We examine the axisymmetric and nonaxisymmetric flows of thin fluid films over a spherical glass dome. A thin film is formed by raising a submerged dome through a silicone oil mixture composed of a volatile, low surface tension species (1 cSt, solvent) and a nonvolatile species at a higher surface tension (5 cSt, initial solute volume fraction $\phi _0$ ). Evaporation of the 1 cSt silicone oil establishes a concentration gradient and, thus, a surface tension gradient that drives a Marangoni flow that leads to the formation of an initially axisymmetric mound. Experimentally, when $\phi _0 \leqslant 0.3\,\%$ , the mound grows axisymmetrically for long times (RodríguezHakim et al. , Phys. Rev. Fluids , vol. 4, 2019, pp. 1–22), whereas when $\phi _0 \geqslant 0.35\,\%$ , the mound discharges in a preferred direction, thereby breaking symmetry. Using lubrication theory and numerical solutions, we demonstrate that, under the right conditions, external disturbances can cause an imbalance between the Marangoni flow and the capillary flow, leading to symmetry breaking. In both experiments and simulations, we observe that (i) the apparent, most amplified disturbance has an azimuthal wavenumber of unity, and (ii) an enhanced Marangoni driving force (larger $\phi _0$ ) leads tomore »
This content will become publicly available on March 10, 2023
Stokes flows in threedimensional fluids with odd and parityviolating viscosities
The Stokes equation describes the motion of fluids when inertial forces are negligible compared with viscous forces. In this article, we explore the consequence of parityviolating and nondissipative (i.e. odd) viscosities on Stokes flows in three dimensions. Parityviolating viscosities are coefficients of the viscosity tensor that are not invariant under mirror reflections of space, while odd viscosities are those which do not contribute to dissipation of mechanical energy. These viscosities can occur in systems ranging from synthetic and biological active fluids to magnetized and rotating fluids. We first systematically enumerate all possible parityviolating viscosities compatible with cylindrical symmetry, highlighting their connection to potential microscopic realizations. Then, using a combination of analytical and numerical methods, we analyse the effects of parityviolating viscosities on the Stokeslet solution, on the flow past a sphere or a bubble and on manyparticle sedimentation. In all the cases that we analyse, parityviolating viscosities give rise to an azimuthal flow even when the driving force is parallel to the axis of cylindrical symmetry. For a few sedimenting particles, the azimuthal flow bends the trajectories compared with a traditional Stokes flow. For a cloud of particles, the azimuthal flow impedes the transformation of the spherical cloud into a more »
 Award ID(s):
 2011854
 Publication Date:
 NSFPAR ID:
 10325756
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 934
 ISSN:
 00221120
 Sponsoring Org:
 National Science Foundation
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