Drop Dynamics Research Articles

Quasi-two-dimensional pseudo-sessile drops

Sessile drops are ubiquitous and important in technological applications. While dynamics of liquid drops have been studied under confinement, the possibility of creating sessile drops with reduced dimensionality has not been explored. Here, we demonstrate a quasi-two-dimensional (Q2D) analogy for axisymmetric sessile three-dimensional (3D) drops. The Q2D drops are created by confining liquids between parallel vertical walls, forming low aspect ratio capillary bridges deformed by gravity. Stationary Q2D drops adopt projected shapes analogous to 3D sessile drops, ranging from circular drops to puddles. When moving, the Q2D drops exhibit capillary and fluid mechanical behaviours conceptually analogous to 3D drops, including impacts and sliding. The Q2D drops also exhibit more complex phenomena such as levitation, various instabilities and pattern formation when subjected to external electric, magnetic and flow fields. The 3D-Q2D analogy suggests that the diverse and often complicated phenomena observed in 3D drops can be studied in the simplified Q2D geometry. Additionally, the Q2D confinement analogy allows exploring phenomena arising from the reduced dimensionality and the altered boundary conditions.

Water drop transportation on wettability switchable surface via anisotropic molecules

Active control of the transportation of liquid drops on a horizontal surface is achieved using surfaces with switchable wettability via remote stimuli. However, the mechanism how the dynamic wettability influences drop dynamics is rarely reported. In this paper, we demonstrate that a surface with switchable wettability induces depinning of the contact line through re-orientation of anisotropic molecules. We investigated the dynamics of contact lines and contact angles during the initiation of drop movement by the advancing and receding angles of the surface. We found that imbalance between advancing and receding angles with respect to the dynamic contact angle provides the force needed to overcome the energy barrier due to contact angle hysteresis on the surface. We discovered that the driving energy is accumulated with oscillations in contact angle until it breaks the pinning energy barrier. Understanding the role of dynamic contact angles in drop movement on switchable surfaces paves the way for designing effective fluid manipulation devices, such as water harvesters, biosensors, and oil–water separators.

Dynamics of a droplet on the surfactant-infested free surface of another liquid

The dynamics of liquid droplets surfing over the surfactant-infested free surface of another liquid have been explored experimentally. We analyze the motion of oil droplets that has been initiated through the creation of a surface tension gradient resulting from the deposition of a drop of surfactant at the water surface contained in the petri dish. The experiments reveal that the location of surfactant deposition with respect to the droplet position influences its motion. Due to the presence of a surface tension gradient, the footprint area of the droplet reduces and its shape changes. We have studied the temporal variation in the velocity (|vx|) of the droplets in relation to their proximity to a wall. Based on the evolution of droplet shape and change in droplet velocity, the drop dynamics can be experimentally divided into four distinct zones. Results indicate that in zone-1, |vx| grows with t as |vx|≈tn, where n is between 0.8 and 1.0. The scaling argument shows that in this zone, the surface tension force dominates the drag force, and thereby, |vx| of the droplets increases linearly with t expressed as |vx|∝t. The experimental investigation and the scaling law exhibit a reasonable agreement. In zone-2, |vx| remains more or less constant, as it is postulated that the surface tension force balances the drag force. In zone-3, a decrease in surface tension force results in a deceleration of the droplets. In zone-4, the deceleration becomes more prominent as the droplet approaches the petri dish wall.

Experimental characterization of dynamics of bed‐scale liquid spreading in a trickle bed

AbstractWe report measurements performed to understand the effects of gas (QG) and liquid (QL) flow rates, surface tension (σGL), liquid viscosity (μL), and particle diameter (dp) on dynamics of local liquid spreading, pressure drop, and overall liquid holdup in a pseudo‐2D trickle bed. We show that an increase in the gas‐phase inertia leads to a decrease in the lateral liquid spreading, whereas an increase in the liquid‐phase inertia leads to an increase in the lateral liquid spreading. We also show that an increase in dp causes a reduction in the lateral liquid spreading. Using dimensionless numbers (AB and We), we propose a regime map showing contributions of different forces to the local liquid spreading. We show that the interplay between the inertia and capillary forces governs the liquid distribution near the inlet, whereas the relative contribution of gravitational force increases toward the outlet. Finally, we propose a relation between AB and We for “bed‐scale” liquid spreading.

Intrinsic dynamics of emulsions: Experiments in microgravity on the International Space Station

HypothesisIn order to understand the basic mechanisms affecting emulsion stability, the intrinsic dynamics of the drop population must be investigated. We hypothesize that transient ballistic motion can serve as a marker of interactions between drops. In 1G conditions, buoyancy-induced drop motion obscures these interactions. The microgravity condition onboard the International Space Station enable this investigation. ExperimentsWe performed Diffusing Wave Spectroscopy (DWS) experiments in the ESA Soft Matter Dynamics (SMD) facility. We used Monte Carlo simulations of photon trajectory to support data analysis. The analysis framework was validated by ground-based characterizations of the initial drop size distribution (DSD) and the properties of the oil/water interface in the presence of surfactant. FindingsWe characterized the drop size distribution and found to be bi-disperse. Drop dynamics shows transient ballistic features at early times, reaching a stationary regime of primarily diffusion-dominated motion. This suggests different ageing mechanisms: immediately after emulsification, the main mechanism is coalescence or aggregation between small drops. However at later times, ageing proceeds via coalescence or aggregation of small with large drops in some emulsions. Our results elucidate new processes relevant to emulsion stability with potential impact on industrial processes on Earth, as well as enabling technologies for space exploration.

Spreading dynamics of a microgel particle-laden thermosensitive polymer drop along smooth and nanofiber surfaces

The research focuses on the influence of 300-μm microgel particles in an aqueous solution of a thermosensitive biopolymer on the spreading and deformation of 3.7-mm drops. The drops impact a smooth hydrophilic and a rough hydrophobic surface. A mass fraction of microgel particles varies in a range of 0–0.2. A universal physical model of the spreading of thermosensitive polymer drops laden with microgel particles along surfaces with significantly different roughness is proposed. It explains the strong inhomogeneity of the contact line stretching due to the deceleration of the continuous phase flow by microgel particles and the increased flow vorticity because of the addition of the surface roughness factor. The validity of the proposed physical model is proven by qualitative and quantitative assessments of the contact line deformation when spreading. An empirical expression for the maximum spreading factor is derived, taking into account the properties of liquids, wall roughness, and microgel particle concentration; it reliably predicts when Re≈110−3100, the surface roughness is 0.5–125 nm, Ca=4.5×10−7, and the number of microgel particles in drops is up to 100. The expression was successfully tested during the modeling of arbitrary surface roughness and the increased concentration of microgel particles relative to those considered in experiments during the formation of a biopolymer layer. When developing the method of additive manufacturing of a functional layer, a practical correlation was established between the volume content of microgel particles, acting as potential containers for living cells, in a drop and the area of the biopolymer layer.

Deformation and time scales of drop dynamics in turbulent field and the effect of physical properties

Deformation and time scales of drop dynamics in turbulent field and the effect of physical properties

Dynamics of Droplets Moving on Lubricated Polymer Brushes.

Understanding the dynamics of drops on polymer-coated surfaces is crucial for optimizing applications such as self-cleaning materials or microfluidic devices. While the static and dynamic properties of deposited drops have been well characterized, a microscopic understanding of the underlying dynamics is missing. In particular, it is unclear how drop dynamics depends on the amount of uncross-linked chains in the brush, because experimental techniques fail to quantify those. Here we use coarse-grained simulations to study droplets moving on a lubricated polymer brush substrate under the influence of an external body force. The simulation model is based on the many body dissipative particle dynamics (MDPD) method and designed to mimic a system of water droplets on poly(dimethylsiloxane) (PDMS) brushes with chemically identical PDMS lubricant. In agreement with experiments, we find a sublinear power law dependence between the external force F and the droplet velocity v, F ∝ vα with α < 1; however, the exponents differ (α ∼ 0.6-0.7 in simulations versus α ∼ 0.25 in experiments). With increasing velocity, the droplets elongate and the receding contact angle decreases, whereas the advancing contact angle remains roughly constant. Analyzing the flow profiles inside the droplet reveals that the droplets do not slide but roll, with vanishing slip at the substrate surface. Surprisingly, adding lubricant has very little effect on the effective friction force between the droplet and the substrate, even though it has a pronounced effect on the size and structure of the wetting ridge, especially above the cloaking transition.

Estimating sliding drop width via side-view features using recurrent neural networks

High speed side-view videos of sliding drops enable researchers to investigate drop dynamics and surface properties. However, understanding the physics of sliding requires knowledge of the drop width. A front-view perspective of the drop is necessary. In particular, the drop’s width is a crucial parameter owing to its association with the friction force. Incorporating extra cameras or mirrors to monitor changes in the width of drops from a front-view perspective is cumbersome and limits the viewing area. This limitation impedes a comprehensive analysis of sliding drops, especially when they interact with surface defects. Our study explores the use of various regression and multivariate sequence analysis (MSA) models to estimate the drop width at a solid surface solely from side-view videos. This approach eliminates the need to incorporate additional equipment into the experimental setup. In addition, it ensures an unlimited viewing area of sliding drops. The Long Short Term Memory (LSTM) model with a 20 sliding window size has the best performance with the lowest root mean square error (RMSE) of 67 µm. Within the spectrum of drop widths in our dataset, ranging from 1.6 to 4.4 mm, this RMSE indicates that we can predict the width of sliding drops with an error of 2.4%. Furthermore, the applied LSTM model provides a drop width across the whole sliding length of 5 cm, previously unattainable.

Rebounding dynamics of ceramic drops on hydrophobic substrates

Rebounding dynamics of ceramic drops on hydrophobic substrates

Heat transport during drop impact onto a heated wall covered with an electrospun nanofiber mat: The influence of wall superheat, impact velocity, and mat thickness

Nanofiber surface coating is a promising method for the enhancement of heat transfer during spray cooling. In the present work, the drop dynamics as well as local and overall heat transfer during single drop impact onto a heated wall covered with a polyacrylonitrile (PAN) nanofiber mat are investigated to obtain insight into the mechanisms governing the heat transport enhancement. The influence of wall superheat, drop impact velocity, and mat thickness on the hydrodynamics and heat transfer from the heated wall to the fluid is studied. The experiments were conducted inside a temperature-controlled test cell with a pure vapor atmosphere maintained with refrigerant FC−72 (perfluorohexane). The temperature field at the solid–fluid interface was observed with a high-speed infrared camera, and the heat flux field was derived by solving a three-dimensional transient heat conduction equation within the substrate. The presence of the nanofiber mat on the heater surface suppresses the drop receding phase due to the pinning of the contact line at the end of the spreading phase. Two different heat transfer scenarios are observed depending on the wall superheat and drop impact velocity: scenario (I), in which the liquid drop completely penetrated through the porous nanofiber mat and made contact with the heater surface; and scenario (II) in which the vapor produced inside the pores of the nanofiber mat prevented the liquid drop from touching the heater surface. In scenario (I), an up 450% heat flow enhancement during the sessile drop evaporation stage has been observed. In scenario (II), a 80% heat flow enhancement at this stage has been registered.

Bouncing Dynamics of Drops' Successive Off-Center Impact.

Bouncing dynamics of a trailing drop off-center impacting a leading drop with varying time intervals and Weber numbers are investigated experimentally. Whether the trailing drop impacts during the spreading or receding process of the leading drop is determined by the time interval. For a short time interval of 0.15 ≤ Δt* ≤ 0.66, the trailing drop impacts during the spreading of the leading drop, and the drops completely coalesce and rebound; for a large time interval of 0.66 < Δt* ≤ 2.21, the trailing drop impacts during the receding process, and the drops partially coalesce and rebound. Whether the trailing drop directly impacts the surface or the liquid film of the leading drop is determined by the Weber number. The trailing drop impacts the surface directly at moderate Weber numbers of 16.22 ≤ We ≤ 45.42, while it impacts the liquid film at large Weber numbers of 45.42 < We ≤ 64.88. Intriguingly, when the trailing drop impacts the surface directly or the receding liquid film, the contact time increases linearly with the time interval but independent of the Weber number; when the trailing drop impacts the spreading liquid film, the contact time suddenly increases, showing that the force of the liquid film of the leading drop inhibits the receding of the trailing drop. Finally, a theoretical model of the contact time for the drops is established, which is suitable for different impact scenarios of the successive off-center impact. This study provides a quantitative relationship to calculate the contact time of drops successively impacting a superhydrophobic surface, facilitating the design of anti-icing surfaces.

Drops of volatile binary mixtures on brush-covered substrates

We introduce a mesoscopic hydrodynamic model for drops of binary mixtures of volatile partially wetting liquids on brush-covered substrates, i.e., we model the coupled dynamics of spreading, evaporation, imbibition, diffusion and partial demixing of the two volatile components across the three phases—brush, drop and gas. The formulation of the model as gradient dynamics on an underlying free energy functional allows us to systematically account for cross-couplings between the six scalar fields needed to describe the dynamics of both components within each of the three phases. The energy accounts for concentration- and brush state-dependent capillarity and wettability, miscibility of the two components within drop and brush, and entropy in the gas. Finally, the usage of the model is illustrated by employing numerical time simulations to study the dynamics of a sessile drop.

Vibration-triggered spreading of nanofluid drops

This study explores the effects of nanoparticles on the dynamics of drop spreading under external vibration, presenting an advance in the understanding of nanofluid behavior on vibrating substrates. This work introduces insights into nanoparticle-mediated drop spreading, offering implications for improving particulate coatings, mini-mixers, and particle segregation technologies. By employing a twofold approach that combines oscillating drop dynamics with internal flow pattern analysis, we find how even small concentrations of hydrophilic or hydrophobized silica nanoparticles inside water sessile droplets significantly alter the spreading process on silanized glass surfaces. Our study allows distinct drop spreading regimes to be identified based on nanoparticle concentration and vibration amplitude, for both hydrophilic and hydrophobized nanoparticles. Through a comprehensive analysis, we demonstrate that the vibration-triggered spreading of nanofluids can lead to a stable and controlled manipulation of complex liquids.

Understanding the Role of Loss Modulus of Viscoelastic Substrates in the Evaporation Dynamics of Sessile Drops.

Viscoelastic properties of soft substrates play a crucial role in the evaporation dynamics of sessile drops. Recent studies have revealed that the modification of the viscoelastic properties of substrates changes the dynamics of the three-phase contact line, consequently affecting the evaporation behavior of sessile drops. Notably, these modifications occur without any noticeable changes to the substrate's wetting characteristics or surface topography. However, the individual role of storage (G') and loss (G″) moduli of substrates on drop evaporation dynamics remains unexplored. In this study, we investigate the evaporation dynamics of water drops on two groups of poly(dimethylsiloxane)-based viscoelastic substrates possessing either identical G' with varying G″ or identical G″ with varying G'. Our study reveals that on a substrate with constant shear modulus (G'), a reduction of an order of magnitude in loss modulus shifts the evaporation process from the constant contact radius mode to the constant contact angle mode. We hypothesize that this observed shift in behavior stems from the varying viscoelastic dissipation influenced by the plateau modulus and characteristic relaxation time of polymer gels. Our hypothesis is further supported from the observation that the evaporation process persists on the substrate with constant loss modulus (G″). Our study advances the current understanding of drop evaporation on soft substrates that may find potential applications involving soft composites, biological entities, tissue engineering, and wearable electronics.

ДОСЛІДЖЕННЯ ПЕРЕХІДНИХ ПРОЦЕСІВ В ЕЛЕКТРИЧНОМУ КОЛІ З СВІТЛОДІОДАМИ

The following documents presents the culmination of theoretical and innovative studies of transient processes in electric technology with a separate LED and their serial, parallel and varied connection. It becomes apparent that the dynamics of current growth in a circuit with an LED has no significant changes when switching from a single LED to their parallel and series connection. Furthermore, the rise time of the current is much longer than the time of its fall. Comparing the dynamics of the current drop in the circuit and the voltage applied to the LED, is shown that they intersect. The suggested equivalent circuit of the LED, represented by the parallel link of the capacitor Cd and resistance Rd connected to the series resistance RS, is in good concurrent with theoretical calculations of transient processes and with the obtained innovative outcomes. The main task in the value of the time constant τ of the transient process is played by the capacitance of the capacitor Сd, which is ascertained by the diffuse capacitance of the heterojunction. Based upon obtained results, it was established that the maximum pulse power frequency of LED lighting devices is 8‧105 Hz. References 11, figures 5, table 1.

Cuboid drop: A low-dimensional model of drop dynamics on a substrate

Cuboid drop: A low-dimensional model of drop dynamics on a substrate

Numerical study of drop dynamics for inkjet based 3D printing of pharmaceutical tablets

Interest in 3D printing has been growing rapidly especially in pharmaceutical industry due to its multiple advantages such as manufacturing versatility, personalization of medicine, scalability, and cost effectiveness. Inkjet based 3D printing gained special attention after FDA’s approval of Spritam® manufactured by Aprecia pharmaceuticals in 2015. The precision and printing efficiency of 3D printing is strongly influenced by the dynamics of ink/binder jetting, which further depends on the ink’s fluid properties. In this study, Computational Fluid Dynamics (CFD) has been utilized to study the drop formation process during inkjet-based 3D printing for piezoelectric and thermal printhead geometries using Volume of Fluid (VOF) method. To develop the CFD model commercial software ANSYS-Fluent was used. The developed CFD model was experimentally validated using drop watcher setup to record drop progression and drop velocity. During the study, water, Fujifilm model fluid, and Amitriptyline drug solutions were evaluated as the ink solutions. The drop properties such as drop volume, drop diameter, and drop velocity were examined in detail in response to change ink solution properties such as surface tension, viscosity, and density. A good agreement was observed between the experimental and simulation data for drop properties such as drop volume and drop velocity.

Coalescence of non-spherical drops with a liquid surface

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 (Ar) 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 Ar>0.67. In contrast to the prolate (Ar<1) and spherical drops (Ar=1), an oblate (Ar>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 surface energies of the system. Finally, we establish an analogy by comparing the dynamics of a freely falling non-spherical drop, undergoing topological oscillations during its descent from a height, with the impact dynamics of parent drops of various shapes striking the liquid surface with an equivalent velocity. Our investigation involving non-spherical drops contrasts the extensive studies conducted by various researchers on the impact of a parent spherical drop just above the free surface of a liquid pool.

Experimental investigation of walking drops: Wave field and interaction with slit structures.

While bouncing walking silicone oil droplets (walkers) do show many quantumlike phenomena, the original, most intriguing, double-slit experiment with walkers has been shown to be an overinterpretation of data. Several experiments and numerical simulations have proven that for at least some parameter region there is no randomness. Still, true randomness was claimed to be observed in an experiment on chaotically bouncing walkers. Also, most of the available phase space has not been investigated. The main goal of this paper is therefore to look for true interference and chaos in the entire phase space. Recently, we made an extensive investigation of drops interacting with slits, but still in a limited range. However, the outcome was always deterministic and only incidentally mimicked the statistics of the corresponding quantum case. We also showed that the extra interference, already seen by others, in the double-slit case was caused by reflection of waves from the outlet of the unused slit after passage and thus was not a true double-slit effect. A new theoretical treatment of bouncing drop dynamics has since given analytic relations for the associated wave field, leading to a proposal for criteria for the possible occurrence of true interference in the double-slit experiment. Satisfying these criteria, requires working close to the onset of the Faraday instability, with two spatial conditions favoring slow walkers, and a temporal condition favoring fast walkers. The regions of high velocity, where the walkers bounce periodically, and of very low velocity, with chaotically bouncing walkers, have not been comprehensively investigated so far. We have therefore looked at these regions, probing the limits for interaction with slits. Furthermore, noting that a short transit time is essential to fulfill the criteria, experiments were done using double-slit barriers only 0.5 and 2mm broad. Nowhere was true interference or a chaotic response found. As the theory has implications for many of the observed quantumlike phenomena involving walkers as, e.g., tunneling and interaction between drops, we have measured the spatial and temporal decay of the wave field. A comparison with the theory shows very good agreement but leads to a reformulation of the above-mentioned criteria.