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Using a minimal hydrodynamic model, we theoretically and computationallystudy active gels in straight and annular two-dimensional channels subject toan externally imposed shear. The gels are isotropic in the absence ofexternally- or activity-driven shear, but have nematic order that increaseswith shear rate. Using the finite element method, we determine the possibleflow states for a range of activities and shear rates. Linear stabilityanalysis of an unconfined gel in a straight channel shows that an externallyimposed shear flow can stabilize an extensile fluid that would be unstable tospontaneous flow in the absence of the shear flow, and destabilize acontractile fluid that would be stable against spontaneous flow in the absenceof shear flow. These results are in rough agreement with the stabilityboundaries between the base shear flow state and the nonlinear flow states thatwe find numerically for a confined active gel. For extensile fluids, we findthree kinds of nonlinear flow states in the range of parameters we study:unidirectional flows, oscillatory flows, and dancing flows. To highlight theactivity-driven spontaneous component of the nonlinear flows, we characterizethese states by the average volumetric flow rate and the wall stress. Forcontractile fluids, we only find the linear shear flow and a nonlinearunidirectional flow in the range of parameters that we studied. For largemagnitudes of the activity, the unidirectional contractile flow develops aboundary layer. Our analysis of annular channels shows how curvature of thestreamlines in the base flow affects the transitions among flow states.

Flow states of two dimensional active gels driven by external shear