Planar Couette geometry

Equation [213] can be equivalently obtained using the Mori-Zwanzig formalism. " It is also seen that, in contrast to LRT developed for shear flow in bulk fluids, the one presented here has two coefficients, (which is similar to the shear viscosity q) and, which has no parallel in bulk fluids. should be interpreted as an average location at which hydrodynamics is found to be nominally invalid. Note that although the surface may have corrugations in the X as well as the y direction, the corrugation in the x direction alone matters to the frictional force in the planar Couette geometry. 

We wish to study the effects of planar Couette flow on a system that is in the NPT (fully flexible box) ensemble. In this section, we consider the effects of the external field alone on the dynamics of the cell. The intrinsic cell dynamics arising out of the internal stress is assumed implicitly. The constant NPT ensemble can be employed in simulations of crystalline materials, so as to perform dynamics consistent with the cell geometry. In this section, we assume that the shear field is applied to anisotropic systems such as liquid crystals, or crystalline polytetrafluoroethylene. For an anisotropic solid, we assume that the shear field is oriented in such a way that different weakly interacting planes of atoms in the solid slide past each other. The methodology presented is quite general hence it is straightforward to apply for simulations of shear flow in liquids in a cubic box, as well. 

Fig. 2 (a) Conventions adopted in this review for the velocity, velocity gradient and vorticity axes characterizing shear flows. Most common geometries of shearing devices producing shear flows (b) planar Couette, (c) cone-and-plate, (d) cylindrical Couette... 

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