Heating analysis of a droplet on stretchable hydrophilic surface

Heating of a droplet on a stretchable hydrophilic surface is investigated and fluid dynamics in the droplet under the heating load is assessed. Elastomer wafers are considered as the sample material and the fixture is designed and manufactured to assure uniform stretching of the droplet located elastomer surface. Droplet adhesion and possible slipping/sliding of the droplet are evaluated during stretching of the sample surface. Numerical simulations are carried out to predict thermal and flow response of the droplet fluid before and after stretching. The effect of droplet volume on heating enhancement is also included in the numerical simulations. Experiments are carried out using a high-speed recording system towards comparing the flow predictions. Findings reveal that predictions are in agreement with their counterparts of experiments. Stretching of sample surface increases wetting area and lowers height of the droplet while influencing thermal flow structures in the fluid. The Nusselt and the Bond numbers increase with enlarging stretching, which becomes more visible for large droplet volume (80 µl). Hence, stretching corresponding to 80% extension of elastomer surface gives rise to 60% improvement in the Nusselt number.     

Simultaneous droplet impingement dynamics and heat transfer on nano-structured surfaces

This study examines the hydrodynamics and temperature characteristics of distilled deionized water droplets impinging on smooth and nano-structured surfaces using high speed (HS) and infrared (IR) imaging at We = 23.6 and Re = 1593, both based on initial drop impingement parameters. Results for a smooth and nano-structured surface for a range of surface temperatures are compared. Droplet impact velocity, transient spreading diameter and dynamic contact angle are measured. The near surface average droplet fluid temperatures are evaluated for conditions of evaporative cooling and boiling. Also included are surface temperature results using a gold layered IR opaque surface on silicon. Four stages of the impingement process are identified: impact, boiling, near constant surface diameter evaporation, and final dry-out. For the boiling conditions there is initial nucleation followed by severe boiling, then near constant diameter evaporation resulting in shrinking of the droplet height. When a critical contact angle is reached during evaporation the droplet rapidly retracts to a smaller diameter reducing the contact area with the surface. This continues as a sequence of retractions until final dry out. The basic trends are the same for all surfaces, but the nano-structured surface has a lower dissipated energy during impact and enhances the heat transfer for evaporative cooling with a 20% shorter time to achieve final dry out.     

Stretchable hydrophobic surfaces and droplet heating

Silicon elastomer surface is treated towards achieving the hydrophobic state. Functionalized nano-silica units are coated onto elastomer surface and resulting texture characteristics are examined prior to stretching, stretched and after stretching. The droplet heating of the hydrophobic elastomer surface is carried out when the surface is subjected to unstretching, stretching and stretch releasing conditions. The thermal-flow field in the liquid is simulated and validated incorporating high speed recording system. Nano-size silica units coated elastomer surface demonstrates the hydrophobic wetting state. The hydrophobic wetting state changes slightly for stretched and stretched released surface. The contact angle is about 154° ± 2° for unstretched surface while it is 152° ± 2° for the stretched released surface; hence, stretch relaxing provides reversible change of the surface wetting state of the elastomer surface. The contact angle reduces to 142° ± 2° when surface is under stretched, which is related to increased pillar spacing on the surface. The droplet heating results in development of Marangoni current in the fluid, which significantly affects the flow and temperature fields and it becomes more apparent for the large size droplets. The maximum flow velocity increases almost 9% in 45 µL as the surface is stretched. The Nusselt number increases with droplet size and the Bond number has the values less than unity; hence, stretching increases the Nusselt number by 60% for droplet of 45 µL.     

High-throughput generation of uniform droplets from parallel microchannel droplet generators and the preparation of polystyrene microsphere material

To prepare uniform polystyrene particles with ten microns of diameter, a parallel scaling-up strategy for the capillary-assembled stepwise microchannel was developed, which created uniform droplets with high-throughput and formed a large amount of emulsion templates for the polymerization of styrene and cross-linker. The microchannel droplet generator was robust for the flow rate deviation of the continuous phase in the jetting flow, and droplet generation frequency up to 2.8 × 10⁴ Hz was achieved with only four parallel droplet generators, which were much more efficient than the parallelly scaled microfluidic devices working in dripping flow. 32–52 μm average diameter droplets with 4.5%–8.4% diameter variation coefficients were successfully prepared from the microchannel device fabricated by low-cost 3D-print method, and the droplets were subsequently turned to solid particles via a two-step polymerization in the platform. The polystyrene particles were further reduced to 16.9–23.5 μm with 5.0%–8.6% diameter variation coefficients due to the accompanying emulsion polymerization, and the working capacity of the platform reached hundred milligrams of particles per hour.     

An analysis of the d-law departure during droplet evaporation in microgravity

The d²-law validity during n-decane droplet vaporization in microgravity environment is examined experimentally. Two sets of experiments are performed, under normal and microgravity, in stagnant hot atmospheric environment. The environment temperature is varied in the range up to 967 K. The droplet is suspended onto the cross point of two micro-fibers of 14 μm in diameter. This technique enables to greatly minimize the effect of fiber on droplet heat and mass transfer. The results show that, for ambient temperatures below approximately 950 K, departure from the d²-law is observed during droplet vaporization in microgravity environment. In addition, the droplet lifetime is longer in microgravity than in normal gravity under the same ambient test conditions. However, for temperatures exceeding approximately 950 K, the experimental results demonstrate that the d²-law holds throughout the entire droplet lifetime, and the mass transfer rate is identical in both microgravity and normal gravity environments.     

Drift of a reacting droplet due to the chemoconcentration capillary effect

The motion of a droplet with a first-order chemical reaction taking place at its surface with the participation of a surfactant dissolved in the external medium is considered. Approximate expressions are obtained for the velocity and other characteristics of the autonomous motion of the droplet caused by the surface capillary forces due to the nonuniform distribution of the surfactant over the surface of the moving droplet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 51–61, May–June, 1990.     

Heat and mass transfer of a fuel droplet evaporating in oscillatory flow

A numerical study of the heat and mass transfer from an evaporating fuel droplet in oscillatory flow was performed. The flow was assumed to be laminar and axisymmetric, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on these assumptions, the conservation equations in a general curvilinear coordinate were solved numerically. The behaviors of droplet evaporation in the oscillatory flow were investigated by analyzing the effects of flow oscillation on the evaporation process of a n-heptane fuel droplet at high pressure.The response of the time history of the square of droplet diameter and space-averaged Nusselt numbers to the main flow oscillation were investigated in frequency band of 1–75 Hz with various oscillation amplitudes. Results showed that, depending on the frequency and amplitude of the oscillation, there are different modes of response of the evaporation process to the flow oscillation. One response mode is synchronous with the main flow oscillation, and thus the quasi-steady condition is attained. Another mode is asynchronous with the flow oscillation and is highly unsteady. As for the evaporation rate, however, in all conditions is more greatly enhanced in oscillatory flow than in quiescent air.To quantify the conditions of the transition from quasi-steady to unsteady, the response of the boundary layer around the droplet surface to the flow oscillation was investigated. The results led to including the oscillation Strouhal number as a criteria for the transition. The numerical results showed that at a low Strouhal number, a quasi-steady boundary layer is formed in response to the flow oscillation, whereas by increasing the oscillation Strouhal number, the phenomena become unsteady.     

A numerical and experimental study of a collapsing bubble-induced droplet ejector

This paper aims to study a novel drop-on-demand droplet generation mechanism in which the oscillation and deformation of a non-equilibrium bubble in close proximity to a free surface induce an axisymmetric liquid spike on the free surface. The evolution of the liquid spike and its deformation due to the effect of surface tension force lead to the formation of a droplet. The free surface can be accorded by either a circular hole on a horizontal flat plate or by the top opening/nozzle of a vertical cylinder. A high-speed camera capable of obtaining images at a frame rate of 15,000 fps is utilized to observe the droplet formation process. Numerical simulations corresponding to the experiments are performed using the boundary integral spatial solution coupled with the time integration, i.e., a mixed Eulerian–Lagrangian method. In the experiments the bubble is generated using a very low voltage (only 55 V) in contrast to the relatively much higher voltages usually employed in reported works. This is very attractive from a safety viewpoint and accords great simplification of the setup. A comparison is made between the numerical and experimental results. A reasonable agreement has been found. The influences of the main design parameters, namely, the bubble-free surface distance and the dimension of the hole/nozzle on the bubble dynamics and on the droplet formation process are discussed and the conditions of the bubble dynamics under which a satellite-free droplet can be generated are sought. Furthermore, the effects of different geometries, namely, the horizontal flat plate and the vertical cylinder on the bubble dynamics and on the droplet features are examined. One important feature of the proposed actuation mechanism is the capability of producing droplets much smaller than the nozzle size. The possible applications of this mechanism are those where the accurate direction of the ejected droplet is of great importance such as inkjet printing.      

A model for droplet entrainment in heated annular flow

The ability to accurately predict droplet entrainment in annular two-phase flow is required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. Most annular flow entrainment models in the open literature are formulated in terms of dimensionless groups, which do not directly account for interfacial instabilities. However, many researchers agree that there is a clear presence of interfacial instability phenomena having a direct impact on droplet entrainment. The present study proposes a model for droplet entrainment, based on the underlying physics of droplet entrainment from upward co-current annular film flow that is characteristic to light water reactor safety analysis. The model is developed based on a force balance and stability analysis that can be implemented into a transient three-field (continuous liquid, droplet, and vapor) two-phase heat transfer and fluid flow systems analysis computer code.     

Comparison of multicomponent fuel droplet vaporization experiments in forced convection with the Sirignano model

The vaporization of multicomponent fuel droplets was studied experimentally in a heated flow and the results were compared to the model proposed by Abramzon and Sirignano. The droplet was suspended on a permanent holder which was set up in a thermal wind-tunnel. This wind-tunnel was fitted with a video recording system and an infra-red camera. The period during which the droplet was suspended on the holder before the opening of the hot air flow damper was recorded. This first sequence corresponds to the droplet vaporization in natural convection, whose initial experiment conditions, especially diameter, temperature, composition of the droplet, are well known. Then the damper was turn on, and the sequence of forced convection begun. The initial diameter of the droplet was recorded by the video system. The other initial conditions of this second sequence cannot be determined experimentally. The distribution of temperature in the droplet and the surface temperature, the mass fraction distribution in the droplet and the surface mass fraction were unknown. These unknown parameters were determined by coupling our experiment with a model using “the film concept” in natural convection. Experimental results were compared with the calculations and found satisfactory, in natural convection as well as in forced convection initiated by this method. The method was tested in the case of a fuel mixture droplets (heptane–decane) for different initial concentrations and variable durations of the sequence in natural convection.     

Hydrodynamics and boiling phenomena of water droplets impinging on hot solid

The collision of single water droplets with a hot Inconel 625 alloy surface was investigated by a two-directional flash photography technique using two digital still cameras and three flash units. The experiments were conducted under the following conditions: the pre-impact diameters of the droplets ranged from 0.53 to 0.60 mm, the impact velocities ranged from 1.7 m/s to 4.1 m/s, and the solid surface temperatures ranged from 170 °C to 500 °C. When a droplet impacted onto the solid at a temperature of 170 °C, weak boiling was observed at the liquid/solid interface. At temperatures of 200 or 300 °C, numerous vapor bubbles were formed. Numerous secondary droplets then jetted upward from the deforming droplet due to the blowout of the vapor bubbles into the atmosphere. No secondary droplets were observed for a surface temperature of 500 °C at the low-impact Weber numbers (∼30) associated with the impact inertia of the droplets. Experiments using 2.5-mm-diameter droplets were also conducted. The dimensionless collision behaviors of large and small droplets were compared under the same Weber number conditions. At temperatures of less than or equal to 300 °C, the blowout of vapor bubbles occurred at early stages for a large droplet. At a surface temperature of 500 °C, the two dimensionless deformation behaviors of the droplets were very similar to each other.     

梯度润湿表面上液滴定向迁移及合并行为的格子Boltzmann模拟

采用改进的格子Boltzmann方法,对梯度润湿性表面上液滴的定向迁移及合并行为进行了数值模拟,该模型在精度和稳定性上都有很大改善,同时,研究了梯度润湿性表面上液滴定向迁移和合并的动力学特性,并对液滴尺寸及润湿梯度对液滴动力学特性的影响规律进行了分析。数值结果表明,液滴在梯度润湿性表面运动时会发生形变,且动态接触角逐渐减小。润湿梯度对液滴定向迁移行为有显著影响,润湿梯度越大,液滴左右侧接触线位移越大,润湿长度增加越快。但是液滴尺寸对接触线位移影响较小。润湿梯度对液桥宽度基本无影响,但对液滴初始合并时间有显著影响。     

Breakup of a droplet at high velocity impacting a solid surface

We have studied the collision between a droplet of different liquids with high impact energy and a solid plate with varied surface roughness, which is characterized by a dimensionless Weber number (We, defined as the impact inertia of the droplet normalized by its surface force) extending up to 12,000 for water. To make such collision, a technique was developed to generate a single droplet with speed up to 42 m/s, which was initially driven by upstream air flow through a nozzle and accelerated to nearly the same velocity of the high-speed flow downstream. Via a high-speed photographing system, the various splashing mechanisms were investigated and a specific prompt splash on a smooth plate was found at sufficiently high We, which was different somehow from the conventionally defined one that was generally believed to occur only on a rough surface. The radius when multiple secondary droplets were shed out of the rim of the expanding lamella was found to scale almost invariantly with We at large values, whereas the coupled effect of liquid viscosity might affect the ultimate value.     

Self-propelling,coalescing droplets

This work proposes and explores a new propulsion mechanism for sessile droplets which could be of interest for microfluidic applications. This mechanism relies on the Marangoni stresses resulting from the surface tension gradient arising when two droplets of different surface tensions coalesce. We argue that the tendency of the fluid to flow towards regions of higher surface tension is sufficient to displace the droplet. The coalescence of two miscible, partially wetting droplets with different surface tensions is investigated theoretically in this paper and modeled in the lubrication approximation framework. The problem is described by a set of three highly non-linear, coupled partial differential equations which is solved with a commercial finite element code. The analysis reveals two important dimensionless numbers which govern the flow characteristics, one related to the strength of the surface tension gradient and the other to the diffusion time scale. The numerical results confirm the occurrence of the self-propulsion behavior and a parametric study is performed to explore the role of the two dimensionless numbers on the propulsion speed and the total displacement. Unsurprisingly, self-propulsion is enhanced for larger values of the surface tension contrast between the two droplets and smaller values of the diffusion time scale which results in more time for the surface tension gradient to act.     

Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers

The dynamics of inkjet droplet of non-Newtonian fluid on glass substrates was investigated experimentally and compared with that of Newtonian fluid. The non-Newtonian fluids used here were 100 ppm solutions of polyethylene oxide (300k, 600k and 900k) dissolved in the 1:1 mixture of water and glycerin. Weber number (We) was 2–35 and Ohnesorge number was fixed at 0.057 ± 0.003. The wettability of solid substrate was also varied. The diameter of inkjet droplets in the present study was about 50 μm and was much smaller than the size of the previous studies on drop impact. Due to the development of a thin and long thread at the rear of the main drop the jetting window of polymer solution was much narrower than that of Newtonian fluid, and hence the experimental range of Weber number was restricted. The impact scenarios of non-Newtonian inkjet droplets were found to be qualitatively different from those of Newtonian droplets during the receding phase while they were almost the same as the Newtonian fluid case during the kinematic phase. The spreading diameter at the equilibrium was well correlated with the modified Weber number (We′ = We/(1 − cos θ_eq)) as in the case of Newtonian fluid, where θ_eq is the equilibrium contact angle. The similarity or disparity between the Newtonian and non-Newtonian cases was discussed considering the conformation of polymer chains during each stage of drop deformation.     

Evaporation phenomenon past a rotating hydrocarbon droplet of ternary components

A numerical study of heat and mass transfer from an evaporating fuel droplet rotating around its vertical axis was performed in forced convection only on the side opposite to the flow. The flow was assumed to be laminar, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on the abovementioned assumption, the conservation equations in a general curvilinear coordinate were solved numerically. The behavior of rotating droplet evaporation in the forced convection flow can be investigated by analyzing the effects of the rotation of the droplet on the evaporation process of multi-component hydrocarbons droplet. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method. Thomas algorithm is used to solve the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hydrocarbon droplet were determined. The thickness of the boundary layer is unknown for this model and therefore, it was determined in function of time. Additionally, the study concerns “Dgheim dimensionless number” which is the ratio of the rotation forces over the viscosity forces. Dgheim dimensionless number is correlated to Nusselt and Sherwood numbers for multi-component hydrocarbon droplets in evaporation by taking into account the effect of heat and mass Spalding, Prandtl and Schmidt numbers respectively. Also, correlations for Nusselt and Sherwood numbers in terms of Reynolds, Prandtl and Schmidt numbers are proposed. These correlations consider the rotation phenomenon and advance the variation of the thermophysical and transport properties in the vapor phase of multi-component blends.     

An experimental study of a water droplet impinging on a liquid surface

An experimental study is presented for water droplet impingement on a liquid surface. The impaction process was recorded using a high-speed digital camera at 1,000 frames/s. The initial droplet diameter was fixed at 3.1 mm ± 0.1 mm, and all experiments were performed in atmospheric air. The impact velocity was varied from 0.36 m/s to 2.2 m/s thus varying the impact Weber number from 5.5 to 206. The impacted liquid surface consisted of two fluids, namely water and methoxy-nonafluorobutane, C₄F₉OCH₃ (HFE7100). The depth of the water and HFE7100 pool was varied from 2 mm to 25 mm. The collision dynamics of water in the HFE7100 pool was observed to be drastically different from that observed for the water droplet impingement on a water pool. The critical impact Weber number for jet breakup was found to be independent of liquid depth. Water–HFE7100 impact resulted in no jet breakup over the range of velocities studied. Therefore, no critical impact Weber number can be defined for water–HFE7100 impact. Received: 27 June 2001/Accepted: 29 November 2001     

Collision of a vortex with a vaporizing droplet

Three-dimensional interactions between an advecting vortex tube and a vaporizing droplet, described by the Navier–Stokes, energy, and species equations, cause fluctuations in the droplet heating and vaporization, manifested by temporal and time-averaged variations in the droplet Nusselt and Sherwood numbers. Stefan flux not only inhibits the droplet heating, it also ‘blocks’ the influence of vortex collision on the droplet interface inhibiting Nusselt number perturbations. The Stefan flux has a primary effect on the Nusselt number and a secondary one on the Sherwood number. Fluctuations in Sherwood number can be significant in magnitude and exhibit self-similarity in both the temporal and time-averaged response. Derived correlations are demonstrated to be valid for at least three common fuel droplets (n-heptane, n-octane, n-decane). Furthermore, they quantify the effect of vortex collision on the droplet vaporization and compliment the accepted correlations for droplets in axisymmetric flows. It follows that, in spray combustion systems, vortical structures could significantly affect transport mechanisms, vaporization rates, and local mixture ratios.     

Normal droplet impact on horizontal moving films: an investigation of impact behaviour and regimes

Investigations of the impact regimes for a liquid droplet impacting onto horizontal moving liquid films are presented here for the first time. The aim of this study is to show the main impact outcomes and to highlight the effect the movement of films has upon these outcomes. The droplet diameters used in this experiment were 2.47 and 3.86 mm with impact Weber number of between 0.6 and 460. The Reynolds number of the moving film was between 351 and 1,818 depending on the flow rate (1–5.5 L/min) with changes in the film height of between 4.3 and 9.4 mm. The results showed that the impact outcomes exhibit the same regimes established for the impact on static liquids but with different transition boundaries. Moreover, the shape of the impact outcomes is unsymmetrical similar to the inclined impact on static liquids. The impact outcomes are shown to undergo a transition as the Reynolds number of the film increases, this occurs at a threshold value close to the expected transition between laminar and turbulent flow.     

Numerical simulations of droplet train and free surface jet impingement

The cooling behavior of the impingement of a droplet train, and free surface jets over a heated and pre-wetted surface is explored employing an Algebraic Volume-of-Fluid methodology. The code is based on a modified version of the two-phase numerical solver interFoam (OpenFOAM) (Trujillo and Lewis, 2012). Two versions of the free surface jet are studied. The first consists of a fully-developed profile exiting the nozzle, and the second is characterized by a uniform velocity distribution. Results show that both jet configurations have higher cooling performance than the droplet train locally and globally, with the fully-developed case being the most effective of the two jet arrangements. Locally, the performance is measured by radial profiles of the boundary-layer-displacement thickness and heat transfer coefficient. Globally, the cooling effectiveness is directly proportional to the surface area that resides within the high-convection region, i.e. before the boundary layer separation point. On a temporal basis, the liquid film within the impingement region of the droplet train exhibits pronounced variations in velocity magnitude and film thickness. This is directly attributed to the nature of continuous droplet impacts affecting the impingement region, and gives rise to an unsteady cooling and heating of the fluid near the wall. In contrast for the jets, the film and the corresponding free surface are nearly steady with only minor perturbations.