Role of inertia in two-dimensional deformation and breakdown of a droplet

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Abstract
We investigate by lattice Boltzmann methods the effect of inertia on the deformation and breakdown of stability of a two-dimensional fluid droplet surrounded by fluid of equal viscosity (in a confined geometry) whose shear rate is increased very slowly. We give evidence that in two dimensions inertia is necessary for the loss of stability, so that at zero Reynolds number there is always a stable stationary droplet shape. We identify two different routes to breakdown, via two-lobed and three-lobed structures and give evidence for a sharp transition between these routes as parameters are varied.
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