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Surface tension and buoyancy‐driven flow in a non‐isothermal liquid bridge
Author(s) -
Zhang Yiqiang,
Alexander J. Iwan D.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650140207
Subject(s) - stream function , surface tension , discretization , mathematics , mechanics , free surface , boundary value problem , capillary surface , buoyancy , flow (mathematics) , classical mechanics , mathematical analysis , vorticity , geometry , physics , thermodynamics , vortex
The Navier–Stokes–Boussinesq equations governing the transport of momentum, mass and heat in a non‐isothermal liquid bridge with a temperature‐dependent surface tension are solved using a vorticity‐stream‐function formulation together with a non‐orthogonal co‐ordinate transformation. The equations are discretized using a pseudo‐unsteady semi‐implicit finite difference scheme and are solved by the ADI method. A Picard‐type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary‐driven flow situations and mixed thermocapillary‐ and bouyancy‐driven flow.