is either expanded or contracted because surface tension gradients are now in effect, Gibbs—Marangoni forces arise and act in opposition to the initial disturbance. The dissipation of surface tension gradients to achieve equilibrium embodies the interface with a finite elasticity. This fact explains why some substances that lower surface tension do not stabilize foams (6) They do not have the required rate of approach to equilibrium after a surface expansion or contraction. In other words, they do not have the requisite surface elasticity. 

Here was adopted for simplicity a = A and a 1 (the latter inequality is satisfied for bubbles with Rg > >1 mkm). Phase plot of this equation is presented in Figme 7.2.2. It is seen that for k = -1 (collapsing cavity) z->Zj ast- oo rfzo>Z2. The stationary point z = Zg is unstable. The rate of the cavity collapse z = Zj in the asymptotic regime satisfies inequality Zp < Zj < 0, where Zp = -RCp is equal to the collapse rate of the cavity in a pure viscous fluid with viscosity of polymeric solution q. It means that the cavity closure in viscoelastic solution of polymer at asymptotic stage is slower than in a viscous liquid with same equilibrium viscosity. On the contrary, the expansion under the same conditions is faster at k = 1, Zp < Zj < z, where Zp = RCp and z = Re = (1 - P) RCp is the asymptotic rate of the cavity expansion in a pure solvent with the viscosity (1 - P)q. This result is ejqrlained by different behavior of the stress tensor component controlling the fluid rheology effect on the cavity dynamics, in extensional and compressional flows, respec-... 

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