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We investigate compound drops composed of two immiscible nonvolatile partially wetting liquids that slide down an inclined homogeneous smooth solid substrate based on a mesoscopic hydrodynamic two-layer model in full-curvature formulation. First, drops of one liquid stationarily sliding on a layer of the other liquid are briefly investigated with a focus on the dependence of drop velocity and interface profiles on inclination and mean thickness of the adaptive substrate. Then, stationary sliding compound drops are studied with a focus on the dependence of their configuration, velocity, dynamic Young and Neumann angles on three control parameters, namely, the inclination, the volume ratio and the viscosity ratio. The reasons for the encountered dependence of the velocity on configuration are clarified based on a discussion of the lateral dissipation profile. Finally, we briefly consider the time-periodic fusion-overtaking-splitting behavior found outside the existence range of the stationary sliding compound drops as determined by saddle-node bifurcations.

Active drops refer to drops with the ability to self-migrate: these drops typically attain this ability by virtue of containing of active particles that derive energy from their environment and undergo directed motion inside the drops, thereby creating intricate stress distribution within these drops. Here we describe the evaporation dynamics of a slender active nematic drop. The stresses induced by active nematic particles present within the drop enables fascinating drop evaporation dynamics, consisting of an initial pinned stage and a late runaway stage. Unlike regular drops, during the pinned stage (for extensile drops) the drops encounter puncturing at their centers, followed by a receding motion of the newly formed inner contact line with the liquid flux pushing the (nematic) particles towards the inner and the outer contact lines: the result is the formation of a unique ring-galaxy-like particle deposition pattern. We identify three non-dimensional parameters, representing the activity, the aspect ratio, and the receding contact angle, which dictate the occurrence of puncturing, the overall evaporation time, and the possible deposit patterns for the extensile drops and the co

Dynamic scene reconstruction from casual videos has seen recent remarkable progress. Numerous approaches have attempted to overcome the ill-posedness of the task by distilling priors from 2D foundational models and by imposing hand-crafted regularization on the optimized motion. However, these methods struggle to reconstruct scenes from extreme novel viewpoints, especially when highly articulated motions are present. In this paper, we present DRoPS, a novel approach that leverages a static pre-scan of the dynamic object as an explicit geometric and appearance prior. While existing state-of-the-art methods fail to fully exploit the pre-scan, DRoPS leverages our novel setup to effectively constrain the solution space and ensure geometrical consistency throughout the sequence. The core of our novelty is twofold: first, we establish a grid-structured and surface-aligned model by organizing Gaussian primitives into pixel grids anchored to the object surface. Second, by leveraging the grid structure of our primitives, we parameterize motion using a CNN conditioned on those grids, injecting strong implicit regularization and correlating the motion of nearby points. Extensive experiments d

When a drop of a leaky dielectric fluid is suspended in another fluid and subjected to a uniform DC electric field, it becomes polarized, leading to tangential electric stresses that drive fluid motion both inside and outside the drop. In the presence of a second drop, the dynamics of the first drop are altered due to electrohydrodynamic interactions with the second, causing the drops to translate due to dielectrophoretic forces and hydrodynamic interactions. We present a semi-analytical nonlinear three-dimensional small deformation theory for a pair of identical, widely-separated leaky dielectric drops suspended in a weakly conducting fluid. This theory is valid under conditions of large drop separation, high drop viscosity, and high surface tension, ensuring that the drops remain nearly spherical. For the first time, we develop a model within the Taylor--Melcher leaky dielectric framework that incorporates both transient charge relaxation and convection. This allows the model to capture the transition to Quincke rotation, a symmetry-breaking phenomenon in which drops begin to spontaneously rotate in sufficiently strong fields. We derive and numerically integrate coupled nonlinear

Over the past decade, there has been a growing interest in the study of multicomponent drops. These drops exhibit unique phenomena, as the interplay between hydrodynamics and the evolving physicochemical properties of the mixture gives rise to distinct and often unregulated behaviors. Of particular interest is the complex dynamic behavior of the drop contact line, which can display self-lubrication effect. The presence of a slipping contact line in self-lubricating multicomponent drops can suppress the coffee-stain effect, conferring valuable technological applications. This review will explain the current understanding of the self-lubrication effect of drops, and cover an analysis of fundamental concepts and recent advances in colloidal assembly. The potential applications of self-lubricating drops across different fields will also be highlighted.

This study investigated the coalescence of polymer solution drops on the solid substrates. When two drops meet at their contact line on a substrate, the liquid bridge connecting the two drops increases in size with time. The height and radius of the liquid bridge have a power law dependence on time. In the early stage of drop coalescence, the exponents $α$ and $β$ of the power law are influenced by the properties of the polymer solution. We argued that the balance between capillarity and viscoelasticity controls the process, where viscoelasticity must be considered in its full time and shear-rate dependency. As a simple proxy for the processes involved, the ratio of the polymer relaxation time to the viscous time of the drop, the elastocapillary ($Ec$), is instructive. In the vicinity of $Ec= 1$ the exponents showed a minimum and increased to lower and higher values of $Ec$. A similar dependency is observed for the damping timescales of the capillary waves. For high elastocapillary numbers, i.e. high polymer relaxation time, drop coalescence on short timescales behaved as in the low viscosity case. In addition, the bridge profile is influenced by a combination of factors including

Viscoelastic materials containing bubbles or drops are encountered in numerous application fields, and are presently the object of much interest. The motion of bubbles and drops in these matrices can be significantly different than in Newtonian fluids. This review is restricted to the case of motion in quiescent fluids (or small Reynolds number) and of small bubbles and drops, that are not appreciably deformed during their motion. It includes a brief description of properties of viscoelastic systems and of the motion of solid particles in these systems. The case of very small drops undergoing Brownian motion is related to recent advances in microrheology. The motion of larger drops and bubbles due to gravity in yield stress fluids is discussed and linked to Ostwald ripening. Recent advances on the understanding of the rheological properties of the composite systems are also briefly discussed.

We employ three-dimensional numerical simulations to explore the impact dynamics of non-spherical drops in a deep liquid pool by varying the aspect ratios $(A_r)$ and Weber numbers $(\We)$. We observe that when a non-spherical drop is gently placed on a liquid pool, it exhibits a partial coalescence phenomenon and the emergence of a daughter droplet for $A_r>0.67$. In contrast to the prolate $(A_r<1)$ and spherical drops $(A_r=1)$, an oblate $(A_r>1)$ drop with a high aspect ratio encapsulates air in a ring-like bubble within the pool and emerges a liquid column that undergoes Rayleigh-Plateau capillary instability, leading to the formation of two daughter droplets with complex shapes. When the parent drop is impacted with finite velocity, our observations indicate that increasing the Weber number leads to elevated crater heights on the free surface for all aspect ratios. A prolate drop produces a less pronounced wave swell and exhibits a prolonged impact duration owing to its negligible impact area. Conversely, an oblate drop generates a much wider wave swell than spherical and prolate drops. We analyze the relationship between rim formation dynamics and the kinetic and s

In a previous report [10] it was shown that emulsion stability simulations are able to reproduce the lifetime of micrometer-size drops of hexadecane pressed by buoyancy against a planar water-hexadecane interface. It was confirmed that small drops (ri<10 μm) stabilized with β-casein behave as nondeformable particles, moving with a combination of Stokes and Taylor tensors as they approach the interface. Here, a similar methodology is used to parametrize the potential of interaction of drops of soybean oil stabilized with bovine serum albumin. The potential obtained is then employed to study the lifetime of deformable drops in the range 10 \leq ri \leq 1000 μm. It is established that the average lifetime of these drops can be adequately replicated using the model of truncated spheres. However, the results depend sensibly on the expressions of the initial distance of deformation and the maximum film radius used in the calculations. The set of equations adequate for large drops is not satisfactory for medium-size drops (10 \leq ri \leq 100 μm), and vice versa. In the case of large particles, the increase in the interfacial area as a consequence of the deformation of the drops genera

We investigate the interactions between two drops in a heated environment and analyze the effect of evaporation on bouncing, coalescence and reflexive separation phenomena. A reliable mass transfer model is incorporated in a coupled level-set and volume-of-fluid framework to accurately model the evaporation process and the evolution of drop interfaces during the interactions. The numerical technique is extensively validated against the benchmark problems involving the evaporation of a single drop. We analyze the contour plots of temperature and vapor mass fraction fields for each collision outcome. Our numerical simulations reveal that vapor entrapment during the separation process, with high-velocity vapor manages to escape. Increasing evaporation rates result in slower post-collision drop separation. Furthermore, the differences in kinetic energy and surface energy are analyzed for different Stefan numbers. The coalescence of drops exhibits energy oscillations until dissipation, while the bouncing and reflexive separations lack such oscillations. In the reflexive separation regime, the kinetic energy of the drops becomes zero after detachment.

We compare the lateral retention forces on sessile drops (which are drops that are placed on top of a solid surface), pendant drops (which are drops that are placed on the underside of the surface), and inverted sessile drops (which are drops that are first placed on top and then on the underside of the surface by flipping the surface). We have found experimentally that the retention force on a truly pendant drop is always smaller than that on a sessile drop. However, the retention force on an inverted sessile drop is comparable to, and usually larger than, that on a sessile drop. Thus, the retention force on a drop depends not only on whether it is placed on top or on bottom of a surface, but also on the history of drop deposition, since such history affects the width, the shape and the contact angles of the drop.

The coalescence of water drops on a substrate is studied experimentally. We focus on the rapid growth of the bridge connecting the two drops, which very quickly after contact ensues from a balance of surface tension and liquid inertia. For drops with contact angles below $90^\circ$, we find that the bridge grows with a self-similar dynamics that is characterized by a height $h\sim t^{2/3}$. By contrast, the geometry of coalescence changes dramatically for contact angles at $90^\circ$, for which we observe $h\sim t^{1/2}$, just as for freely suspended spherical drops in the inertial regime. We present a geometric model that quantitatively captures the transition from 2/3 to 1/2 exponent, and unifies the inertial coalescence of sessile drops and freely suspended drops.

The coalescence of liquid drops has conventionally been thought to have just two regimes when the drops are brought together slowly in vacuum or air: a viscous regime corresponding to the Stokes-flow limit and a later inertially-dominated regime. Recent work [Proc. Natl. Acad. Sci. 109, 6857 (2012)] found that the Stokes-flow limit cannot be reached in the early moments of coalescence, because the inertia of the drops cannot be neglected then. Instead, the drops are described by an "inertially limited viscous" regime, where surface tension, inertia, and viscous forces all balance. The dynamics continue in this regime until either viscosity or inertia dominate on their own. I use an ultrafast electrical method and high-speed imaging to provide a detailed description of coalescence near the moment of contact for drops that approach at low speed and coalesce as undeformed spheres. These measurements support a description of coalescence having three regimes. Signatures both before and after contact identify a threshold approach-speed for deformation of the drops by the ambient gas.

Ensembles of interacting drops that slide down an inclined plate show a dramatically different coarsening behavior as compared to drops on a horizontal plate: As drops of different size slide at different velocities, frequent collisions result in fast coalescence. However, above a certain size individual sliding drops are unstable and break up into smaller drops. Therefore, the long-time dynamics of a large drop ensemble is governed by a balance of merging and splitting. We employ a long-wave film height evolution equation and determine the dynamics of the drop size distribution towards a stationary state from direct numerical simulations on large domains. The main features of the distribution are then related to the bifurcation diagram of individual drops obtained by numerical path continuation. The gained knowledge allows us to develop a Smoluchowski-type statistical model for the ensemble dynamics that well compares to full direct simulations.

Oppositely charged drops have long been assumed to experience an attractive force that favors their coalescence. In this fluid dynamics video we demonstrate the existence of a critical field strength above which oppositely charged drops do not coalesce. We observe that appropriately positioned and oppositely charged drops migrate towards one another in an applied electric field; but whereas the drops coalesce as expected at low field strengths, they are repelled from one another after contact at higher field strengths. Qualitatively, the drops appear to `bounce' off one another. We directly image the transient formation of a meniscus bridge between the bouncing drops.

We study the deformation of drops squeezed between the floor and ceiling of a microchannel and subjected to a hyperbolic flow. We observe that the maximum deformation of drops depends on both the drop size and the rate of strain of the external flow and can be described with power laws with exponents 2.59 +/- 0.28 and 0.91 +/- 0.05 respectively. We develop a theoretical model to describe the deformation of squeezed drops based on the Darcy approximation for shallow geometries and the use of complex potentials. The model describes the steady-state deformation of the drops as a function of a non-dimensional parameter Ca d^2, where Ca is the capillary number (proportional to the strain rate and the drop size) and d is a confinement parameter equal to the drop size divided by the channel height. For small deformations, the theoretical model predicts a linear relationship between the deformation of drops and this parameter, in good agreement with the experimental observations.

Drops placed on a surface with a temperature above the Leidenfrost point float atop an evaporative vapor layer. In this fluid dynamics video, it is shown that for roughened surfaces the Leidenfrost point depends on the drop size, which runs contrary to previous claims of size independence. The thickness of the vapor layer is known to increase with drop radius, suggesting that the surface roughness will not be able to penetrate the vapor layer for drops above a critical size. This size dependence was experimentally verified: at a given roughness and temperature, drops beneath a critical size exhibited transition boiling while drops above the critical size were in the Leidenfrost regime. These Leidenfrost drops were unstable; upon evaporation down to the critical size the vapor film suddenly collapsed.

When two liquid drops touch, a microscopic connecting liquid bridge forms and rapidly grows as the two drops merge into one. Whereas coalescence has been thoroughly studied when drops coalesce in vacuum or air, many important situations involve coalescence in a dense surrounding fluid, such as oil coalescence in brine. Here we study the merging of gas bubbles and liquid drops in an external fluid. Our data indicate that the flows occur over much larger length scales in the outer fluid than inside the drops themselves. Thus we find that the asymptotic early regime is always dominated by the viscosity of the drops, independent of the external fluid. A phase diagram showing the crossovers into the different possible late-time dynamics identifies a dimensionless number that signifies when the external viscosity can be important.