We derive a novel and rigorous correction to the classical Reynoldslubrication approximation for fluids with viscosity depending upon thepressure. Our analysis shows that the pressure dependence of viscosity leads toadditional nonlinear terms related to the shear-rate and arising from a nonnegligible cross-film pressure. We present a numerical comparison between theclassical Reynolds equation and our modified equation and conclude that themodified equation leads to the prediction of higher pressures and viscositiesin the flow domain.
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