Fingering instability of a suspension film spreading on a spinning disk

TL;DR

This study investigates the fingering instability of a suspension film on a spinning disk, revealing non-monotonic dependencies of critical radius and wavelength on particle fraction, supported by flow visualization and stability analysis.

Contribution

It provides new experimental insights into how particle concentration affects instability patterns in suspension films on spinning disks, extending previous theoretical models.

Findings

Critical radius increases then decreases with particle fraction.

Wavelength exhibits non-monotonic dependence on particle fraction.

Results align with linear stability analysis of suspension films.

Abstract

The spreading of a thin film of suspension on a spinning disk and the accompanying contact line instability is studied through flow visualization experiments. The critical radius for the onset of instability shows an increase with increase in the particle fraction ($\phi_{p}$) before decreasing slightly at the highest value of $\phi_{p}$ studied, while the instability wavelength ($\lambda$) exhibits a non-monotonic dependence. The value of $\lambda$ is close to that for a partially wetting liquid at lower $\phi_{p}$, it decreases with increasing $\phi_{p}$ to a minimum before increasing again at largest $\phi_{p}$. The non-monotonic trends observed for $\lambda$ are discussed in light of the linear stability analysis of thin film equations derived for suspensions by Cook {\it et al.} [Linear stability of particle-laden thin films, Eur. Phys. J.: Spec. Top. {\bf 166}, 77 (2009)] and Balmforth {\it et al.} [Surface tension driven fingering of a viscoplastic film, J. Non Newtonian Fluid Mech. {\bf 142}, 143 (2007)].