• Brinkman fluid;
  • Charge-regulated bi-functional particle;
  • Double-layer polarization;
  • Gel electrophoresis

Adopting a Brinkman fluid model, we analyzed the electrophoresis of a charged-regulated, bi-functional particle containing both acidic and basic functional groups in a gel solution. Both the long-range hydrodynamic effect arising from the liquid drag and the short-range steric effect from particle–polymer interaction are considered. The type of particle considered is capable of simulating both biocolloids such as microorganisms and cells, and particles with adsorbed polyelectrolyte or membrane layer. Our model describes successfully the experimental data in the literature. The presence of gel has the effect of reducing the particle mobility and alleviating double-layer polarization so that the particle behavior is less complicated than that in the case where gel is absent. On the other hand, both the quantitative and qualitative behaviors of a particle depend highly on solution pH and background salt concentration, yielding interesting and significant results. These results provide valuable information for both experimental data interpretation and electrophoresis devices design.