Transition flow rate in viscous withdrawal.

We present the results of a numerical study of viscous selective withdrawal. In this system, two immiscible layers of different viscosities are laid in a container. A straw through which fluid is withdrawn is then introduced in the upper fluid. Above a certain transition flow rate, Q, the lower layer also becomes entrained. We determine numerically the dependence of Q on the straw height and viscosity ratio. The transition flow rate corresponds to the point where viscous entrainment from the upper fluid overcomes the resistance of surface tension. Knowing the lengthscales relevant to the flow and interface shape, one can estimate the transition flow rate. Our results were favorably compared with previously published experimental data.