Microscopic origin of viscosity

The phenomenon of viscosity is related to the transport of momentum between contiguous layers of fluid, moving at different velocities. 

In order to illustrate this assertion it is convenient to consider a particular motion in which a liquid between two flat parallel plates is moved under the action of one of the plates. This mobile plate moves at a constant velocity in the x direction. For this simple shearing motion the layers of the fluid slide on each other. The fluid has a constant velocity at every altitude z. The velocity has components [w(z), 0, Oj relative to the orthogonal rectilinear axes. 

Two kinds of coupling between adjoining layers cause the exchange of momentum between them (i) intermolecular forces between the particles are the origin of a 

For a gas, only the latter effect should be expected to be important. Although we are rather concerned here with the case of liquids, the consideration of gases is very instructive so as to highlight the microscopic origin of viscosity. Besides, gases and liquids are very similar in that their velocity distributions are both Maxwellian at equilibrium (local equilihrium in a layer). 

The assumption is made that the particles at distances of the order of L from the interface carry their horizontal momentum into the contiguous layer, before they experience a new collision with the surrounding particles, by which they transfer their excess of momentum. Then the horizontal momentum transfer downwards in a time Ai is 

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In this section, we will examine the microscopic origins of viscosity for each material type, and we will see how viscosity is much more complex than simply serving as a proportionality constant in Eq. (4.3). Ultimately, we will find that viscosity is not a constant at all, but a complex function of temperature, shear rate, and composition, among other things. 

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