Axial variations in geometry and presence of viscous displaced fluid are known to alter the diffusive-dynamics of capillary imbibition of a wetting liquid. We here show that the coupled effect of axially varying capillary geometry and finite viscosity of the displaced fluid can lead to significant variations in both short and long time dynamics of imbibition. Based on a theoretical model and lattice Boltzmann simulations, we analyze capillary displacement of a viscous liquid in straight and diverging capillaries. At short times, the imbibition length scales proportionally with time as opposed to the diffusive-dynamics of imbibition of a single wetting liquid. Whereas, at long times, geometry-dependent power-law behavior occurs which qualitatively resembles single liquid imbibition. The distance at which the crossover between these two regimes occurs depends strongly on the viscosities of the imbibing and the displaced liquid. Additionally, our simulations show that the early time imbibition dynamics are also affected by the dynamic contact angle of the meniscus.

In the present study, we develop a theoretical approach to predict the maximum spread of a liquid droplet on a dry solid surface. By using the dynamics of the gas layer entrapped underneath the droplet during initial stages of spreading, we determine the initial spread velocity of the droplet. The predicted spread velocity is used to model viscous dissipation and spread time of the droplet, post-impact. We also reformulate the surface energy of the droplet at the maximum spread to account for the presence of a rim formed at the periphery of the droplet. Incorporating the renewed terms into an energy conservation equation, the maximum spread of the droplet is predicted. The constructed model is validated with both the in-house experiments and the literature performed for various liquids and surfaces. The study also examines the existing scaling laws available to predict the maximum spread in inertial and viscous regimes and compares them with the model. Results reveal that the proposed model effectively predicts maximum spread values even at a low Weber number, despite variations in wettability values. The scaling laws were found to be inefficient in predicting the maximum spread for water at a low Weber number as they do not account for the effect of the surface wettability.

We present a mathematical model for dropwise condensation (DWC) heat transfer on a surface with wettability gradient. We adapt well-established population balance model for DWC on inclined surfaces to model DWC on a surface with wettability gradient. In particular, our model takes into account the effect of wettability gradient and energy released during drop coalescence to determine the drop departure size. We validate our model with published experimental data of DWC heat flux and drop size distribution. Based on various experimental studies on drop motion, we also propose a mechanism that explains how the energy released during drop coalescence on a surface with wettability gradient and in a condensation environment aids drop motion. The mechanism correctly explains the shift of center of mass of two coalescing drops on a surface with wettability gradient toward the drop on high wetting region. Using the model, we analyze the effect of wettability gradient on the DWC heat flux. Our model predictions show that the optimal choice of wettability gradient is governed by differential variations in population density and heat transfer through a drop with change in wettability of the surface. We also demonstrate that contact angle at which there is maximum heat transfer through a drop varies with thickness of coating layer leading to change in optimal wettability gradient.

We present an investigation of symmetric and asymmetric coalescence of two droplets of equal and unequal size on a solid surface in the inertia-dominated regime. Asymmetric coalescence can result due to the coalescence of two unequal-sized droplets or coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. Based on the solution of an analytical model and lattice Boltzmann simulations, we analyze symmetric and asymmetric coalescence of two droplets on a solid surface. The analysis of coalescence of identical droplets show that the liquid bridge height grows with time as (t*)1/2 for θ = 90° and (t*)2/3 for θ < 90°, where t* is dimensionless time. Our analysis also yields the same scaling law for the coalescence of two unequal-sized droplets on a surface with homogeneous wettability. We also discuss the coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. We show that the prediction of bridge height with time scales as (t*)2/3 irrespective of contact angles of droplet with the surface.

Predicting the rheological properties of emulsions is one of the most challenging and complicated problems in material and fluid sciences. Substantial complications in prediction of rheology arise due to the deformability and aggregation of emulsions. Thus a better understanding of deformation and aggregation of emulsions can lead to a better understanding of the shear thinning region of emulsions. Though numerous experimental and theoretical studies were performed to obtain rheological correlations of emulsions, their inability to visualize and understand the droplet deformation in the presence of large volume fractions has stagnated our understanding of the shear thinning behavior of emulsions. With the aid of a numerical tool, which can help in visualizing the droplet deformation and correlate it to rheological behavior of emulsions, we have made an attempt to understand the physics behind the shear thinning behavior and also predict its rheological characteristics for emulsions at different volume fractions. In this article, we try to obtain a theoretical understanding of the influence of deformation and de-aggregation of droplets on the emulsion rheology. Simulations performed in this article using a multi-component lattice Boltzmann model are used to quantify (a) relative viscosity of emulsions with change in shear rate, (b) relative viscosity of emulsions with change in time, (c) effect of deformation of droplets on the shear thinning region in emulsions, and (d) relative viscosity of emulsions with change in volume fraction.