Physical conditions and geometric implications are determined if two stationary, MHD aligned flows have the same streamline patterns. This study is carried out for incompressible and irrotational compressible plane flows; incompressible axially symmetric flow and incompressible spatial doubly laminar flow.
Plane steady state viscous fluid flows, in which the magnetic field and velocity field are constantly inclined to one another, are considered. Necessary and sufficient physical conditions have been derived for flows with zero current density and the general solutions for these flows are obtained. Irrotational flows and flows with straight streamlines are also studied.
We show how the dilute n → 0 spin vector model introduced originally by Wheeler and co-workers for describing the polymerization phenomenon in solutions of liquid sulphur and of living polymers may be conveniently adapted for studying phase separation in systems containing long flexible micelles. We draw an isomorphism between the coupling constant appearing in the exchange Hamiltonian and the surfactant energies in the micellar problem. We solve this problem within the mean-field approximation and compare the main results we have obtained with respect to polymer theory and previous theories of phase separation in micellar solutions. We show that the attractive interaction term χ between monomers renormalizes the aggregation energy and subsequently the corresponding size distribution. Under these conditions, we observe that the general aspect of the phase diagram in the ( , χ ) plane (where is the surfactant concentration) is different from previous results. The spinodal line shows a reentrant behaviour and, at low concentrations, we point out the possibility of specific nucleation phenomena related to the existence of a metastable transition line between a region composed of spherical micelles and another one corresponding to a dilute solution of long flexible micelles. †
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