The effect of oscillatory shear flow on step bunching

During crystal growth, an imposed shear Row at the crystal-fluid interface can alter the conditions for the onset of morphological instability. In pre vious work, we studied the effect of time-independent shear flows and aniso tropic interface kinetics on the morphological stability of a crystal growi ng from supersaturated solution. The model assumes that growth is by the mo tion of elementary steps, which is treated by a macroscopic anisotropic kin etic law; morphological instability corresponds to the bunching of elementa ry steps. Predictions from linear stability theory indicate that a solution flowing above a vicinal face of a crystal can either enhance or prevent th e development of step bunches, depending on the direction of the steady she ar flow in relation to the direction of step motion: this is also observed in experiments. Here we extend the linear stability analysis to include the effect of an oscillatory shear flow on the morphological stability of a cr ystal growing from solution and present results for a model system for a ra nge of oscillatory shear rate amplitudes and frequencies both with and with out a steady shear component. In the presence of a steady shear flow, modul ation can either stabilize or destabilize the system, depending on the modu lation amplitude and frequency. Numerical solutions of the linearized Navie r-Stokes and diffusion equations and an approximate analytical treatment Sh ow that the flow oscillations weakens both the stabilization and destabiliz ation induced by steady-state flow. This weakening comes from mixing of sol ution above the perturbed interface and a modification to the phase shift b etween the interface perturbation wave and the corresponding concentration and flow waves. Optimal values of modulation frequency and amplitude are fo und when the steady flow is destabilizing. (C) 2000 Elsevier Science B.V. A II rights reserved.