Droplet Impact and Spreading on Inclined Surfaces.

Introducing surface inclination in the case of droplet impact on solid substrates results in complicated dynamics post impact. The present work investigates the dynamics involved in the spreading phase of the droplet on inclined substrates. Experiments are conducted with water droplets impinging on inclined dry solid substrates with varying wettability values. The results reveal the presence of three phases in the droplet spread behavior. In the first phase, the droplet is observed to depict a close radial symmetry and is dominated by inertia forces. Phase 1 ends when the upstream droplet lamella post impact gets pinned to the surface or starts retracting as a consequence of surface forces becoming dominant. A scaling analysis developed to predict the pinning time of the droplet shows that the pinning time is independent of impact velocity, which is also observed during experiments. The asymmetries in the radial evolution of the droplet appear in phase 2 and become dominant in phase 3. Phase 2 terminates when the droplet attains the maximum lateral spread, which is established as a function of the normal component of the Weber number. Phase 3 is initiated when the droplet starts retracting in the lateral direction while the longitudinal expansion continues. Using an energy-based model constructed to predict the maximum spread, we show that the impact inertia of the droplet controls the longitudinal droplet spread in phases 1 and 2, while the gravity forces are primarily responsible for the droplet spread in phase 3. The model results were validated with the experiments conducted in-house and were found to be in good agreement.

Capillary Displacement of Viscous Liquids in Geometries with Axial Variations.

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.

Lattice Boltzmann finite-difference-based model for fully nonlinear electrohydrodynamic deformation of a liquid droplet.

Electric field-induced flows involving multiple fluid components with a range of different electrical properties are described by the coupled Taylor-Melcher leaky-dielectric model. We present a lattice Boltzmann (LB)-finite difference (FD) method-based hybrid framework to solve the complete Taylor-Melcher leaky-dielectric model considering the nonlinear surface charge convection effects. Unlike the existing LB-based models, we treat the interfacial discontinuities using direction-specific continuous gradients, which prevents the miscalculation arising due to volumetric gradients without directional derivatives, simultaneously maintaining the electroneutrality of the bulk. While fluid transport is recovered through the LB method using a multiple relaxation time (MRT) scheme, the FD method with a central difference scheme is applied to discretize the charge transport equation at the interface, in addition to the electric field governing equations in the bulk and at the interface. We apply the developed numerical model to study the different regimes of droplet deformation due to an external electric field. Similar to the existing analytical and other numerical models, excluding the surface charge convection (SCC) term from the charge transport equation, the present methodology has shown excellent agreement with the existing literature. In addition, the effect of SCC in each of the regimes is analyzed. With the present numerical model, we observe a strong presence of SCC in the oblate deformation regime, contrary to the weak effect on prolate deformations. We further discuss the reason behind such differences in the magnitude of nonlinearity induced by the SCC in all the regimes of deformation.

A fully coupled hybrid lattice Boltzmann and finite difference method-based study of transient electrokinetic flows.

Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability.

Molecular dynamics simulations of nanoscale and sub-nanoscale friction behavior between graphene and a silicon tip: analysis of tip apex motion.

A sliding object on a crystal surface with a nanoscale contact will always experience stick-slip movement. However, investigation of the slip motion itself is rarely performed due to the short slip duration. In this study, we performed molecular dynamics simulation and frictional force microscopy experiments for the precise observation of slip motion between a graphene layer and a crystalline silicon tip. The simulation results revealed a hierarchical structure of stick and slip motion. Nanoscale stick and slip motion is composed of sub-nanoscale stick and slip motion. Sub-nanoscale stick and slip motion occurred on a timescale of a few ps and a force scale of 10(-1) nN. The relationship between the trajectories of the silicon tip and stick-slip peak revealed that in-plane and vertical motions of the tip provide information about stick and slip motion in the sub-nanoscale and nanoscale ranges, respectively. Parametric studies including tip size, scan angle, layer thickness, and flexibility of the substrate were also carried out to compare the simulation results with findings on lateral force microscopy.

Study for optical manipulation of a surfactant-covered droplet using lattice Boltzmann method.

In this study, we simulated deformation and surfactant distribution on the interface of a surfactant-covered droplet using optical tweezers as an external source. Two optical forces attracted a single droplet from the center to both sides. This resulted in an elliptical shape deformation. The droplet deformation was characterized as the change of the magnitudes of surface tension and optical force. In this process, a non-linear relationship among deformation, surface tension, and optical forces was observed. The change in the local surfactant concentration resulting from the application of optical forces was also analyzed and compared with the concentration of surfactants subjected to an extensional flow. Under the optical force influence, the surfactant molecules were concentrated at the droplet equator, which is totally opposite to the surfactants behavior under extensional flow, where the molecules were concentrated at the poles. Lastly, the quasi-equilibrium surfactant distribution was obtained by combining the effects of the optical forces with the extensional flow. All simulations were executed by the lattice Boltzmann method which is a powerful tool for solving micro-scale problems.

Effect of hydrodynamic and fluid-solid interaction forces on the shape and stability of a droplet sedimenting on a horizontal wall.

In this paper, we study the sedimentation of droplet onto horizontal surfaces using a Shan and Chen multicomponent lattice Boltzmann model [Shan and Chen, Phys. Rev. E 47, 1815 (1993)]. Numerical simulations are performed for static nonwetting droplets and are compared with a theoretical model. Further simulations are performed using wetting droplets and changing the wetting characteristics of the surface. Novel study of droplet sedimentation with different wetting characteristics of wall surface shows three different regimes of droplet shapes. The process of different regimes can be controlled by changing the wetting characteristics of surface. It is observed that the droplet attains nonequilibrium region as the attraction force of surrounding droplet with the wall increases. This can lead to eventual breakup of the droplet.

Two-phase numerical model for thermal conductivity and convective heat transfer in nanofluids.

Due to the numerous applications of nanofluids, investigating and understanding of thermophysical properties of nanofluids has currently become one of the core issues. Although numerous theoretical and numerical models have been developed by previous researchers to understand the mechanism of enhanced heat transfer in nanofluids; to the best of our knowledge these models were limited to the study of either thermal conductivity or convective heat transfer of nanofluids. We have developed a numerical model which can estimate the enhancement in both the thermal conductivity and convective heat transfer in nanofluids. It also aids in understanding the mechanism of heat transfer enhancement. The study reveals that the nanoparticle dispersion in fluid medium and nanoparticle heat transport phenomenon are equally important in enhancement of thermal conductivity. However, the enhancement in convective heat transfer was caused mainly due to the nanoparticle heat transport mechanism. Ability of this model to be able to understand the mechanism of convective heat transfer enhancement distinguishes the model from rest of the available numerical models.

Investigation of heat transfer in turbulent nanofluids using direct numerical simulations.

A numerical study has been performed by using a combined Euler and Lagrangian method on the convective heat transfer of Cu and Al2O3 nanofluids under the turbulent flow conditions. The effects of volume fraction of nanoparticles, nanoparticle sizes, and nanoparticle material are investigated. The mechanism of convective heat transfer enhancement in nanofluids has also been investigated, by studying the influence of particle dispersion and two-way interaction between fluid and particle temperature. The results show significant enhancement of heat transfer of nanofluids. The numerical data are compared with the correlation data of the experiments and reasonably good agreement is achieved.