Hydrodynamics substantially affects induced structure formation in magnetic fluids

Abstract

Magnetorheological fluids consist of micrometer-sized magnetic particles in a carrier liquid. Sufficiently strong external magnetic fields lead to the formation of string-like particle aggregates. We demonstrate that hydrodynamic interactions, that is, mutual couplings via induced flows, play a substantial role during structure formation. Hydrodynamics supports the emergence of string-like aggregates, while magnetic interactions align them. This fundamental insight is substantial from an application perspective, due to the enormous technical importance and potential of magnetorheological fluids.

Figures (3)

• Figure 1: Structure formation with and without hydrodynamic interactions (HI) for an area fraction of $\theta \approx 0.15$. (a) Simulations start from the same configuration of roughly equally distributed particles. (b--d) Snapshots of the "dry" system at times $t=1600$, $2400$, and $10000$. The color scale refers to the magnetization field within the particles. (f--h) Snapshots of the system involving hydrodynamic interactions and fluid flows at the same times. Blue arrows indicate the flow field. (e) Magnified part of (f) showing the emergence of large-scale flows and the mutual amplification of local magnetization for particles that are close to each other. The external field strength is set to $|\mathbf{H}_\mathrm{ext}|/M_\mathrm{sat} = 0.2$.
• Figure 2: Same as in Fig. \ref{['fig:snapshotsLJ_050']}, yet for an elevated area fraction of $\theta \approx 0.31$ and snapshots in (b--d) and (f--h) taken at times $t=400$, $800$, and $10000$. Here, chain formation promoted by hydrodynamic interactions (HI) leads to branching and string-like structures when compared to the more compact clusters that emerge without hydrodynamics.
• Figure 3: Evolution of the chain-likeness parameter $\chi$ for an area fraction of (a) $\theta \approx 0.15$, (b) $\theta \approx 0.23$, and (c) $\theta \approx 0.31$. Hydrodynamic interactions (HI) consistently lead to more chain-like structures when compared to the "dry" case without HI. Shaded areas indicate standard errors, that is, standard deviations divided by the square root of the sample size.