Interfacial Balance Research Articles

Investigation of sessile droplet evaporation using a transient two-step moving mesh model

The evaporation of droplets on surfaces is a ubiquitous phenomenon essential in nature and industrial applications ranging from thermal management of electronics to self-assembly-based fabrication. In this study, water droplet evaporation on a thin quartz substrate is analyzed using an unsteady two-step arbitrary Lagrangian-Eulerian (ALE) moving mesh model, wherein the evaporation process is simulated during the constant contact radius (CCR) and contact angle (CCA) modes. The numerical model considers mass transfer in the gas domain, flow in the liquid and gas domains, and heat transfer in the solid, liquid, and gas domains. Besides, the model also accounts for interfacial force balance, including thermocapillary stresses, to obtain the instantaneous droplet shape. Experiments involving droplet evaporation on unheated quartz substrates agree with model predictions of contact radius, contact angle, and droplet volume. Model results indicating temperature and velocity distribution across an evaporating water droplet show that the lowest temperatures are at the liquid-gas interface, and a single vortex exists for the predominant duration of the droplet's lifetime. The temperature of the unheated substrate is also significantly reduced due to evaporative cooling. The interfacial evaporation flux distribution, which depends on heat transfer across the droplet and advection in the surrounding medium, shows the highest values near the three-phase contact line. In addition, the model also predicts evaporation dynamics when the substrate is heated and exposed to different advection conditions. Generally, higher evaporation rates result from higher substrate heating and advection rates. However, substrate heating and advection in the surrounding gas have minimal effects on the relative durations of CCR and CCA modes for a given receding contact angle. Specifically, in this case, a 40× increase in substrate heating rate or 7.5× increase in gas velocity can only change these relative durations by 3%. This study also highlights the importance of surface wettability, which affects evaporation dynamics for all the conditions explored by the numerical model.

Stability of interfacial thermal balance in thick β-Ga2O3 crystal growth by EFG

When n-type β-Ga2O3 crystals with large thickness are grown by edge-defined film-fed growth (EFG), fusing often occurs, due to the massive release of latent heat of crystallization and infrared absorption of crystals, which affects the integrality and quality of crystals. In order to solve this problem, a furnace structure with larger axial temperature gradient (from 17.40 K/mm to 27.46 K/mm) over the die was designed by ANSYS FLUENT software. Considering the interface thermal and the pressure balance of the meniscus, the relationship between the overheating temperature on the upper surface of the die and the pulling speed was calculated. It is found that the overheated fusing starts from the center of the crystal and then to the edge, which is consistent with the actual growth of the crystal. The pulling speed of 20 mm/h was selected for the growth experiment. Through the optimization of thermal field environment and the selection of pulling speed, high-quality two-inch β-Ga2O3 crystals without overheat fusing was realized. This work provides more help for understanding β-Ga2O3 crystal growth by EFG.

Analyzing the surfactant classification confusion through the HLD formulation equation

The qualitative presentation from Winsor on an interfacial balance of interactions between the surfactant and the oil and water phases has been transformed into a multivariable linear equation so-called hydrophilic-lipophilic deviation (HLD). This relation involves at least 6 independent variables (surfactant head and tail specifications, water salinity, oil nature, temperature, and pressure) with a MacLaurin series first order approximation, i.e., a linear multivariable expression. After 40 years of practical experience, it can be said that the HLD relation matches well the experimental data, with only very few exceptions with complex mixtures. Herein, we clear the confusion concerning the meaning and the mathematical handling of the surfactant parameter in the HLD equation. We start with a presentation of simple surfactant systems with only 4 parameters (water salinity, oil nature, surfactant nature, and temperature) as was done 40 years ago. Later, we present a critical discussion on the surfactant term, concerning binary surfactant systems, and on strategies for applications in ternary surfactant mixtures. We have found that the surfactant parameters can only be compared in a series of surfactants with the same head group, where the surfactant parameter is a linear function of the surfactant tail length.

The effects of material properties on solute transport during entrapment of a bubble subject to horizontal solidification

Solute transport in the presence of a pore resulting from an entrapped bubble during horizontal solidification of water containing carbon dioxide is numerically and parametrically investigated. Structural material containing pores degrade microstructure, whereas materials with pores can also be functionally used to enhance efficiencies of engineering, foods and biomedical industries, and control outcome of geophysics and global warming, etc. In this study, transport equations including mass, momentum, energy and concentration transport equations satisfied by their interfacial balances between liquid, gas pore, and solid were solved with the COMSOL commercial computer code. Extending previous work dealing with influence of fluid flow, the present results further find that the effects of metallurgical and thermal properties on solute transport processes during entrapment of a bubble. Decreases in Henry's law constant, partition coefficient and liquid solute diffusivity, and increases in solid thermal conductivity increase solute concentration in solid around an entrapped pore. Predicted contact angle during solidification is in good accordance with computed analytical results confirmed by measured data. The findings of this study can help for better understanding of pore formation in the solid during horizontal solidification.

A dual lithiated alloy interphase layer for high-energy–density lithium metal batteries

Lithium metal batteries represent potential candidates for high-energy–density batteries. However, non-uniform Li deposition and dendrite growth limit the practical applications of Li anodes in solid-state and liquid-phase battery systems. This report investigates the conversion mechanism of an aluminum coordination compound (Al(MMP)3) at the interface of a lithium metal anode. Based on the proposed mechanism, a novel dual alloy comprising a LixAl-LixP hybrid interphase is designed to promote interfacial charge balance. Under the synergic effect of a fluoropolymer, the organic/inorganic protective layer containing the dual lithiated alloy exhibits short-term Li storage and rapid Li+ transport, thereby limiting the accumulation of inactive lithium and decreasing the Li+ migration barrier. Upon implementing the hybrid anode, the electrochemical life span of the Li metal battery exceeds 2000 h. Moreover, pairing with a Ni-rich cathode leads to excellent capacity retention and stable coulomb efficiency. The developed strategy can guide future advancements in lithium metal batteries with long cycle lives.

Transport processes for a bubble entrapment during horizontal solidification

Transport processes coupling with shape development of a bubble captured by a solidification front advancing in a horizontal direction are numerically studied. Porosity in solid plays important roles on microstructure of materials and functional materials in biology, tissue, MEM, micro- or nano-engineering, foods, and geophysics, etc. In view of significant force torque, pore shape development during horizontal solidification is more significant than that during vertical solidification. In this work, transport equations of fluid flow, energy and concentration with sources governing interfacial balance of momentum, energy and concentration in the presence of a bubble entrapped by the solidification front were solved by the commercial COMSOL computer code. The results find the pore shape development affected by velocity, pressure and concentration fields for different gravity forces and flow boundary conditions. Prediction of contact angle agrees with that from Abel's equation during solidification, previously confirmed by experimental data. Controlling pore formation in solid via selecting different gravitational acceleration or ambient pressure and flow boundary conditions can therefore be achieved.

Solute segregation due to a bubble entrapped as a pore in solid during unidirectional solidification

Solute segregation of carbon dioxide in water during entrapment of a bubble by a solidification front is numerically investigated. The bubble can be initiated by supersaturation ahead of the solidification front. Porosity influences not only microstructure of materials, but also formation of functional materials in biology, engineering, foods, and geophysics, and so on. The model was proposed in a previous work accounting for conservation equations with interfacial balances of mass, momentum, energy and concentration. Using commercial COMSOL computer code, this study further finds that different solute distributions in liquid and solid in the presence of an entrapping bubble can be attributed to solute diffusivity of liquid and partition coefficient. A high solute diffusivity of liquid enhances solute diffusion away from the pore along the solidification front, leading to negligible solute transport from liquid to solidification front, whereas a low solute diffusivity of liquid gives rise to significant solute transport from the solidification front to liquid. A decrease in solute diffusivity of liquid or partition coefficient therefore results in high solute accumulation and a high concentration region covering liquid and solid in a triangle shape near the triple-phase line. In contrast to exponential decrease for a high solute diffusivity of liquid, radial variation of solute concentration in solid in the vicinity of pore jumps to high value through the high concentration region and maintains relative constant for a low diffusivity of liquid. Solute concentration in solid significantly decreases as solute diffusivity of liquid or partition coefficient increases. Predicted contact angle agree with solutions of Abel's equation of the first or second kind. This work is critical to understand solute segregation induced by formation of a pore in solid.

Electrical switching of a surfactant coated drop in Poiseuille flow

Electrical effects can impart a cross-stream component to drop motion in a pressure-driven flow, due to either an asymmetric charge distribution or shape deformation. However, surfactant-mediated alterations in such migration characteristics remain unexplored. By accounting for three-dimensionality in the drop motion, we analytically demonstrate here a non-trivial switching of drop migration with the aid of a surfactant coating on its surface. We establish this phenomenon as controllable by exploiting an interconnected interplay between the hydrodynamic stress, electrical stress and Marangoni stress, manifested so as to achieve a net interfacial force balance. Our results reveal that under different combinations of electrical conductivity and permittivity ratios, the relative strength of the electric stress with respect to the hydrodynamic stress, the applied electric field direction and the surfactants alter the longitudinal and cross-stream velocity components of the droplets differently. The effect of drop deformation on its speed is found to be altered with the increased sensitivity of the surface tension to the surfactant concentration, depending on the competing effects of the electrohydrodynamic flow modification and the tip stretching phenomenon. Further, with a suitable choice of electrical property ratios, the Marangoni effects can be exploited to direct the drop in reaching a final transverse position towards or away from the channel centreline. These results may turn out to be of immense consequence in providing an insight to the underlying complex physical mechanisms dictating an intricate control on the drop motion in different directions.

Relationship of nanostructure and thermo-chemical response/thermal ablation of carbon aerogels

ABSTRACTIn this work, the interfacial mass balance relations combined with the non-parametric kinetic (NPK) analysis results were used for evaluating the thermo-chemical ablation process and oxidation mechanism of carbon aerogels with various porous structure. It was found that the two-parameter model of Nomen–Sempereis was able to describe the kinetics of the oxidation reaction and to reveal the structure-dependent contribution of two main processes with chemical and physical nature. The porosity of the carbon aerogel, rather than the other microstructural features, was realized more effective on the rate of ablation.

Collective Cell Migration in Embryogenesis Follows the Laws of Wetting

Collective cell migration is a fundamental process during embryogenesis and its initial occurrence, called epiboly, is an excellent in vivo model to study the physical processes involved in collective cell movements that are key to understanding organ formation, cancer invasion, and wound healing. In zebrafish, epiboly starts with a cluster of cells at one pole of the spherical embryo. These cells are actively spreading in a continuous movement toward its other pole until they fully cover the yolk. Inspired by the physics of wetting, we determine the contact angle between the cells and the yolk during epiboly. By choosing a wetting approach, the relevant scale for this investigation is the tissue level, which is in contrast to other recent work. Similar to the case of a liquid drop on a surface, one observes three interfaces that carry mechanical tension. Assuming that interfacial force balance holds during the quasi-static spreading process, we employ the physics of wetting to predict the temporal change of the contact angle. Although the experimental values vary dramatically, the model allows us to rescale all measured contact-angle dynamics onto a single master curve explaining the collective cell movement. Thus, we describe the fundamental and complex developmental mechanism at the onset of embryogenesis by only three main parameters: the offset tension strength, α, that gives the strength of interfacial tension compared to other force-generating mechanisms; the tension ratio, δ, between the different interfaces; and the rate of tension variation, λ, which determines the timescale of the whole process.

Pressure-driven liquid-liquid separation in Y-shaped microfluidic junctions

On-chip phase separation of multiphase microflows at the divergence point of Y-shaped microfluidic junctions is an effective way for integrating continuous microstructured devices. In this study, flow pattern maps of various solvent pairs based on the volumetric flow rates of both phases have been drawn experimentally and compared with numerical prediction to investigate the effective domain for which complete phase separation occurred. Furthermore, sufficient separation of aqueous and organic phases at the end of the microchannel was achieved by controlling the pressure difference at the liquid-liquid interface via loading back-pressure on the organic phase. A mathematical model based on interfacial pressure balance was derived. It was found that organic phase outlet tube should be kept between the upper and lower values calculated from the model. Only narrow discrepancy between the model and experimental observation can be seen in using viscous organic solvents.

Triple-layer configuration for stable high-speed lubricated pipeline transport

A novel methodology for efficient transport of heavy oil via a core-annular flow using a viscoplastic fluid is presented. In this triple layer structure, the viscoplastic fluid acts as an intermediate shaped skin layer to eliminate interfacial instability and balance buoyancy of the core fluid.

Continuous bodies with thermodynamically active singular sharp interfaces

The subject of this comprehensive study is the general (mathematical) modeling of sharp (i.e. two-dimensional) interfaces without and with their own thermodynamical activity. We provide essential tools for the modeling of body-interface systems. Important items of the kinematics of singular (moving) interfaces as well as balance equations at interfaces will be addressed. Problems connected with material representation will be discussed. Special interfacial balances for mass, impulse, angular momentum, energy, mass of a tracer and of entropy will be considered including the discussion of special cases. As an illustrative example, a continuous model for a body with loss of material (e.g. due to mechanical treatment) will be developed in the framework presented.

Tumour angiogenesis as a chemo-mechanical surface instability.

The hypoxic conditions within avascular solid tumours may trigger the secretion of chemical factors, which diffuse to the nearby vasculature and promote the formation of new vessels eventually joining the tumour. Mathematical models of this process, known as tumour angiogenesis, have mainly investigated the formation of the new capillary networks using reaction-diffusion equations. Since angiogenesis involves the growth dynamics of the endothelial cells sprouting, we propose in this work an alternative mechanistic approach, developing a surface growth model for studying capillary formation and network dynamics. The model takes into account the proliferation of endothelial cells on the pre-existing capillary surface, coupled with the bulk diffusion of the vascular endothelial growth factor (VEGF). The thermo-dynamical consistency is imposed by means of interfacial and bulk balance laws. Finite element simulations show that both the morphology and the dynamics of the sprouting vessels are controlled by the bulk diffusion of VEGF and the chemo-mechanical and geometric properties at the capillary interface. Similarly to dendritic growth processes, we suggest that the emergence of tree-like vessel structures during tumour angiogenesis may result from the free boundary instability driven by competition between chemical and mechanical phenomena occurring at different length-scales.

A CSF-SPH method for simulating drainage and imbibition at pore-scale resolution while tracking interfacial areas

We present a conservative smoothed particle hydrodynamics (SPH) model to study the flow of multiple, immiscible fluid phases in porous media using direct pore-scale simulations. Particular focus is put on continuously tracking the evolution of interfacial areas, which are considered to be important morphological quantities affecting multiphase transport in porous media. In addition to solving the Navier–Stokes equations, the model accounts for the effects of capillarity at interfaces and contact lines. This is done by means of incorporating the governing interfacial mass and momentum balances using the continuum surface force (CSF) method, thus rendering model calibration routines unnecessary and minimizing the set of constitutive and kinematic assumptions. We address the application of boundary conditions at rigid solid surfaces and study the predictive capability of the model as well as optimal choices for numerical parameters using an extensive model validation procedure. We demonstrate the applicability of the model to simulate multiphase flows involving partial wettability, dynamic effects, large density ratios (up to 1000), large viscosity ratios (up to 100), as well as fragmentation and coalescence of fluid phases. The model is used to study the evolution of fluid–fluid interfacial areas during saturation-controlled primary drainage and main imbibition of heterogeneous pore spaces at low capillary numbers. A variety of pore-scale effects, such as wetting phase entrapment and fragmentation due to snap-off, are observed. Specific fluid–fluid interfacial area is observed to monotonically increase during primary drainage and hysteretic effects are apparent during main imbibition.

On the Modeling and Simulation of Reaction-Transfer Dynamics in Semiconductor-Electrolyte Solar Cells

The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. In this work, we propose a macroscopic mathematical model, a system of nonlinear partial differential equations, for the complete description of charge transfer dynamics in such systems. The model consists of a reaction-drift-diffusion-Poisson system that models the transport of electrons and holes in the semiconductor region and an equivalent system that describes the transport of reductants and oxidants, as well as other charged species, in the electrolyte region. The coupling between the semiconductor and the electrolyte is modeled through a set of interfacial reaction and current balance conditions. We present some numerical simulations to illustrate the quantitative behavior of the semiconductor-electrolyte system in both dark and illuminated environments. We show numerically that one can replace the electrolyte region in the system with a Schottky contact only when the bulk reductant-oxidant pair density is extremely high. Otherwise, such replacement gives significantly inaccurate description of the real dynamics of the semiconductor-electrolyte system.

Hydrophilic/hydrophobic surface pattern design for oil repellent function in water

Oil droplets on a hydrophilic surface are easier to remove than that on a hydrophobic surface in water due to the difference in interfacial force balances. Properly designed hydrophilic/hydrophobic pattern promotes the motion of droplet contact line which leads to self-cleaning surface. This study aims to discuss the surface design in addition to the measurement of oil droplet adhesion force. It was found that star-like hydrophobic pattern propels oil droplet better than dot or rectangular pattern with the help of directional force component. Finally, proper specification was discussed based on the experiments.

EXPERIMENTAL INVESTIGATION ON BEHAVIORS AND HEAT TRANSFER IN SHEAR-DRIVEN LIQUID FILM FLOW

Experimental investigation on heat transfer characteristics of shear-driven liquid film in co-current gas flow is presented at different heat fluxes up to 300 kW/m2, gas Reynolds numbers up to 3175, liquid film Reynolds numbers of 27.6 − 75.7 and inlet liquid temperatures of 25, 40, and 80° C. Water and nitrogen are used as test liquid and gas, respectively. The heated section is a rectangular duct with 30 mm in width and 5 mm in height. The heated length is 100 mm divided into 10 segments in the flow direction by the structure of thermally insulated, which makes possible the evaluation of local heat transfer coefficients. The unexpected initiation of liquid film rupture at the upstream edge of heated section is observed under some combinations of heat fluxes and inlet liquid temperatures. In addition, the decrease in the width of dry area towards the downstream is observed with increasing interfacial temperature. The local heat transfer coefficient is increased towards the downstream because of the reduction of liquid film thickness by the enhanced interfacial shear stress exerted by the increased gas flow rate due to the evaporation, while it is decreased by the extension of dry area with increasing gas Reynolds number. A simple analysis for the interfacial force balance of the shear stresses in liquid and gas phases and the thermocapillary stress is performed to confirm the importance of thermocapillary force on the behaviors of liquid film. The variation of surface tension with temperature plays an important role in the liquid film behaviors and the corresponding heat transfer.

Calculation of contact angles at triple phase boundary in solid oxide fuel cell anode using the level set method

A level set method is applied to characterize the three dimensional structures of nickel, yttria stabilized zirconia and pore phases in solid oxide fuel cell anode reconstructed by focused ion beam-scanning electron microscope. A numerical algorithm is developed to evaluate the contact angles at the triple phase boundary based on interfacial normal vectors which can be calculated from the signed distance functions defined for each of the three phases. Furthermore, surface tension force is estimated from the contact angles by assuming the interfacial force balance at the triple phase boundary. The average contact angle values of nickel, yttria stabilized zirconia and pore are found to be 143°–156°, 83°–138° and 82°–123°, respectively. The mean contact angles remained nearly unchanged after 100hour operation. However, the contact angles just after reduction are different for the cells with different sintering temperatures. In addition, standard deviations of the contact angles are very large especially for yttria stabilized zirconia and pore phases. The calculated surface tension forces from mean contact angles were close to the experimental values found in the literature. Slight increase of surface tensions of nickel/pore and nickel/yttria stabilized zirconia were observed after operation. Present data are expected to be used not only for the understanding of the degradation mechanism, but also for the quantitative prediction of the microstructural temporal evolution of solid oxide fuel cell anode.

Interfacial stress balances in structured continua and free surface flows in ferrofluids

Interfacial linear and internal angular momentum balances are obtained for a structured continuum and for the special case of a ferrofluid, a suspension of magnetic nanoparticles in a Newtonian fluid. The interfacial balance equations account for the effects of surface tension and surface tension gradient, magnetic surface excess forces, antisymmetric stresses, and couple stresses in driving interfacial flows in ferrofluids. Application of the interfacial balance equations is illustrated by obtaining analytical expressions for the translational and spin velocity profiles in a thin film of ferrofluid on an infinite flat plate when a rotating magnetic field is applied with axis of rotation parallel to the ferrofluid/air interface. The cases of zero and non-zero spin viscosity are considered for small applied magnetic field amplitude. Expressions for the maximum translational velocity, slope of the translational velocity profile at the ferrofluid/air interface, and volumetric flow rate are obtained and their use to test the relevance of spin viscosity and couple stresses in the flow situation under consideration is discussed.