Srinivas Mettu

Motion of Drops on a Surface Induced by Thermal Gradient and Vibration

It is well known that a liquid drop with a low contact angle (approximately 45 degrees ) and low wetting hysteresis moves toward the colder region of a temperature gradient substrate as a result of the thermal Marangoni force. A moderately sized water drop, however, usually does not move on such a surface because of the overwhelming effect of hysteresis. The water drop can, however, be forced to move when it is vibrated on a temperature gradient surface with its velocity exhibiting maxima at the respective Rayleigh frequencies. A simple model is presented that captures the dependence of drop velocity on hysteresis, vibration amplitude, and the forcing and resonance frequencies of vibration.

Motion of Liquid Drops on Surfaces Induced by Asymmetric Vibration: Role of Contact Angle Hysteresis

Hysteresis of wetting, like the Coulombic friction at solid/solid interface, impedes the motion of a liquid drop on a surface when subjected to an external field. Here, we present a counterintuitive example, where some amount of hysteresis enables a drop to move on a surface when it is subjected to a periodic but asymmetric vibration. Experiments show that a surface either with a negligible or high hysteresis is not conducive to any drop motion. Some finite hysteresis of contact angle is needed to break the periodic symmetry of the forcing function for the drift to occur. These experimental results are consistent with simulations, in which a drop is approximated as a linear harmonic oscillator. The experiment also sheds light on the effect of the drop size on flow reversal, where drops of different sizes move in opposite directions due to the difference in the phase of the oscillation of their center of mass.

Vibration spectroscopy of a sessile drop and its contact line.

Resonance frequencies of small sessile liquid drops (1-20 μL) were estimated from the power spectra of their height fluctuations after subjecting them to white noise vibration. Various resonance modes could be identified with this method as a function of the mass of the drop. Studies with water drops on such supports as polystyrene (θ ≈ 80°) and a superhydrophobic surface of microfibrillar silicone rubber (θ ≈ 162°) demonstrated that the resonant frequency decreases with the contact angle, θ. This trend is in remarkable agreement with the current models of the resonant vibration of sessile drops. A novel aspect of this study is the analysis of the modes of a slipping contact line that indicated that its higher frequency modes are more severely damped than its lower ones. Another case is with the glycerol-water solutions, where the resonance frequency decreases with the concentration of glycerol purely due to the capillary effects. The interface fluctuation, on the other hand, is strongly correlated with the kinematic viscosity of the liquid. Thus, these experiments provide a means to measure the surface tension and the viscosity of very small droplets.

Stochastic relaxation of the contact line of a water drop on a solid substrate subjected to white noise vibration: roles of hysteresis.

Relaxation of the three phase contact line of a sessile drop of water on a low energy surface is studied by subjecting it to a white noise vibration. While a spring force acts on the contact line whenever the contact angle deviates from its equilibrium value, it is opposed by hysteresis. The drop, therefore, remains pinned at a metastable state. With an appropriate amount of vibration, the drop can reach a global equilibrium state irrespective of its initial state, be it advanced or retreated. While the end state is free of hysteresis, the current study sheds light on the dynamics of relaxation that is analyzed in conjunction with a modified Langevin equation. Instead of exhibiting a smooth relaxation as predicted by the Langevin equation with a smooth background potential, stepwise relaxation is observed in most cases. These stepwise relaxations can be explained if the background potential is made slightly corrugated that signifies the existence of metastable states of a drop on a surface. The fluctuation of the displacement of the contact line is highly non-Gaussian. It is shown that an exponential distribution of the displacement fluctuation arises due to the nonlinear hysteresis term in the Langevin equation. The observations of stick-slip motion, the large time of relaxation, and the anomalous displacement fluctuation suggest that hysteresis is present during the relaxation process of the drop even though the final state reached by the drop is free of hysteresis. Finally, we compare the displacement fluctuations of the contact line on two different surfaces: a silicone rubber and a fluorocarbon monolayer. Although the displacement fluctuation is exponential in both cases, the later surface exhibits a greater variance of the distribution than the former plausibly due to differences in hysteresis. This result indicates that the fluctuation of displacement may be used as a tool to study the surface property of a low energy substrate.

Effect of roughness geometry on wetting and dewetting of rough PDMS surfaces.

Rough PDMS surfaces comprising 3 μm hemispherical bumps and cavities with pitches ranging from 4.5 to 96 μm have been fabricated by photolithographic and molding techniques. Their wetting and dewetting behavior with water was studied as model for print surfaces used in additive manufacturing and printed electronics. A smooth PDMS surface was studied as control. For a given pitch, both bumpy and cavity surfaces exhibit similar static contact angles, which increase as the roughness ratio increases. Notably, the observed water contact angles are shown to be consistently larger than the calculated Wenzel angles, attributable to the pinning of the water droplets into the metastable wetting states. Optical microscopy reveals that the contact lines on both the bumpy and cavity surfaces are distorted by the microtextures, pinning at the lead edges of the bumps and cavities. Vibration of the sessile droplets on the smooth, bumpy, and cavity PDMS surfaces results in the same contact angle, from 110°-124° to ∼91°. The results suggest that all three surfaces have the same stable wetting states after vibration and that water droplets pin in the smooth area of the rough PDMS surfaces. This conclusion is supported by visual inspection of the contact lines before and after vibration. The importance of pinning location rather than surface energy on the contact angle is discussed. The dewetting of the water droplet was studied by examining the receding motion of the contact line by evaporating the sessile droplets of a very dilute rhodamine dye solution on these surfaces. The results reveal that the contact line is dragged by the bumps as it recedes, whereas dragging is not visible on the smooth and the cavity surfaces. The drag created by the bumps toward the wetting and dewetting process is also visible in the velocity-dependent advancing and receding contact angle experiments.

Rust‐Mediated Continuous Assembly of Metal–Phenolic Networks

The use of natural compounds for preparing hybrid molecular films-such as surface coatings made from metal-phenolic networks (MPNs)-is of interest in areas ranging from catalysis and separations to biomedicine. However, to date, the film growth of MPNs has been observed to proceed in discrete steps (≈10 nm per step) where the coordination-driven interfacial assembly ceases beyond a finite time (≈1 min). Here, it is demonstrated that the assembly process for MPNs can be modulated from discrete to continuous by utilizing solid-state reactants (i.e., rusted iron objects). Gallic acid etches iron from rust and produces chelate complexes in solution that continuously assemble at the interface of solid substrates dispersed in the system. The result is stable, continuous growth of MPN films. The presented double dynamic process-that is, etching and self-assembly-provides new insights into the chemistry of MPN assembly while enabling control over the MPN film thickness by simply varying the reaction time.

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.

Experimental investigation of the drift and diffusion of small objects on a surface subjected to a bias and an external white noise: roles of coulombic friction and hysteresis.

We study the stochastic motion of a small solid block or a small water drop on a flat solid support in the presence of an external noise and a bias. The bias is caused either by inclining the plane of the support, as is the case with the solid block, or by creating a gradient of wettability, as is the case with a water drop. Both the solid block and the water drop exhibit drifted Brownian-like motion. There are, however, differences between the motion described here and that of a classical drifted Brownian motion, in that the Coulombic friction (for solid on solid) or wetting hysteresis (for water drops on a solid) accounts for a significant resistance to motion in addition to the kinematic friction. Although the displacement distribution here is non-Gaussian, the variance of the distribution increases with time, indicating that the overall motion follows simple diffusion. The diffusivity and the mobility of the solid object are considerably lower than the values expected when the diffusion is governed by only kinematic friction. The experimental diffusivity increases with the power of the noise with an exponent of 1.61, which is close to that (1.74) of an analysis based on the Langevin equation when the Coulombic friction is taken into account in addition to the kinematic friction. The ratio of diffusivity and mobility increases slightly sublinearly with the power of the noise with an exponent of about 0.8. The experimentally observed relaxation time of the process is, however, considerably smaller than the Langevin relaxation time. When the experimental ratio of diffusivity and mobility is taken into account in the distribution function of the displacement, the later quantity becomes amenable to an analysis that is similar to the conventional fluctuation relations.

Brownian motion of a drop with hysteresis dissipation.

Small water drops placed on a low-energy substrate with a slight tilt were vibrated parallel to the support with bands of Gaussian white noise of different powers. The drops drifted downward on the inclined support accompanied with random forward and backward movements. For a hysteresis free surface, the drift velocity should only be the product of the component of the gravitational acceleration and the Langevin relaxation time, being independent of the power of noise. On the other hand, in the presence of hysteresis, as is the case here, the drift velocity depends strongly on the power of the noise. This result illustrates the role of hysteresis in the drifted motion of drops on a surface subjected to vibration, which has important bearings on various forms of work fluctuation relations.

Charge and Film Drainage of Colliding Oil Drops Coated with the Nonionic Surfactant C12E5

The interaction forces between colliding tetradecane drops were measured in the presence of the nonionic surfactant pentaethylene glycol monododecyl ether (C12E5). The force behavior was measured in the range of premicellar compositions of the nonionic surfactant in various salt solutions and was consistent with the presence of a surface charge even though the surfactant was nonionic in nature. The surface potential of oil drops was found to decrease with an increase in C12E5 concentration. The measured electrophoretic mobilities and ζ potentials of emulsified tetradecane drops also decreased with an increase in the C12E5 concentration. The surface potential decreased with an increase in the electrolyte at a constant C12E5 concentration, further confirming the presence of a charged oil-water interface. In addition to the charging behavior, the nonequilibrium film drainage between the tetradecane drops coated with C12E5 was also measured. In contrast to some existing experiments in the literature, it was found that oil drops coated with the nonionic surfactant were stable against coalescence, even when the drops were deformed on the order of their radii. These findings have significant implications on the stability of emulsions in food, personal care, and detergent industries.