interfering with the integrity of the cells. In recent years, Experimental observations, previously reported in the low frethe methods of dielectrophoresis and electrorotation have quency regime of the spectrum in dielectrophoresis and electroroemerged as two powerful techniques. An extensive amount tation of plant protoplasts, have revealed serious discrepancies of literature is now available on these subjects. For example, between the predictions of the ''Shelled Model'' and measurean excellent discussion of the underlying principles can be ments. Much work has also been carried out in the theoretical found in a book written by Pohl (1) and in a more recent realm to reconcile these discrepancies by introducing such mechabook by Jones (2). In Refs. (3) and (4), by Kaler et al., nisms as charge flow on the surface of the cell and micromotion, some of the experimental techniques recently developed and but in all this the effects of electrode polarization have been ne-
the unusual observations made thereby may be found. In glected. Part of the problem lies in the rather formidable nature of the analysis that must be carried out with nonuniform fields addition these papers also contain a large number of essential since the entire system of governing partial differential equations background references. From a theoretical standpoint the somust be considered. In the case of uniform fields it is convenient called ''Shelled Model'' of Pauly and Schwan (5) has played to formulate the problem in the language of ordinary differential a highly significant role in the interpretation of the data. equations. This problem is further exacerbated by the lack of a Although the theory of electrode polarization developed in well defined boundary condition at the outer limit of the double this paper is applicable to both dielectrophoresis and eleclayer. We have used the method of Green's functions, since this trorotation, its application to the former will be discussed allows the consideration of partial differential equations in a more only from an illustrative point of view. From both experinatural way than the other methods, in order to formulate the mental and theoretical points of view the quantity of primary problem. The lack of a well defined boundary condition at the importance is the time averaged dielectrophoretic force, F DEP outer surface is dealt with by taking an integral transform of the (derived by Sauer (6)), experienced by a cell of radius R, governing equations and thus recovering a relationship between the applied and the far fields. The results of our analysis show in a nonuniform field of magnitude E, and suspended in a that the double layer relaxation, in the selected model, is a very medium of permittivity e m , simple single relaxation process and its effect is to diminish the discrepancies between theory and experiment. α§ 1997 Academic Press F DEP Γ
2pR 3 e m Re[K(v)]ΓE 2 , [1]