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Theory of electrophoresis: Fate of one equation
Author(s) -
Gaš Bohuslav
Publication year - 2009
Publication title -
electrophoresis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.666
H-Index - 158
eISSN - 1522-2683
pISSN - 0173-0835
DOI - 10.1002/elps.200900133
Subject(s) - conservation law , partial differential equation , dispersion (optics) , mathematical analysis , traveling wave , mathematics , nonlinear system , differential equation , electrolyte , boundary (topology) , physics , quantum mechanics , electrode
Electrophoresis utilizes a difference in movement of charged species in a separation channel or space for their spatial separation. A basic partial differential equation that results from the balance laws of continuous processes in separation sciences is the nonlinear conservation law or the continuity equation. Attempts at its analytical solution in electrophoresis go back to Kohlrausch's days. The present paper (i) reviews derivation of conservation functions from the conservation law as appeared chronologically, (ii) deals with theory of moving boundary equations and, mainly, (iii) presents the linear theory of eigenmobilities. It shows that a basic solution of the linearized continuity equations is a set of traveling waves. In particular cases the continuity equation can have a resonance solution that leads in practice to schizophrenic dispersion of peaks or a chaotic solution, which causes oscillation of electrolyte solutions.