Viscous Behavior of Two-Dimensional Phases

Our discussion of two-dimensional phases has drawn heavily on the analogy between bulk and surface behavior. This analogous behavior is not restricted to thermodynamic observations, but extends to other areas also. The viscosity of surface monolayers is an excellent example of this. To illustrate the parallel between bulk and surface viscosity, let us retrace some of the introductory notions of Chapter 4, restricting the flow to the surface region. 

Next let us consider how surface viscosities can be measured. A variety of methods for measuring rjs exist, including a method based on concentric rings, the two-dimensional equivalent of the concentric cylinder viscometer. We limit our discussion to the analog of the 

Integrating Equation (26) and using the nonslip condition at the wall (v = 0 at r = h) to evaluate the constant of integration yields 

The rate of emergence of area, A/t, of the monolayer from the channel is twice the integral of vdr between r = 0 and r = h  

This is the two-dimensional equivalent of Poiseuille s equation. All of the other quantities besides 175 in Equation (28) are measurable, so 17s can be evaluated by measuring the rate at which the monolayer flows through the channel. In practice, a second barrier is moved along in front of the advancing interface to maintain a constant film pressure for an insoluble monolayer. 

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