Drop Motion Research Articles

Gold Drop Formation and Motion over a Si(111) Substrate: Monte Carlo Simulation

Gold Drop Formation and Motion over a Si(111) Substrate: Monte Carlo Simulation

Study of the trapping mechanism of merging drops moving under thermocapillary migration on a surface with wettability contrast

Trapping of drops due to wettability contrast in porous materials emerges in a variety of subsurface and manufacturing applications. In carbon capture and storage, carbon dioxide must be trapped in order to avoid its release into the atmosphere, while trapped oil must be displaced. Both carbon dioxide and oil can exist as drops in porous media. The migration of a single drop attached to a wall can be hindered if the wall surface has a different wettability. However, the trapping condition becomes more complicated in the presence of two or more drops. In this work, we aim to study the trapping mechanism during thermocapillary migration of a merging drop on a heterogeneous surface. To do so, numerical simulations have been performed using the Front-Tracking/Finite Volume Method, where the Navier-Stokes equations are coupled with the conservation equations. The generalized Navier boundary condition (GNBC) has been used as the slip model to remove the viscous singularity. The combined finite-volume and tracking method is able to deal with different types of discontinuities in compressible or incompressible fluid flows, as e.g., interfaces. The material properties of the drop and the ambient fluid are different, and surface tension depends on the temperature. The results have shown that there exist three regimes characterizing the motion of merging drops, including the passage of the leading drop, the trapping of the merging drop, and the partial trapping, which correspond to the trapping of the leading drop but the passage of the merging drop. We show that there is a critical wettability contrast at which the merging drop gets trapped. The effects of Marangoni number (Ma) and viscosity ratio are investigated. The critical wettability contrast decreases with the increase of Ma number and the regime shift as a function of the viscosity and Marangoni number. These findings have implications for the design of geological carbon dioxide storage, improvement of oil recovery and microfluidic device development.

3D trajectories and velocities of rainfall drops in a multifractal turbulent wind field

Abstract. Weather radars measure rainfall in altitude, whereas hydro-meteorologists are mainly interested in rainfall at ground level. During their fall, drops are advected by the wind, which affects the location of the measured field. The governing equation of a rain drop's motion relates the acceleration to the forces of gravity and buoyancy along with the drag force. It depends non-linearly on the instantaneous relative velocity between the drop and the local wind, which yields complex behaviour. Here, the drag force is expressed in a standard way with the help of a drag coefficient expressed as a function of the Reynolds number. Corrections accounting for the oblateness of drops greater than 1–2 mm are suggested and validated through a comparison of the retrieved “terminal fall velocity” (i.e. without wind) with commonly used relationships in the literature. An explicit numerical scheme is then implemented to solve this equation for a 3+1D turbulent wind field, and hence analyse the temporal evolution of the velocities and trajectories of rain drops during their fall. It appears that multifractal features of the input wind are simply transferred to the drop velocity with an additional fractional integration whose level depends on the drop size, and a slight time shift. Using an actual high-resolution 3D sonic anemometer and a scale invariant approach to simulate realistic fluctuations of wind in space, trajectories of drops of various sizes falling form 1500 m are studied. For a strong wind event, drops located within a radar gate in altitude during 5 min are spread on the ground over an area of the size of a few kilometres. The spread for drops of a given diameter is found to cover a few radar pixels. Consequences on measurements of hydro-meteorological extremes that are needed to improve the resilience of urban areas are discussed.

On the determination of critical micelle concentration of partially dissociated ionic surfactants using contact angle data

The contact angle (CA) data has been utilized for determining the critical micelle concentration (cmc) of fully dissociated surfactant SDS, but not for nonionic surfactants Triton X-100 and C12E6 [Thu et al., J.Mol.Liq (2019) 111582]. Could this approach work for a partially dissociated ionic surfactant such as dodecyltrimethylammonium bromide (DTAB)? To verify this, this work studied the evaporation process of DTAB(aq) solution drops on parafilm. The relaxations of CA, wetting diameter, and drop volume were recorded during evaporation to determine the advancing/receding (θa and θr) CA’s. The data revealed that the breakpoints of θa and θr matched well with the cmc from the ST data; thereby, confirming that the aforementioned approach is viable for a partially dissociated ionic surfactant. Additional examination of the relaxation data and drop profiles revealed that the movement of a solution drop’s triple line (pinning-depinning behavior) during the evaporation process is primarily dependent on the localized surface morphology.

Effect of Contact Angle Hysteresis on Evaporation Dynamics of a Sessile Drop on a Heated Surface

Contact angle hysteresis (CAH) is a significant factor affecting the drop motion on solid substrates. A model of CAH is introduced to explore the influence of CAH on the dynamics of a sessile drop on a uniformly heated surface, and a two-dimensional evolution equation of the drop thickness is established using the lubrication approximation and Navier slip boundary conditions. A numerical simulation is performed to examine the dynamic behaviors of an evaporating drop, and the drop profile, contact angle, contact line, and moving speed are investigated. Simulated results indicate that the drop evolution process involves drop spreading, pinning, and depinning of the contact line. In the drop spreading stage, when the hysteresis angle increases, the spreading period is shortened, and the spreading radius and spreading speed are reduced; in contrast, the pinning period is raised, and the mass of the drop is apparently reduced with increasing hysteresis angle. In the depinning stage, the CAH declines the contact angle, and a flatter pattern is evolved, thereby improving the heat transfer performance, promoting drop evaporation, and shortening the depinning time. The presence of CAH can speed up the drying of the drop, and the large hysteresis angle leads to faster evaporation. Regulating the CAH is an effective way to manipulate the motion of the contact line for an evaporating drop.

Dust control efficiency improvement

High dustiness of operating space in coal mines and active methane emission detains faster driving of coal production and weakens competitive ability of coal mines. From the physical research of inertia movement of rotation liquid drops, the mathematical model of the circulation in the gas environment is constructed to develop more effective dust catching techniques. It is proved that the equation of fluid whirl diffusion in motion of a liquid drop along a spiral line is identical to the equation of thermal conductivity with dispersion coefficient of liquid drop rotation energy. It is confirmed that circulation of liquid drops, both in super Stokes and Stokes flows, enlarges the relaxation time owing to reduction in aerodynamic drag factor of the gas environment, conditioned by the increase in the effective value of the Reynolds number with the increased rotational velocity of liquid drops. The averaging of the aerodynamic drag factors of liquid drop movement allows using the obtained formulas for calculating  hydraulic vortex coagulation in a wide range of the Reynolds number, 1 < Re < 104. For enhancing energy of high-head hydraulic dedusting, the mathematical model and technology of hydro-vortex dust collection are proposed. The similarity criteria and indicators of the hydro-vortex dust collection efficiency are obtained. The experiments prove that dedusting efficiency depends not on the fluid flow rate but on the energy of dynamic head of liquid drops and on their dispersion degree. The hydro-vortex dust collection technique allows enhancing the dust control efficiency up to 99 % owing to the increased rotational velocity of liquid drops.

Drop motion during mass transfer accompanied by interphase convection

The article deals with the experimental study of the mass transfer of acetic acid from the dispersed phase (butyl acetate) to the continuous phase (water). The experiments were carried out on a laboratory column with single floating drops. The presence of the Marangoni effect during the movement of drops and its influence on the trajectories of movement of drops and the kinetics of mass transfer during extraction are shown. The influence of the Marangoni effect is most clearly observed when the driving force of the process is 0.1...0.2 mol/l.

Drops with circular stagnation lines: combined effects of viscoelastic and inertial forces on drop shape

For viscoelastic drops falling through Newtonian fluids it is well known that, on increasing the elastic properties of the interior phase, the drop will lose its sphericity and form a dimple at the trailing end. Here we analytically determine the flow distribution around and inside a viscoelastic droplet falling within a low inertia regime. We use these solutions to theoretically investigate the motion and deformation of viscoelastic drops. The reliability of the analytical solution is confirmed with dedicated experiments which show a reasonable agreement between the two approaches. We then extend our analytical work and show that as the size of the viscoelastic drop is increased, the stagnation points at both the trailing and leading sides of the drop expand to create a region of elongational dominated flows. As the size of drop is increased further, this elongational region splits to form an additional circular stagnation line that appears on the trailing and leading sides of the drop surface in the external field. These, newly found, kinematic changes around the drop surface are shown to underpin the shape transformation, that is the appearance of both dimple and cusps, of falling viscoelastic drops.

An energy-conservative many-body dissipative particle dynamics model for thermocapillary drop motion

The thermocapillary motion of a drop on a solid substrate is a common phenomenon in daily life and many industrial fields. The motion can be significantly affected by the temperature gradient of the substrate and the properties of the liquid, such as surface tension, viscosity, thermal coefficient, density, and diffusivity. In this study, a numerical model based on modified many-body dissipative particle dynamics was developed to capture correctly the temperature dependence of a fluid. The momentum, thermal diffusivity, viscosity, and surface tension of liquid water at various temperatures ranging from 273 to 373 K were used as examples to verify the proposed model. The results calculated with this model for heat conduction in a liquid–solid system are in good agreement with those calculated with Fourier's law. The approach successfully modeled the thermocapillary motion of a liquid water droplet on a hydrophobic substrate with a temperature gradient. The migration of the droplet on a flat solid substrate was induced by the difference in surface tension due to the temperature gradient. The migration velocity increased with the temperature difference, which is in agreement with the present theoretical analysis and dynamic van der Waals theory. The modified numerical model proposed in this work could be used to study heat and mass transfer across a free interface, such as Marangoni convection in multiphase fluid flow.

Spontaneous charging affects the motion of sliding drops

Water drops moving on surfaces are not only an everyday phenomenon seen on windows but also form an essential part of many industrial processes. Previous understanding is that drop motion is dictated by viscous dissipation and activated dynamics at the contact line. Here we demonstrate that these two effects cannot fully explain the complex paths of sliding or impacting drops. To accurately determine the forces experienced by moving drops, we imaged their trajectory when sliding down a tilted surface, and applied the relevant equations of motion. We found that drop motion on low-permittivity substrates is substantially influenced by electrostatic forces. Our findings confirm that electrostatics must be taken into consideration for the description of the motion of water, aqueous electrolytes and ethylene glycol on hydrophobic surfaces. Our results are relevant for improving the control of drop motion in many applications, including printing, microfluidics, water management and triboelectric nanogenerators.

Oscillatory motion of viscoelastic drops on slippery lubricated surfaces

The introduction of slippery lubricated surfaces allows for the investigation of the flow of highly viscous fluids, which otherwise will hardly move on standard solid surfaces. Here we present the study of the gravity induced motion of small drops of polymeric fluids deposited on inclined lubricated surfaces. The viscosity of these fluids decreases with increasing shear rate (shear thinning) and, more importantly, they exert normal forces on planes perpendicular to shear directions (elasticity). Despite the homogeneity of the surface and of the fluids, drops of sufficiently elastic fluids move downward with an oscillating instantaneous speed whose frequency is found to be directly proportional to the average speed and inversely to the drop volume. The oscillatory motion is caused by the formation of a bulge at the rear of the drop, which will be dragged along the drop free contour by the rolling motion undergone by the drop. This finding can be considered as a kind of new Weissenberg effect applied to moving drops that combines dynamic wetting and polymer rheology.

Weakly nonlinear shape oscillations of a Newtonian drop

Nonlinear axisymmetric shape oscillations of a Newtonian drop in a vacuum are investigated theoretically, for fundamental interest and for their relevance in transport processes across the drop surface. The weakly nonlinear analysis is carried out for, but not limited to, the modes of initial drop deformation up to m = 4. The drop Ohnesorge number covers the range between 0.01 and 1. The weakly nonlinear approach, which is carried to third order, accounts for the coupling of different oscillation modes. With increasing surface deformation, the oscillations develop an asymmetry of the times during one period the drop spends in different states of deformation, a frequency decrease below the linear value, and quasi-periodicity of the motion. In contrast to the inviscid case [D. Zrnić and G. Brenn, “Weakly nonlinear shape oscillations of inviscid drops,” J. Fluid Mech. 923, A9 (2021)], the present analysis reveals the frequency decrease and the quasi-periodicity already in the second-order approximation. The results are positively validated against relevant literature. The theory quantifies the effects of viscosity, measured by the drop Ohnesorge number, dampening the nonlinear behavior and enhancing the coupling of different oscillation modes [E. Becker et al., “Nonlinear dynamics of viscous droplets,” J. Fluid Mech. 258, 191 (1994)]. The present theory reveals the quasi-periodicity of nonlinear viscous drop shape oscillations at strong deformation. The resultant drop motion, starting from a higher-order mode of initial deformation, for which the drop exhibits aperiodic linear behavior, may turn into damped oscillatory with ongoing time due to the coupling to lower-order modes.

Effect of mask-film properties on the initial GaAs nanowire growth stages

The initial self-catalyze GaAs nanowire (NW) growth stages were studied using Monte Carlo simulation. We analyzed the effect of the mask-film etching rate with liquid gallium for different thicknesses on the initial nanowire formation stages. At a high etching rate NWs do not form on thick mask-films. A high etching rate of a thin film-mask can lead to lateral Ga drop motion over the crystalline substrate surface, which delays the nanowire formation onset. It is shown that, for the NW formation, it is necessary to maintain the correct ratio between the film thickness, etching rate, Ga and As2 flux intensities.

Dynamic characteristics of drops on tilted hydrophobic ratchet surfaces

Asymmetric ratchet surfaces are used to manipulate drops, which have received extensive attention due to their wide potential applications. In this study, using aluminum sheets as substrates, some hydrophobic ratchet surfaces with different geometric parameters were prepared. The dynamic behavior of drops in the initial movement stage on the tilted surfaces was captured by a high-speed camera. Compared with the behavior on the flat tilted aluminum sheet, the velocity and acceleration of the drop on the tilted ratchet surfaces exhibit non-linear characteristics. The forces acting on the drop were analyzed, and a theoretical model was proposed to elucidate the dynamic behavior, which was in agreement with the experimental results. Moreover, by changing the tilt angle of the substrate, the geometric parameters of ratchets and the size of the drops, the factors that affect the drop movement were investigated.

Chemical design of self-propelled Janus droplets

Chemical design of self-propelled Janus droplets

Self-Moving blooming drops of dimethyl sulfoxide containing benzyne intermediate for solutal transport

Drop motion can be achieved on surfaces with low to negligible contact angle hysteresis. The droplets can be made to move under the influence of an external force or droplets can show self-propelled motion. The studies on drop motion are crucial for the design and application of surfaces for controlling drop motion. In this work, self-propelled motion of non-aqueous drops containing an active solute on a total wetting glass surface is reported. The benzyne intermediate 2(-Trimethylsilyl) phenyltrifluoromethane sulfonate (TPS) in DMSO (dimethyl sulphoxide) and octadecylamine in hexadecane were used as active components of binary/ternary drops showing self-induced motion. When drops of these were casted on high-temperature treated glass surface, random drop motion was observed followed by complete spreading of the drop. In case of DMSO, the drop periphery expanded with time while forming a rim, a central spherical cap inside the spreading drop was formed that shows random motion. This behaviour of drop was referred as a confused spreading-blooming drop, as spreading of DMSO drop occurs with rim formation outside and a self-moving drop formed inside the casted area. The unique non-aqueous drop spreading was evaluated by varying the solutal concentrations. This work depicts the unique combination of surface and drops showing potential application in self-propelled drop motion.

Swimming dynamics of a self-propelled droplet

Chemically active droplets often show intriguing self-propulsion behaviour in a surfactant solution. The drop motion is controlled by the nonlinear coupling among chemical transport in the bulk fluid, consumption of surfactant at the drop surface, and the fluid flow driven by the self-generated Marangoni stress. To quantify the underlying hydrodynamics, this work investigates the swimming motion of a two-dimensional drop that is determined by two dimensionless parameters, the Péclet number ($Pe$) and Damköhler number ($Da$). The weakly nonlinear analysis shows that near the instability threshold, the drop undergoes a supercritical bifurcation with velocity $U\sim \sqrt {Pe-Pe_c}$, where $Pe_c$ is the critical Péclet number for the onset of dipole mode. In the highly nonlinear regime, the drop transits from steady translation of pusher swimming to unsteady motion of mixed pusher–puller swimming along zigzaging trajectories of quadrangle and/or triangle waves. Mode decomposition shows that the zigzag motion is directly related to the interaction between the secondary wake of low surfactant concentration and the primary wake.

Symmetry-breaking, motion and bistability of active drops through polarization-surface coupling.

Cell crawling crucially depends on the collective dynamics of the acto-myosin cytoskeleton. However, it remains an open question to what extent cell polarization and persistent motion depend on continuous regulatory mechanisms and autonomous physical mechanisms. Experiments on cell fragments and theoretical considerations for active polar liquids have highlighted that physical mechanisms induce motility through splay and bend configurations in a nematic director field. Here, we employ a simple model, derived from basic thermodynamic principles, for active polar free-surface droplets to identify a different mechanism of motility. Namely, active stresses drive drop motion through spatial variations of polarization strength. This robustly induces parity-symmetry breaking and motility even for liquid ridges (2D drops) and adds to splay- and bend-driven pumping in 3D geometries. Intriguingly, then, stable polar moving and axisymmetric resting states may coexist, reminiscent of the interconversion of moving and resting keratocytes by external stimuli. The identified additional motility mode originates from a competition between the elastic bulk energy and the polarity control exerted by the drop surface. As it already breaks parity-symmetry for passive drops, the resulting back-forth asymmetry enables active stresses to effectively pump liquid and drop motion ensues.

Investigation of the features of crystallization of granules of high-strength aluminum alloys of the Al-Zn-Mg-Cu system at ultra-high cooling rates

The article presents the results of studies of the process of obtaining granular materials from high-strength aluminum alloys of the Al - Zn - Mg - Cu system by centrifugation of the melt with ultra-high cooling rates of granules. The concept of a «steam jacket» is introduced, namely, a steam layer that occurs between the granule body and the cooling liquid, which prevents the intensity of heat removal and is an obstacle to increasing the crystallization rate due to the lower thermal conductivity of water vapor. It is established that the formation of a vapor layer always occurs due to the heating of the cooling liquid in contact with the melt drop to boiling temperatures and the transition of the cooler from the liquid phase to steam. The technology of increasing the rate of crystallization of granules due to the constant removal of the vapor layer is proposed. The removal (knocking down) of the vapor shell that occurs around the drop occurs due to the high speed of the drop movement in the cooling medium. Fundamentally important in the industrial implementation of this technology is not so much the design of the device for obtaining pellets by centrifugation of the melt, namely, the high required rotation speed of the spraying crucible of the device under consideration. The results of experimental data are presented to determine the necessary rotation speed of the perforated cup, which ensures the creation of a sufficient initial velocity of the drop movement, leading to a constant churning of the «steam jacket». It is determined that an increase in the rates of heat removal from the crystallized granules and, as a result, an increase in the crystallization rate leads to an increase in the strength characteristics of granular aluminum alloys of the Al-Zn-Mg-Cu system. In particular, in the production of pressed semi-finished products from alloys of the Al-Zn-Mg-Cu system, such as B95, B96c. the increase in the strength characteristics of the material of the press products is up to 15 % compared to the same granular materials obtained by traditional methods with industrial crystallization rates of melt droplets. It is established that this method, based on the removal of the vapor layer around the formed granule, is the only possible one for further increasing the cooling rate and, as a result, the crystallization rate. Reducing the size of granules to the size of powders leads to serious technological problems in the further consolidation of granules and, in fact, is a dead end branch of the further development of granulation methods.

Thermocapillary effects on viscoelastic drops suspended in axisymmetric pressure driven flows

Dynamics and deformation of a viscoelastic drop in another immiscible viscoelastic medium in the presence of externally imposed pressure and temperature gradients are analyzed asymptotically in the present work. Both of the phases obey the linear Phan–Thien–Tanner constitutive model, capable of accounting for shear thinning behavior in polymeric fluids. The first two asymptotic corrections to the leading order Newtonian behavior are reported here, in the limit of small Deborah and Capillary numbers, which, respectively, characterize the extent of viscoelasticity and interfacial deformation. We establish that the viscoelastic properties of the inner phase strongly influence the migration velocity and the interfacial deformation of the drop. Our analysis reveals the possibility of realizing a maximum migration velocity for an intermediate viscosity of the interior phase, provided it has stronger viscoelastic characteristics than the suspending medium. We further compute the critical thermal gradient required to completely arrest the drop's motion and demonstrate that the same depends on the Deborah number as well as the viscosity of the inner phase. The viscoelastic stresses also dictate the deformation as the drop's shape changes from prolate to oblate when those stresses become significant. Our results may find potential applications in areas such as polymer processing and handling of biologically relevant media in medical diagnostics.