We study how an axisymmetric drop of inviscid fluid breaks under the action of surface tension. The evolution of various initial shapes is calculated numerically using a boundary-element method, and finite-time breakage is observed in detail. The pinchoff region is shown to have lengths scaling as t 2͞3 , where t is the time remaining until pinchoff, and is found to adopt a unique shape with two cones of angles 18.1 ± and 112.8 ± , independent of the initial conditions. The velocity potential in the intermediate region between the small pinchoff region and the large bulk of the drops is shown to take the form Ar 1͞2 P 1͞2 ͑cos u͒ 1 Bt͞r 1 . . . . [S0031-9007(97)05092-8]
Several recent papers discuss a viscous micropump consisting of Poiseuille flow of
fluid between two plates with a cylinder placed along the gap perpendicular to the
flow direction (e.g. Sen, Wajerski & Gad-el-Hak 1996). If the cylinder is not centred,
rotating it will generate a net flow and an additional pressure drop along the channel,
due to the net tangential viscous stresses along its surface. The research reported here
complements existing work by examining the lubrication limit where the gaps between
the cylinder and the walls are small compared to the cylinder radius. Lubrication
analysis provides analytical relations among the flow rate, torque, pressure drop and
rotation rate. Optimization of the flow parameters is shown in order to determine
the optimal geometry of the device, which can be used by micro-electrical-mechanical
systems designers. It is also shown, for example, that a device cannot be developed
that achieves maximum flow rate and rotation simultaneously. In addition, since the
Reynolds number can be smaller than 1, the Stokes equations are solved for this
configuration using a numerical boundary integral method. The numerical results
match the lubrication solution for small gaps, and determine the limits of validity for
using the lubrication results.
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