TY - JOUR
T1 - Migrating boundaries of interacting systems I. Hyperbolic boundaries
JF - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
JO - Proc R Soc Lond A Math Phys Sci
SP - 153
LP - 165
M3 - 10.1098/rspa.1970.0108
VL - 317
IS - 1529
AU -
AU -
AU -
Y1 - 1970/06/16
UR - http://rspa.royalsocietypublishing.org/content/317/1529/153.abstract
N2 - The migration of single and multi-solute systems subjected to a uniform potential gradient is considered in terms of the nature of boundaries which might arise when the effects of diffusional flows are neglected. Continuity equations are derived for each system in terms of constituent quantities and their geometrical interpretation is discussed, with particular reference to the formation of hypersharp boundaries. It is shown, in general, that boundaries may be classified as hyperbolic, elliptic and parabolic types on the basis of the nature of the roots of the characteristic equation of the determinant formed by the derivatives ∂(vici)/∂cj, where vi and ci are the velocity and concentration of the ith constituent. Detailed examination of the purely hyperbolic case leads to the following conclusions, which find illustration in certain migration patterns presented by earlier workers. With n constituents n+1 plateaux are formed, separated by n boundaries. One constituent vanishes across each boundary and all boundaries across which two or more constituent concentrations change are spread. The loci of constant composition within each boundary are straight lines on the distance-time plane, converging on the origin.
ER -