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Colloidal solutions of magnetic particles find an increasing number of applications in biomedicine and microfluidics. This is due to the fact that the transport of these particles can be remotely controlled through application of a local magnetic field. The biocompatibility and non-toxicity of magnetic colloids has led to their extensive use in the following: targeted drug delivery [1–6]; clinical diagnostics as contrast agents for magnetic resonance imaging [6–10]; tumor therapy by controlled hyperthermia [9–12]; cytological studies [13–17]; and in catheter embolization of blood vessels [18]. The precise control and numerous manipulation techniques for magnetic delivery enable its applications in chemical analysis and processing [19–21], lab-on-a-chip construction [21–23], and in the fabrication of functional materials [24–26]. When magnetic deposition is used for guided transport and assembly of colloidal matter, the electric double layer forces can match or even exceed the driving magnetic force. However, this type of interaction is generally omitted from theoretical studies of field guided magnetic particle transport [2, 27–30]. The aim of this work is to develop a theoretical description of magnetic particle deposition that accounts for the colloidal electric double layer interactions between the particles and the vessel walls.

Mathematical modeling of magnetic field guided colloidal particle deposition with significant electric double layer interactions