Marangoni Flows in a Bilayer Liquid Microfilm Interface on Wave-Contoured Hot Substrates

This study explores the thermal Marangoni hydrodynamics in an immiscible, binary-liquid thin-film system, which is open to the gas phase at the top and rests on a heated substrate with wavy topology. The sinusoidal contour of the heated (constant-temperature) substrate results in temperature gradients along the liquid-liquid and liquid-gas interfaces, causing fluctuations in the interfacial tension, ultimately leading to Marangoni hydrodynamics in the liquid-liquid films. This type of flow is notable in liquid film coatings on patterned surfaces, which are widely used in MEMS/NEMS applications (Weinstein, S. J.; Palmer, H. J. Liquid Film Coating: Scientific Principles and Their Technological Implications; 1997, pp 19-62; Palacio, M.; Bhushan, B. Adv. Mater. 2008, 20, 1194-1198) and biological cell sorting operations (Witek, M. A.; Freed, I. M.; Soper, S. A. Anal. Chem. 2019, 92, 105-131). We solve the coupled Navier-Stokes and energy equations by the perturbation technique to obtain approximate analytical solutions and an understanding of the thermal and hydrodynamic transport in the system domain. Our study explores the parametric influence of the relative thermal conductivity of the liquid layers (k), film thickness ratio (r), and the system's Biot number (Bi) on these transport phenomena. While the strength of the thermal Marangoni effect that is generated reduces with an increase in the relative thermal conductivity (k), the impact of r depends on the k value. We observe that for k > 1 the intensity of Marangoni flow increases with r; however, the opposite holds for k < 1. Furthermore, larger values of Bi induce higher resistance to the vertical conduction from the wavy substrate compared to the convection resistance offered at the top surface, destructively interfering with the ability of the patterned substrate to generate interfacial temperature fluctuations and hence weakening the Marangoni flow.

Droplet evaporation on soft solid substrates

Droplet evaporation on soft solid substrates is relevant to applications such as fabrication of microlenses and controlled particle deposition. Here, we develop a lubrication-theory-based model to advance fundamental understanding of the important limiting case of a planar droplet evaporating on a linear viscoelastic solid. A set of partial differential equations describing the time evolution of the liquid-air and liquid-solid interfaces is derived and solved with a finite-difference method. A disjoining-pressure/precursor-film approach is used to describe contact-line motion, and the one sided model is used to describe solvent evaporation. Parametric studies are conducted to investigate the effect of solid properties (thickness, viscosity, shear modulus, wettability) and evaporation rate on droplet dynamics. Our results indicate that softer substrates speed up droplet evaporation due to prolonged pinning of the contact line. Results from our model are able to qualitatively reproduce some key trends observed in experiments. Due to its systematic formulation, our model can readily be extended to more complex situations of interest such as evaporation of particle-laden droplets on soft solid substrates.

How coronavirus survives for days on surfaces

Our previous study [R. Bhardwaj and A. Agrawal, "Likelihood of survival of coronavirus in a respiratory droplet deposited on a solid surface," Phys. Fluids 32, 061704 (2020)] showed that the drying time of typical respiratory droplets is on the order of seconds, while the survival time of the coronavirus on different surfaces was reported to be on the order of hours in recent experiments. We attribute the long survival time of the coronavirus on a surface to the slow evaporation of a thin nanometer liquid film remaining after the evaporation of the bulk droplet. Accordingly, we employ a computational model for a thin film in which the evaporating mass rate is a function of disjoining and Laplace pressures inside the film. The model shows a strong dependence on the initial thickness of the film and suggests that the drying time of this nanometric film is on the order of hours, consistent with the survival time of the coronavirus on a surface, seen in published experiments. We briefly examine the change in the drying time as a function of the contact angle and type of surface. The computed time-varying film thickness or volume qualitatively agrees with the measured decay of the coronavirus titer on different surfaces. The present work provides insights on why coronavirus survival is on the order of hours or days on a solid surface under ambient conditions.

Drying of Droplets of Colloidal Suspensions on Rough Substrates

In many technological applications, excess solvent must be removed from liquid droplets to deposit solutes onto substrates. Often, the substrates on which the droplets rest may possess some roughness, either intended or unintended. Motivated by these observations, we present a lubrication-theory-based model to study the drying of droplets of colloidal suspensions on a substrate containing a topographical defect. The model consists of a system of one-dimensional partial differential equations accounting for the shape of the droplet and depth-averaged concentration of colloidal particles. A precursor film and disjoining pressure are used to describe the contact-line region, and evaporation is included using the well-known one-sided model. Finite-difference solutions reveal that when colloidal particles are absent, the droplet contact line can pin to a defect for a significant portion of the drying time due to a balance between capillary-pressure gradients and disjoining-pressure gradients. The time-evolution of the droplet radius and contact angle exhibits the constant-radius and constant-contact-angle stages that have been observed in prior experiments. When colloidal particles are present and the defect is absent, the model predicts that particles will be deposited near the center of the droplet in a cone-like pattern. However, when a defect is present, pinning of the contact-line accelerates droplet solidification, leading to particle deposition near the droplet edge in a coffee-ring pattern. These predictions are consistent with prior experimental observations, and illustrate the critical role contact-line pinning plays in controlling the dynamics of drying droplets.