Capillary imbibition of shear-thinning fluids: From Lucas-Washburn to oscillatory regimes

We studied the filling dynamics of a shear-thinning fluid in a capillary tube. In regimes where inertial effects can be neglected, we generalize the Lucas-Washburn scaling relation to shear-thinning fluids, showing that the classical 1/2 scaling law holds only if an a00exd h00exo00exc time-dependent effective viscosity that applies to both Newtonian and shear-thinning fluids is introduced. In regimes where inertia competes with viscous and gravity effects, the system shows an oscillating behavior. The shear-thinning effect acts on the system, favoring such oscillating behavior.