Fingering instability of partially wetting evaporating liquids

A numerical study of the fingering instability of the leading edge of a film of evaporating partially wetting liquid flowing down an inclined solid substrate is presented. The effects of capillarity, gravity, disjoining pressure, and evaporation are included in the formulation of our lubrication-type model. The disjoining pressure is assumed to be a linear combination of two components to account for both van der Waals forces and electrostatic effects. Consistent with previously published results, evaporation has a stabilizing effect on fingering instability and can completely suppress the instability if the evaporation number, a nondimensional measure of evaporation intensity, is above a critical value. The critical evaporation number decreases as the inclination angle is decreased. Increasing the apparent contact angle by suitable changes in the disjoining pressure parameters, has a destabilizing influence on the contact line. Also investigated is the length of the fingers in the regime when the instability develops, and it is found that this length decreases as the evaporation number is increased.     

Marangoni-induced deformation of evaporating liquid films on composite substrates

Marangoni convection plays an important role in hydrodynamics of evaporating liquid films and sessile drops. Evaporation of liquid films induces unsteady nonuniform temperature distribution across the liquid layer and in a substrate. If the substrate is composed of parts with different thermal properties, the interface temperature distribution becomes non-uniform, leading to appearance of Marangoni stresses, convective vortices, and film deformation. In this article, a model describing evaporation, Marangoni effect and interface dynamics of liquid films on composite substrates is developed. The film dynamics is described in the framework of long-wave theory. The unsteady heat conduction in the substrate is described using the Laplace transform method for semi-infinite substrates and using the separation of variables technique for substrates of finite thickness. The non-uniformity of substrate thermal properties has a pronounced effect on film dynamics.     

Experimental Investigation of Pendant and Sessile Drops in Microgravity

The experiments regarding the contact angle behavior of pendant and sessile evaporating drops were carried out in microgravity environment. All the experiments were performed in the Drop Tower of Beijing, which could supply about 3.6 s of microgravity (free-fall) time. In the experiments, firstly, drops were injected to create before microgravity. The wettability at different surfaces, contact angles dependance on the surface temperature, contact angle variety in sessile and pendant drops were measured. Different influence of the surface temperature on the contact angle of the drops were found for different substrates. To verify the feasibility of drops creation in microgravity and obtain effective techniques for the forthcoming satellite experiments, we tried to inject liquid to create bigger drop as soon as the drop entering microgravity condition. The contact angle behaviors during injection in microgravity were also obtained.     

The shape and stability of wall-bound and wall-edge-bound drops and bubbles

The behavior of wall-bound drops and bubbles is fundamental to many natural and industrial processes. Key characteristics of such capillary systems include interface shape and stability for a variety of gravity levels and orientations. Significant solutions are in hand for axisymmetric pendent drops for a variety of uniform boundary conditions along the contact line with gravity acting normal to a planar wall. The special case of a wall-bound drop or bubble that is also pinned at an edge (i.e. a ‘wall-edge-bound’ drop) is considered here where numerical solutions are obtained for interface shape and stability as functions of drop volume, contact angle, fluid properties, and uniform gravity vector. For a semi-infinite zero-thickness planar wall (plate), a critical contact angle is identified below which wall-edge-bound drops are always stable. The critical contact angle is computed as a function of the gravity vector. The numerical procedure, which makes no account for contact angle hysteresis, predicts that such wall-edge-bound drops are unconditionally unstable for any gravity field with a component that is tangent to the wall while inwardly normal to the edge. Select experiments are conducted that support the conclusions drawn from the numerical results.     

Stability of sessile and pendant liquid drops

The solution space of axisymmetric liquid drops attached to a horizontal plane is investigated, and the stability of hydrostatic shapes is assessed by a novel numerical linear stability analysis involving discrete perturbations. For a given contact angle and Bond number, multiple interfacial shapes exist with compact, lightbulb, hourglass, and more convoluted pearly shapes. It is found that more than one solution branch can be stable, and that negative curvature at the contact line of a pendant drop is not a prerequisite for instability. Numerical simulations based on the boundary-integral method for Stokes flow illustrate the process of unstable drop detachment. Unstable drops transform into elongated threads with a spherical head whose volume is determined by a Bond number expressing the significance of surface tension. A complementary investigation of the shape and stability of two-dimensional drops attached to a horizontal or inclined plane reveals that hydrostatic shapes are least stable in the inclined configuration and most stable in the pendant or sessile configuration.     

Times of capture of moderately large nonvolatile aerosol particles by growing or evaporating drops

The time of the total clearing of particles from a given volume around growing or evaporating drops is calculated on the basis of the theory of motion of moderately large nonvolatile aerosol particles in binary gas mixtures which are nonuniform in temperature and concentration.     

Leidenfrost point for subheated drops

A theory of the heat-exchange crisis on a heated surface with drops evaporating on it is proposed. The critical temperature is found in the form of a function of the physical parameters, size, and initial subheating of the drops.     

Sessile Drop in Microgravity: Creation, Contact Angle and Interface

We present in this paper the results obtained from a parabolic flight campaign regarding the contact angle and the drop interface behavior of sessile drops created under terrestrial gravity (1g) or in microgravity (μg). This is a preliminary study before further investigations on sessile drops evaporation under microgravity. In this study, drops are created by the mean of a syringe pump by injection through the substrate. The created drops are recorded using a video camera to extract the drops contact angles. Three fluids have been used in this study : de-ionized water, HFE-7100 and FC-72 and two heating surfaces: aluminum and PTFE. The results obtained evidence the feasibility of sessile drop creation in microgravity even for low surface tension liquids (below 15 mN m^− 1) such as FC-72 and HFE-7100. We also evidence the contact angle behavior depending of the drop diameter and the gravity level. A second objective of this study is to analyze the drop interface shape in microgravity. The goal of the these experiments is to obtain reference data on the sessile drop behavior in microgravity for future experiments to be performed in an French-Chinese scientific instrument (IMPACHT).     

Effects of nonuniform heating and thermocapillarity in evaporating films falling down an inclined plate

Summary. The dynamics of a thin evaporating liquid film falling down an inclined plate is studied in the cases of both uniformly and nonuniformly heated plates. The film flow is influenced by gravity, mean surface tension, thermocapillary force and mass loss. The dynamics of the two-dimensional evaporating film is studied by the use of long-wavelength theory. Numerical solution of the evolution equation indicates that the evaporation has a strong stabilizing effect on the film instability and that a sequence of instability, stability and then instability of the falling film during its evaporation exists. The effect of nonuniform heating is dominant prior to film disappearance and it enforces film rupture. Due to the joint action of thermocapillarity and evaporating mass loss, the film evolution exhibits the formation of multi-hump structures, the downstream propagation of which is suppressed. When the nonuniformities in the imposed temperature differences are increased, large deformations of the liquid-vapor interface occur that lead to an enhancement of the heat transfer processes.     

Vapor-Liquid Steady Meniscus at a Superheated Wall: Asymptotics in an Intermediate Zone Near the Contact Line

The study concerns steady configurations of a perfectly wetting liquid in contact with its pure vapor and a superheated substrate/wall maintained at a constant temperature. Despite the perfect wetting, the system is characterized by a finite apparent contact angle formed at a microscale, within a steady microstructure of the contact line, the finiteness owing itself to an actually dynamic situation caused by the evaporation process. The angle is assumed to be small here, which is the case for sufficiently small superheats. When macroscopically treating a steady meniscus, one typically implies that the wall is met at the contact angle given by the microstructure. This remains somewhat an intuitive, heuristic approach unless a more rigorous asymptotic matching is carried out between the meniscus and the microstructure, which is accomplished in the present paper by studying an intermediate zone connecting these two regions. The analysis, based upon a standard one-sided planar model of an evaporating liquid layer in the lubrication approximation, confirms the validity of the mentioned approach. A possible uncertainty in the definition of the contact angle is shown to be small given that the macroscopic curvature (i.e. that of the meniscus and of the wall) is small on the scale of the contact line microstructure.     

Interactive simulation and visualization of massless, massed, and evaporating particles

Most software packages available for particle tracing focus on visualizing steady or unsteady vector fields by using massless particle trajectories. For many applications, however, the use of massed and evaporating particles would provide a model of physical processes that could be used in product testing or design. In this article we describe the TrackPack toolkit, which provides an integrated interface for computing massless, massed, and evaporating particle trajectories in steady flow. In all cases, we assume a noncoupled model and compute particle trajectories through an existing vector field by numerically integrating with forward Euler, fourth-order Runge-Kutta, or an analytic streamline calculation. The TrackPack software effort was motivated by an industrial application to model pollution control systems in industrial boilers. We briefly describe the project and the visualization environment, and we demonstrate the necessity for massed, evaporating models in the application.     

Mathematical modelling of dropwise condensation on textured surfaces

Vapor-to-liquid phase change in the form of discrete drops on or underneath a substrate is called dropwise condensation. The process is hierarchical in the sense that it occurs over a wide range of length and timescales. As the associated heat transfer coefficient is much higher than the film and mixed mode of condensation, it is of considerable interest in applications. The present study is focused on mathematical modelling of dropwise condensation process at multiple scales. The model includes formation of drops at the atomistic scale, droplet growth, coalescence, instability, slide off and fall-off, followed by fresh nucleation of liquid droplets. The model shows that the largest stable cluster size in the atomic model matches the minimum drop radius estimated from thermodynamic considerations. The minimum drop radius is insensitive to surface texturing and does not provide controllability at larger length and timescales. A closer examination of droplet distribution over the substrate reveals that small drops are locations of high heat transfer rates, which diminishes with increasing drop radius. The largest drop diameter depends on its stability and hence, the interfacial forces at phase boundaries. Therefore, drop instability controls the heat transfer coefficient in dropwise condensation. Enhancement of heat transfer necessitates that these drops grow with time, become unstable and be swept away as quickly as possible. Enhancement may be achieved either by (i) inclining the substrate or (ii) by creating an interfacial force at the three-phase contact line by a wettability gradient over the horizontal substrate, inducing drop motion. Wall heat transfer and shear stress under moving drops have been determined using a CFD model. A simple model of coalescence has been adopted in this work. Simulation studies on the effect of fluid properties, surface inclination and its wettability condition on drop size distribution, cycle time, heat transfer coefficient, and wall shear stress are comprehensively discussed in the present article.     

Numerical simulation of the head-on collision of two equal-sized drops with van der Waals forces

The head-on collision of two equal-sized drops in a hyperbolic flow is investigated numerically. An axisymmetric volume-of-fluid (VOF) method is used to simulate the motion of each drop toward a symmetry plane where it interacts and possibly coalesces with its mirror image. The volume-fraction boundary condition on the symmetry plane is manipulated to numerically control coalescence. Two new numerical methods have been developed to incorporate the van der Waals forces in the Navier–Stokes equations. One method employs a body force computed as the negative gradient of the van der Waals potential. The second method employs the van der Waals forces in terms of a disjoining pressure in the film depending on the film thickness. Results are compared to theory of thin-film rupture. Comparisons of the results obtained by the two methods at various values of the Hamaker constant show that the van der Waals forces calculated from the two methods have qualitatively similar effects on coalescence. A study of the influence of the van der Waals forces on the evolution and rupture of the film separating the drops reveals that the film thins faster under stronger van der Waals forces. Strong van der Waals forces lead to nose rupture, and small van der Waals forces lead to rim rupture. Increasing the Reynolds number causes a greater drop deformation and faster film drainage. Increasing the viscosity ratio slows film drainage, although the effect is small for small viscosity ratio.     

Sessile Drop Wettability in Normal and Reduced Gravity

This paper presents initial work performed to develop a database of contact angles of sessile drops in reduced gravity. Currently, there is no database of wettability of sessile drops in reduced gravity. The creation of such a database is imperative for continued investigations of heat and/or mass transfer in reduced gravity and future engineering designs. In this research, liquid drops of water and ethanol were created on aluminum and PTFE substrates. The formed drops were characterized by their dimensions including contact angle, wetted perimeter and droplet shape in both normal gravity and reduced gravity. The droplets were recorded during testing with high definition video and the images obtained digitally analyzed, post-test, to determine their characteristics as a function of the experimental parameters. The Queensland University of Technology (QUT) Drop Tower Facility was utilized for the reduced gravity experimentation. For droplets with diameters above their capillary length, the changes in drop dimensions and/or wettability was observed. The Young-Laplace equation was validated to accurately predict the contact angle in reduced gravity for small droplets, however it was not adequate to describe the contact angle for larger drops (above the drops associated capillary length).     

The effect of substrate surface roughness on the wettability of Sn-Bi solders

The effect of substrate surface roughness on the wettability of Sn-Bi solders is investigated by the eutectic Sn-Bi alloy on Cu/Al₂O₃ substrates at 190 °C. To engineer the surface with different roughnesses, the Cu-side of the substrates is polished with sandpaper with abrasive number 100, 240, 400, 600, 800, 1200, and 1 m alumina powder, respectively. Both dynamic and static contact angles of the solder drops are studied by the real-time image in a dynamic contact angle analyzer system (FTA200). During dynamic wetting, the wetting velocity of the solder drop decreases for the rougher surface. However, the time to reach the static contact angle seems to be identical with different substrate surface roughness. The wetting tip of the solder cap exhibits a waveform on the rough surface, indicating that the liquid drop tends to flow along the valley. As the solder drops reach a static state, the static contact angle increases with the substrate surface roughness. This demonstrates that the wettability of solders degrades as the substrates become rough.     

Drop spreading and drifting on a spatially heterogeneous film: capturing variability with asymptotics and emulation

A liquid drop spreading over a thin heterogeneous precursor film (such as an inhaled droplet on the mucus-lined wall of a lung airway) will experience perturbations in shape and location as its advancing contact line encounters regions of low or high film viscosity. Prior work on spatially one-dimensional spreading over a precursor film having a random viscosity field (Xu and Jensen, Proc R Soc A 472:20160270, 2016) has demonstrated how viscosity fluctuations are swept into a narrow region behind the drop’s effective contact line, where they can impact drop dynamics. In this paper, we investigate two-dimensional drops, seeking to understand the relationship between the statistical properties of the precursor film and those of the spreading drop. Assuming the precursor film is much thinner than the drop and viscosity fluctuations are weak, we use asymptotic methods to derive explicit predictions for the mean and variance of drop area and the drop’s lateral drift. For larger film variability, we use Gaussian process emulation to estimate the variance of outcomes from a restricted set of simulations. Stochastic drift of the droplet is predicted to be the greatest when the initial drop diameter is comparable to the correlation length of viscosity fluctuations.     

Controlling charge on levitating drops

Levitation technologies are used in containerless processing of materials, as microscale manipulators and reactors, and in the study of single drops and particles. Presented here is a method for controlling the amount and polarity of charge on a levitating drop. The method uses single-axis acoustic levitation to trap and levitate a single, initially neutral drop with a diameter between 400 microm and 2 mm. This drop is then charged in a controllable manner using discrete packets of charge in the form of charged drops produced by a piezoelectric drop-on-demand dispenser equipped with a charging electrode. The magnitude of the charge on the dispensed drops can be adjusted by varying the voltage applied to the charging electrode. The polarity of the charge on the added drops can be changed allowing removal of charge from the trapped drop (by neutralization) and polarity reversal. The maximum amount of added charge is limited by repulsion of like charges between the drops in the trap. This charging scheme can aid in micromanipulation and the study of charged drops and particles using levitation.     

Influence of Bond Number on Behaviors of Liquid Drops Deposited onto Solid Substrates

The problem of spreading behaviors of pendant and sessile drops was studied experimentally and numerically under the action of gravity force and surface tension. Bond number was considered to be a main factor of the influence on shape behaviors of liquid drops. This study was performed in the framework of an experimental investigation of drop behaviors in microgravity onboard a Chinese satellite in future. The experiments were carried out in the Drop Tower of Beijing, which could supply about 3.6?s of microgravity (free-fall) time. The surface shape change of liquid drops was investigated and the contact angle variety in sessile and pendant drops were measured from normal gravity to microgravity. A sharp decrease and oscillatory variation of the contact angle for both sessile and pendant drops were found with the sudden decrease of Bond number. The succedent comparison between experimental and numerical results suggests that Bond number has a significant influence on the drop contact angle. Additionally, the drop shapes and the bulk flows inside sessile and pendant drops were analyzed numerically, and it was found that the bulk flows could affect the free-surface shape of liquid drops apparently. Comparison of the moving velocity of contact line between sessile and pendant drops indicated that the pendant drops had a faster response to Bond number.     

Interception of two spherical drops in linear Stokes flow

A boundary-integral method is developed for computing the interception of two spherical drops with arbitrary radii and viscosities in infinite linear Stokes flow. At any instant, the flow is computed in a frame of reference with origin at the center of one drop, using a cylindrical polar coordinate system whose axis of revolution passes through the center of the second drop. Taking advantage of the axial symmetry of the interfaces in the drop coordinates, the problem is formulated as a system of integral equations for the zeroth, first, and second Fourier coefficients of the normal component of the jump in the interfacial traction and for the meridional and azimuthal components of the interfacial velocity with respect to the meridional angle. The integral equations are solved with high accuracy using a boundary-element method featuring adaptive boundary-element distribution and automatic time-step adjustment according to the interfacial gap. Simulations of two drops intercepting in uniaxial straining flow provide accurate data on the drop collision velocity and particle stress tensor for gaps as small as 10⁻⁴ times the drop radius. Simulations of two drops intercepting in simple shear flow confirm that slightly offset drops collide during the interception. Accurate data are presented for Batchelor’s relative mobility functions in linear Stokes flow used to describe the relative droplet motion.     

Dynamics of electrically charged transient evaporating sprays

The evolution of an evaporating spray plume typical of those under consideration for use in direct injection spark ignition (DISI) engines, for early and late fuel injection strategies is investigated. Here the effect of electric charge, present on individual drops, upon the spray dispersal and evaporation rate is investigated with the aim of optimizing these parameters with respect to typical engine timescales and injection strategy. The predictions suggest that applying electric charge to drops in sprays injected early into the intake stroke does not have a beneficial effect. The spray evaporation rate is not significantly enhanced, and the long time interval between fuel injection and ignition actually promotes spray wall deposition. Conversely, applying electric charge to sprays injected late encourages secondary atomization and the increase in surface area greatly improves the evaporation rate. This is also true at higher engine speeds, corresponding to a much reduced time between fuel injection and ignition. Therefore it is suggested that the selective use of electric charge is viable way of tuning the spray character without effecting fuel metering when moving from an early to a late injection strategy in DISI engines when variable loads are required. Copyright © 2006 John Wiley & Sons, Ltd.