An Isogeometric Boundary Element Formulation for Electrokinetic Particle Manipulation in Microfluidics

  • Erdogan, Ege (Bilkent University)
  • Sarbakhshian, Omid (Bilkent University)
  • Cetin, Barbaros (Bilkent University)

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Electrokinetic particle manipulation in microfluidic systems has long motivated the development of numerical methods capable of resolving coupled electric and hydrodynamic fields together with particle motion. In our earlier work, a boundary element formulation was developed to investigate direct current electrokinetic and dielectrophoretic (DC-DEP) motion of finite-sized particles in microfluidic confinements. In that study, the electric potential was obtained by solving the Laplace equation, and particle trajectories were predicted using a Lagrangian force-based framework, demonstrating the ability of boundary element methods to accurately capture particle–field and particle–boundary interactions under DC electric fields [1]. More recently, this line of research was extended to isogeometric boundary element formulations for deformable particles in microchannel confinement, enabling exact geometric representation and stable long-time simulations of particle deformation in Stokes flow [2]. The isogeometric framework was shown to provide enhanced accuracy and robustness, particularly for problems in which geometric fidelity and interface evolution are critical. Building on these developments, the present work aims to establish a unified isogeometric boundary element formulation for multiphysics particle motion in microfluidic systems, with a particular emphasis on DC-DEP applications. The Laplace equation governing the electric potential is solved using an isogeometric boundary element approach, and the resulting electric field is consistently coupled with particle dynamics within a single geometric framework. The proposed formulation provides a natural pathway toward fully-coupled multiphysics simulations that integrate electrokinetics with particle manipulation, offering a scalable and extensible foundation for next-generation microfluidic modeling.