Numerical and theoretical solutions for a drop spreading below a free fluid surface.

Details Numerical and theoretical solutions for a drop spreading below a free fluid surface. Numerical and theoretical solutions for a drop spreading below a free fluid surface.

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995jfm...287..251k&link_type=abstract

Journal of Fluid Mechanics, Vol. 287, No., p. 251 - 278

Computer Science

14

Planets: Mantles

Scientific paper

Numerical solutions are derived for a viscous, buoyant drop spreading below a free fluid surface. The numerical solutions for the approach and initial spread of the drop below the fluid surface are obtained using the boundary integral method. To facilitate an investigation over a larger range of viscosity contrasts and for longer time periods, they solve for the motion of gravity currents at the fluid surface. For extensive drop spreading, the motion is described by asymptotic solutions. Three asymptotic solutions are derived, which apply for different values of the viscosity contrast relative to the aspect ratio. For very low-viscosity drops, the greatest resistance to spreading occurs at the drop rim, and the asymptotic solution is found using slender body theory. Drops with intermediate viscosity contrast are slowed primarily by shear stresses at the lower drop surface, and a lubrication solution applies. The greatest resistance to the spread of very viscous drops comes from the radial stresses within the drop, and the asymptotic solution is independent of the outer fluid. Theoretical results are compared with numerical and experimental results for drops and gravity currents spreading at a fluid surface. The solutions can be applied to aspects of planetary mantle flow.

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