Fingering Instability of a Suspension Film Spreading on a Spinning Disk

We have experimentally investigated the spreading of a suspension drop when rotated atop a spinning disc using flow visualization techniques. The suspension is created from 53−106 micron glass beads suspended in a low viscosity, partially wetting Newtonian liquid having same density as the glass beads. The suspension drop (of differing particle volume fractions) is placed centrally on a horizontal disc and the disc is then rotated at a desired speed. The spreading behavior is captured using a high speed camera and the acquired images are analyzed to find the edges of the spreading drop. For all particle volume fractions (ϕ_p), the suspension drop spreads upto a critical radius, before the contact line (drop edge) develops instabilities which further grow into fingers. The dependence on ϕ_p is, however, found to be quite remarkable. The critical radius for the onset of instability shows an increase with increase in the particle fraction (ϕ_p) before decreasing slightly at the highest value of ϕ_p studied, while the instability wavelength (λ) exhibits a non-monotonic dependence. The value of λ is close to that for a partially wetting liquid at lower ϕ_p, it decreases with increasing ϕ_p to a minimum before increasing again at largest ϕ_p. The non-monotonic trends observed for λ are discussed in light of the linear stability analysis of thin film equations derived for suspensions by Cook et al., ^[1] and Balmforth et al., ^[2].

References:

[1] B. P. Cook, O. Alexandrov, and A. L. Bertozzi, “Linear stability of particle-laden thin films,” Eur. Phys. J. Special Topics 166, 77 (2009).

[2] N. Balmforth, S. Ghadge, and T. Myers, “Surface tension driven fingering of a viscoplastic film,” J. Non-Newtonian Fluid Mech. 142, 143 (2007).