Effect of externally imposed shear flow on an active gel in a straight channel

Using a minimal hydrodynamic model, we theoretically and computationally study active fluids in a two-dimensional straight channel with the bottom wall translating at a fixed velocity along the channel direction. Using the finite element method, we calculate the critical activity for the fluids to be unstable to spontaneous shear flows and observe that the externally imposed shear flow can stabilize extensile fluids. Additionally, there are three kinds of spontaneous flow states found for extensile fluids: unidirectional flows, translating flows and dancing flows. We characterize these states by the average flow rate and the shear stress imposed by the active flow on the moving wall. Interestingly, we find that contractile fluids can also create a macroscopic spontaneous unidirectional flow when the absolute value of the activity is large enough and the externally imposed shear rate is greater than the liquid crystal relaxation rate.