Jeffery's equation describes the dynamics of a non-inertial ellipsoidal particle immersed in a Stokes liquid and is used in various models of fiber suspension flow. However, it is not valid in close neighbourhood of a rigid wall. Geometrically impossible orientation states with the fiber penetrating the wall can result from this model. This paper proposes a modification of Jeffery's equation in close proximity to a wall so that the geometrical constraints are obeyed by the solution. A class of models differing in the distribution between the translational and rotational part of the response to the contact is derived. The model is upscaled to a Fokker–Planck equation. Another microscale model is proposed where recoiling from the wall upon the collision is permitted. Numerical examples illustrate the dynamics captured by the models.
Ozolins, A., & Strautins, U. (2014). Simple Models for Wall Effect in Fiber Suspension Flows. Mathematical Modelling and Analysis, 19(1), 75-84. https://doi.org/10.3846/13926292.2014.893263
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