Numerical investigation of meniscus deformation and flow in an isothermal liquid bridge subject to.h
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A comparatively new technique to introduce deﬁned ﬂow structures or to control timedependent convective regimes in crystal growth from the melt is the vibration of the solid–liquid
interface. Especially for growth arrangements with free melt surfaces like ﬂoating-zone growth,
the vibrating boundary generates surface ﬂows away from the interface and therefore can be used
to counterbalance the ﬂow due to the thermocapillary forces [1,2]. But the modeling of such a
ﬂoating-zone growth is very complex, and it is important to ﬁrstly consider a more fundamental
study of the vibration-driven ﬂow inside an isothermal liquid bridge subject to vibrations. Nonlinear response of liquid bridges subjected to axial low-frequency vibrations is studied in Refs.
[3,4]. One-dimensional non-linear viscous model is developed in Ref.  to study streaming
generated in a long liquid bridge due to vibrations of an endwall. The present paper deals with the
eﬀects of high-frequency vibrations w
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