Capillary Wave Motion by Insoluble Surfactants

DAMPING OF CAPILLARY WAVE MOTION BY INSOLUBLE SURFACTANTS 

Mass transfer across a fluid interface is enhanced by convection in the vicinity of the interface. One source of such convection is wave motion. An increase in the rate of damping of waves can thus be expected to reduce mass transfer rates. As we shall now show, surfactants can cause a significant increase in the damping of capillary waves at a liquid-gas interface. 

We consider the simplest case of an insoluble surfactant. In the initial motionless state with a flat interface, the surfactant is uniformly distributed and interfacial tension is uniform. During wave motion, the local concentration of surfactant varies with position along the interface, with the result that interfacial tension gradients arise. Because these gradients influence the interfacial momentum 

The solution of the equations of motion and application of the boundary conditions proceeds as before except for an additional term (dy/dx) on the right side of Equation 5.38. If fluid B is a gas, we obtain instead of Equations 5.44 and 5.45  

The general boundary condition for conservation of mass of some species in the interfacial region is derived in Chapter 6. For the present case of an insoluble surfactant, and in the absence of surface diffusion, we anticipate that the first two terms of Equation 5.32 should suffice with T replaced by A  

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