Viscous effects in liquid encapsulated liquid bridges

• Published in: The International journal of heat and fluid flow 2002-12, Vol.23 (6), p.844-854
• Main Author: Johnson, Duane T.
• Format: Article
• Language: English
• Subjects: Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Growth from melts; zone melting and refining; Hydrodynamic stability; Liquid bridges; Marangoni flow; Materials science; Methods of crystal growth; physics of crystal growth; Physics; Shear-driven flow; Surface-tension-driven instability; Thermocapillarity
• ISSN: 0142-727X; 1879-2278
• DOI: 10.1016/S0142-727X(02)00186-8

An analytical derivation of the surface deflections and the streamfunctions for the flow inside a liquid encapsulated liquid bridge has been derived using an asymptotic expansion about a small capillary number. The model assumes an initially flat and cylindrical interface under the assumption that the densities of both fluids are equal. To simplify the analysis, the top and bottom walls are assumed to be stress-free and the Reynolds number is assumed to be negligible. Flow is generated either by a moving outer wall (shear-driven flow) or by applying a temperature difference across the top and bottom walls (Marangoni-driven flow). The resulting equations show that for the shear-driven flow, as the viscosity ratio increases, the surface deflections increase monotonically. For the Marangoni-driven flow there exist values of the viscosity ratio where the surface deflections reach a minimum and then switch signs. This investigation shows that it may be possible in more realistic systems to use an outer encapsulating liquid of the proper viscosity ratio to stabilize the liquid–liquid interface during float zone crystal growth.