What Is Shear Viscosity?

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The shear viscosity is a transport coefficient for momentum in inhomogeneous flows. This transport coefficient, which is widely used to describe both plasmas and fluids, relates two hydrodynamic quantities: shear stress and shear rate. The shear stress Pxy is the off-diagonal element of a pressure tensor, and the shear rate γ is the transverse gradient of the flow velocity u. For a flow in the y direction, γ=∂uy∂x. (1)The shear viscosity η relates these two hydrodynamic quantities through the constitutive relation1 Pxy=−ηγ. (2)In this paper, we will use Eq. (2) to determine the viscosity with an input of experimental measurements of Pxy and γ. In a plasma, viscosity arises from Coulomb collisions among individual charged particles. This is so for both weakly and strongly coupled plasmas, where the particles in a strongly coupled plasma have an interparticle potential energy that is larger than the thermal kinetic energy. There is a particular interest in viscosity of strongly coupled plasmas2,3 because they are dominated by Coulomb collisions. Among the many types of strongly coupled plasmas, one that is especially well suited for experiments is the dusty plasma.4–8 It consists of three familiar components of a…show more content…
The temperature dependence of viscosity can be very strong; for example, in motor oil, η can diminish ten-fold with only a 10% increase in the absolute temperature. Therefore, if temperature is not uniform but varies with position in a flow, one cannot obtain a single value for its viscosity. The other dependence of viscosity, on shear rate, is a non-Newtonian property of some fluids; this effect is called “shear thinning” if η diminishes with increasing γ.31 Shear thinning can be avoided in an experiment by applying a small shear stress, so that conditions are relatively close to

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