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Electrophoretic motion of nonuniformly charged particles suspended in arbitrary background flows: An exact reduced-order approach

Rajnandan Borthakur* and Uddipta Ghosh†

  • *Contact author: rajnandanb@iitgn.ac.in
  • †Contact author: uddipta.ghosh@iitgn.ac.in
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Phys. Rev. Fluids 11, 073702 – Published 14 July, 2026

DOI: https://doi.org/10.1103/ypxb-ydp3

Abstract

Electrophoresis is a widely used method for separating charged entities such as DNA, proteins, cells, and other biological and colloidal particles. In many instances, it is often combined with background flows to improve the separation efficiency. At the same time, most particles bear nonuniform surface charge profiles, and their kinetics can be quite fascinating when suspended in external flows, and yet they remain poorly explored so far. In this article, we thus devise a fairly general and exact reduced-order model based on a set of coupled ordinary differential equations to predict the trajectories of nonuniformly charged particles suspended in an arbitrary background flow and subject to an externally imposed electric field. While a fundamental approach can be built for this purpose, we establish that the reduced-order model is computationally efficient and has the added advantage of providing useful insights into the nonlinear physics of particle motion. Using this framework, we show that in general, the particle rotates, which makes its surface charge evolve over time with respect to a laboratory-fixed frame. This may result in a multitude of particle trajectories depending on the precise nature of the imposed flow, the variability of the particle's surface charge, its starting position and orientation within the flow field, and the relative strengths of the flow and electrophoretic propulsion. For instance, we show that under certain conditions, axisymmetric particles suspended in a Poiseuille flow tend to migrate towards the flow centerline, while nonaxisymmetric ones tend to settle at a distance from the same. We expect that our framework will enhance the fundamental understanding of electrophoretic motion and contribute towards more efficient separation of charged entities using electric fields.

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Phys. Rev. Fluids 11, 073702– Published 14 July, 2026
  • Received 12 January 2026
  • Accepted 23 June 2026
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