DYNAMICS OF MAGNETIC SPHEROIDS IN THE PRESENCE OF SHEAR AND AN OSCILLATING MAGNETIC FIELD

Magnetic particles suspended in a fluid can be actuated by magnetic fields for a variety of applications. One interesting application is to use the torque exerted by the particles on the fluid to introduce mixing in inherently laminar microscale systems. Previous studies have examined the single particle dynamics in the presence of shear and a constant magnetic field. In the current study the combined effect of shear and an oscillating magnetic field on magnetic spheroids is explored in terms of the dimensionless numbers Σ, ratio of magnetic and hydrodynamic torques, and 𝜔*, the ratio of field frequency and strain rate. The rotation number 𝑅^*, is the ratio of the particle angular velocity and scaled magnetic field frequency, and

𝜔^∗_𝐽 is the ratio of Jeffrey frequency of the spheroid in a shear flow and the shear strain rate. For Σ ≫ 1, the spheroids rotate in the shear-plane with rotation number one. As Σ

reduces, for 𝜔^∗< 𝜔^∗_𝐽, there are discontinuous changes in the rotation number to progressively larger odd values. For Σ→0, they eventually lead to the Arnold tongues at 𝜔∗= 𝜔^∗_𝐽/(2𝑛₀), where 𝑛₀ is an odd integer. However, Arnold tongues are absent for the singular limit of the thin rod. A common scaling for the boundaries of the Arnold tongues in terms of the aspect ratio is found in this study. In the limit, 𝜔^∗≫ 1, there is a uniform transition from the synchronised in-plane rotations to the quasi-periodic, initial condition dependent rotations at a boundary with the scaling Σ = exp(Σ/𝜔∗) for all aspect ratios. For a thin rod, there are strips of constant 𝑅^∗strips of ratio of co-prime numbers less than 1, which are initial condition dependent. In the limit

𝜔^∗≪1, these strips tend to the line Σ= √2 (𝜔^∗)²/𝑛1 , where 𝑛₁= 1/3, 1/5, ⋯.



The torques exerted on the spheroids in all the regimes have also been evaluated. This will result in an anisotropic part of the stress tensor for the flow due to magnetically actuated particles by an oscillating field.