Bicomponent flow problems in rheological fluid mechanics
Abstract
The arrangement of components in steady flow of immiscible liquids is typically nonunique. The problem of selection of arrangements is defined and is studied by variational methods under the hypothesis that the realized arrangements are the ones that maximize the speed on exterior boundaries for prescribed boundary tractions, or the ones that minimize the tractions for prescribed speeds. The arrangements which minimize tractions also minimize the dissipation by putting the lowviscosity liquid in regions of high shear. In fact some kind of shielding of highviscosity liquids is always observed. Another problem involving flow of immiscible liquids is jets of the liquid into another. If the change in the momentum of the entrained lighter liquid is neglected the jet will ultimately reach a modified Torricelli limit. An extended unsteady problem including effects of intrainment is formulated in terms of nonlinear ordinary differential equations which also account for weak radial variations of the velocity across the crosssection of the jet.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1984
 Bibcode:
 1984PhDT.........7N
 Keywords:

 Jet Flow;
 Liquids;
 Solubility;
 Steady Flow;
 Viscous Flow;
 Asymptotic Methods;
 Calculus Of Variations;
 Differential Equations;
 Emulsions;
 Fluid Mechanics;
 Rheology;
 Viscosity;
 Fluid Mechanics and Heat Transfer