Shomeek Mukhopadhyay

Instabilities in Droplets Spreading on Gels

We report a novel surface-tension driven instability observed for droplets spreading on a compliant substrate. When a droplet is released on the surface of an agar gel, it forms arms or cracks when the ratio of surface-tension gradient to gel strength is sufficiently large. We explore a range of gel strengths and droplet surface tensions and find that the onset of the instability and the number of arms depend on the ratio of surface tension to gel strength. However, the arm length grows with an apparently universal law L proportional t(3/4).

Comment on "Sonoluminescence as Quantum Vacuum Radiation"

We argue that the available experimental data is not compatible with models of sonoluminescence which invoke dynamical properties of the interface without regard to the compositional properties of the trapped gas inside the bubble.

Starbursts and wispy drops: Surfactants spreading on gels

The spreading dynamics of surfactant-laden droplets have been studied for both solid [1] and thin liquid [2] substrates. In general, the presence of a surfactant modifies the contact line dynamics due to the Marangoni effect, which creates a surface tension gradient and thus generates pattern-forming instabilities. To determine the effects of varying substrate mobility from a liquid to a solid, we examine the intermediate case of a viscoelastic substrate. We observe novel instabilities of the surfactant-laden drop influenced by both the substrate fluidity and the surfactant concentration. The experimental apparatus consists of a petri dish containing a gel substrate composed of 0.04% to 0.16% agar (by weight) in deionized water. The droplets are solutions of Triton X-305 (a noninonic surfactant) in deionized water at concentrations from 5 to 1000 ppm, released from a micropipette with a droplet size of 5 mL. Figure 1 shows a phase diagram with shadowgraph images as a function of gel and surfactant concentration. For weak gels, the droplet spreads in a starburst formation, with 3-10 distinct arms (red images). For intermediate gels, the central drop remains but is decorated with thin, branching wisps (blue images). For sufficiently weak gels, the droplet spreads out as upon a liquid, and no central droplet remains (green images). On the strongest gels, the surfactant drops remain circular (not shown). For very low surfactant concentrations (i 5 ppm), the behavior resembles that of pure water droplets, and no arm structures are observed. This work has been supported under NSF Grant DMS-0244498.

Wetting dynamics of thin liquid films and drops under Marangoni and centrifugal forces

This paper presents an experimental study on thin liquid drops and films under the combined action of centrifugal forces due to rotation and radial Marangoni forces due to a corresponding temperature gradient. We shall examine thinning of a given liquid layer both with and without rotation and also consider the onset of the fingering instability in a completely wetting liquid drop. In many of the experiments described here, we use an interferometric technique which provides key information on height profiles. For thick rotating films in the absence of a temperature gradient, when an initially thick layer of fluid is spun to angular velocities where the classical Newtonian solution is negative, the fluid never dewets for the case of a completely wetting fluid, but leaves a microscopic uniform wet layer in the center. Similar experiments with a radially inward temperature gradient reveal the evolution of a radial height profile given by h(r) = A(t)r(α), where A(t) decays logarithmically with time, and [Formula: see text]. In the case where there is no rotation, small centrally placed drops show novel retraction behavior under a sufficiently strong temperature gradient. Using the same interferometric arrangement, we observed the onset of the fingering instability of small drops placed at the center of the rotating substrate in the absence of a temperature gradient. At the onset of the instability, the height profile for small drops is more complex than previously assumed.

Dynamics of perfectly wetting drops under gravity.

We study the dynamics of small droplets of polydimethylsiloxane silicone oil on a vertical, perfectly wetting, silicon wafer. Interference videomicroscopy allows us to capture the dynamics of these droplets. We use droplets with a volumes typically ranging from 100 t o500nl (viscosities from 10 to 1000 cSt) to understand long time derivations from classical solutions. Past researchers used one dimensional theory to understand the typical t(1/3) scaling for the position of the tip of the droplet in time t . We observe this regime in experiment for intermediate times and discover a two-dimensional similarity solution of the shape of the droplet. However, at long times our droplets start to move more slowly down the plane than the t(1/3) scaling suggests and we observe deviations in droplet shape from the similarity solution. We match experimental data with simulations to show these deviations are consistent with retarded van der Waals forcing which should become significant at the small heights observed.