B334 両面間で温度差のある薄い液体シートの振る舞い

概要

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Behavior of a free viscous liquid sheet subject to a temperature difference between both surfaces is examined analytically. In consideration of the thermocapillary effect, nonlinear long wave equations for the sheet thickness and velocity are derived for sufficiently small Prandtl number, while a nonlinear relation between the position of the sheet centerline and the sheet thickness is obtained. It is found that there exist certain critical temperature difference and Biot number above which the sheet becomes linearly unstable. In the neighborhood of the critical temperature difference, a reduced weakly nonlinear equation is obtained for the sheet thickness. Numerical analysis of this equation for the unstable case shows that initial disturbances evolve into the waves which consist of flat troughs and large crests on both surfaces. However, since the critical temperature difference is estimated to be so large, the sheet may be practically stable as far as linear temperature dependence of the surface tension is assumed.
2000-07-25