Related Experiment Video
Updated: Jul 3, 2026

Label-free Isolation and Enrichment of Cells Through Contactless Dielectrophoresis
Published on: September 3, 2013
Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the
1Dipartimento di Fisica, Universita' di Parma, Viale G.P. Usberti 7/A, I-43100 Parma, Italy. leonardo.ferrari@fis.unipr.it
Abstract:
The problem of the derivation of the diffusion equation exactly following from the Fokker-Planck (or Klein-Kramers) equation for heavy (or large) particles in a fluid in an external force field is solved in the case in which the particles are ions subject to a uniform (but in general time-varying) electric field. It is found that such a diffusion equation maintains memory of the initial ion velocity distribution, unless sufficiently large values of time are considered. In such temporal asymptotic limit, the diffusion equation exactly becomes (i) the Smoluchowski equation when the electric field is constant in time, and (ii) a new equation generalizing the Smoluchowski equation, when the electric field is arbitrarily time varying. Finally, it is shown that the obtained exact (or asymptotic) results make questionable the procedures and the results of approximate theories developed in the past to get a "corrected" Smoluchowski equation when the external force can also be, in general, position dependent.
Related Concept Videos
Carrier Transport
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
Poisson's And Laplace's Equation
The Electrical Double Layer
Electrostatic Boundary Conditions
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Debye–Huckel–Onsager Conductance Equation
Differential Form of Maxwell's Equations

