Importance of Basset History Force for the Description of Magnetically Driven Motion of Magnetic Particles in Air

Abstract

Lungs are used as an attractive possibility for administration of different therapeutic substances for a long time. An innovative method of such administration widely studied nowadays is the application of aerosolized magnetic particles as the carriers to the lungs in the external non-homogeneous magnetic field. For these reasons we have studied dynamics of such a system on a level of particle trajectory in air in the presence of magnetic force as a driving force exerted on micrometric magnetic particle. On two typical examples of magnetically driven systems—motion of magnetic particle in a gradient magnetic field and cyclotron-like motion of a charged particle in homogeneous magnetic field in microscale, where the external accelerating forces are very large and the relevant time scale is of the order from fraction of milliseconds to seconds, we have examined the importance of these forces. As has been shown, for particles with high initial acceleration, not only the commonly used Stokes force but also the Basset history force should be used for correct description of the motion.

Oxygen-Selective Diffusion-Bubbling Membranes with Core–Shell Structure: Bubble Dynamics and Unsteady Effects

“…Because of the difficulties associated with calculating the integral term, Basset hereditary force is often ignored. However, in a number of studies, − it is shown that Basset hereditary force could influence the bubble dynamics. An integral/quadrature scheme has been developed for the numerical estimation of the Basset hereditary force …”

A Theoretical Analysis of Magnetic Particle Alignment in External Magnetic Fields Affected by Viscosity and Brownian Motion

“…We consider not only a simple system of ordinary differential equations (ODEs) but also stochastic integro-differential equations (SIDEs), which do not possess a simple analytic or numerical solution. Recently, we showed in [5,47,48] how to approach a similar system of integro-differential equations (IDEs) containing a non-local Basset acceleration history term numerically, with a variable timestep order of one, quadrature scheme. However, the current situation is more complex because the stochastic term brings the additional difficulty of solving the current system of SIDEs with a similar method.…”