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The effect of a shielding gas on the plasma flow of an electric arc and molten metal is studied. The effect of the shielding gas on the plasma flow of the electric arc of molten metal is simulated, and a mathematical model is developed that describes the flow of the plasma-forming gas inside a device that forms the necessary directions of plasma flows to form a droplet of molten electrode metal of the required size. It is established that the shielding gas and its pressure affect the gas outflow rate and the formation and size of an electrode metal drop. The time of the formation and detachment of the droplet changes at the increase in the pressure of the shielding gas, the higher the gas pressure, the smaller the volume of the droplet. Argon and carbon dioxide have different effects on the plasma flow of the electric arc, the length of the arc, the formation and detachment of the droplet. The process of the droplet formation can be controlled by changing the gas composition, pressure, and gas velocity. It is determined that the gas flow rate increases from 1.2 to 5.2 m/s and the volume of a droplet of molten electrode metal decreases at the increase in the gas flow from 10 to 30 L/min. The droplet volume can be changed on average by 65% depending on the shielding gas. [ABSTRACT FROM AUTHOR]

• Liquid atomization on two counter-rotating wheels was studied experimentally. • Predominant atomization mechanism is by ligament breakup and head droplet pinching. • At same Weber numbers, droplet diameters are lower than for spinning discs and cups. • Liquid impingement point and wheel gap largely affect mass transfer between wheels. • Significant splashing of liquid can occur after impingement due to a hydraulic jump. This paper presents an experimental study of the liquid disintegration process on an atomizer with two counter-rotating wheels by high-speed imaging. The process was investigated for a wide range of wheel rotational speeds, liquid flow rates and impingement positions. Compared to flat disc and cup atomizers operating at similar Weber numbers, proposed atomizer design is capable of producing much finer droplets in the ligament formation mode (mean diameter under 0.15 mm when We = 106) and at a significantly larger liquid throughput. Despite the atomizer gap flow complexity, approximation of mean liquid trajectories with tangent lines proved to be fairly accurate. We were able to identify two main challenges in atomizer operation, namely the occurrence of hydraulic jump upon liquid impingement causing the formation of large droplets, and escaping of the liquid spray through the wheel gap. Nevertheless, both issues can be largely mitigated by optimization of atomizer geometry and operating parameters. [ABSTRACT FROM AUTHOR]

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For the first time, the evolution of the spreading pattern of a fallen water drop over the surface of a cavity and a crown in a deep layer of oil has been traced by high-resolution video and photography. At the stage of active drop submergence, the double layer formed by the contacting surfaces of immiscible fluids is the most rapid component of the flow. Droplets containing both fluids fly out from the tops of the spikes on the edge of the crown. The water covering the inner surface of the cavity and the crown flows unevenly downwards after submergence of the drop. Isolated anhydrous areas, voids, are formed on the surface of the crown and are separated by narrow bands of water, which eventually break up into separate drops. The bulk of the water unevenly submerges to the bottom of the cavity and, at its collapses, remains in the bulk of the liquid in the form of individual fragments, gradually tightening into smooth droplets. The regularities of the temporal changes in the splash height and in the shape of the cavity section are revealed. [ABSTRACT FROM AUTHOR]

With a purpose for textile material coating applications, a process of spraying the polymer flow is considered. The equipment for determining the polymer drop size is designed. The formulas for estimating the size of polymer droplets are validated. For controlling and measuring the polymer drop size in real time, the multi-frequency phase method is suggested to be used. Classification is needed to find a category, within which the measurement will be done. Photos of various particles are obtained while experiments of spraying polymers are conducted. The sizes of those particles are determined. It is ascertained with the laser measurement and the corresponding software that when polymer drops get onto a textile material, they cool rapidly. The quality of the material is maintained. For properly spraying the polymer, the pressure of 6 MPa and the nozzle diameter of 2 mm are sufficient. The structure of the textile material along with the coating is maintained best with these parameters. [ABSTRACT FROM AUTHOR]

• Spreading dynamics of a sessile viscoelastic drop on a horizontal surface is studied. • Simplified Phan–Thien–Tanner model represents the rheology of the viscoelastic drop. • Theoretical results are validated with our experimental results. • Elastic nature of the viscoelastic fluids reduces the spreading rate of the drop. We study the spreading dynamics of a sessile viscoelastic drop on a horizontal surface, where a simplified Phan–Thien–Tanner (sPTT) model is considered to represent the rheology of viscoelastic drop. We have adopted a macroscopic approach to obtain the temporal evolution of the spreading drop, while to establish the efficacy of the theoretical model, we have validated the results obtained from the mathematical formulation with the experimental results for both the Newtonian (Si-oil) and viscoelastic (PDMS and aqueous solution of CMC and glycerin) drops. Following the framework of Seaver–Berg approximation, the spherical shape of the drop is assumed as a cylindrical disk here. We observe from this study that an increment in the elasticity of the fluid enhances the velocity gradient and increases the viscous dissipation in the drop volume, leading to a reduction in the spreading rate. [ABSTRACT FROM AUTHOR]

The phenomenon of drop formation at a single plain hole and a single nozzle hole in a plate submerged in a quiescent continuous phase is studied by carrying out numerical simulations. Phase-field method has been used for tracking the evolution of the interface between the drop phase and the continuous phase. The computational approach used in the numerical simulations is validated using the data reported in literature. The validated computational approach is then used for parametric analysis to understand the effects of various independent variables on the phenomenon of drop formation. For identical conditions, the drops formed at a nozzle hole are found to be smaller than the drops formed at a plain hole. The drop detachment time is more for a plain hole than for a nozzle hole. The drop detachment height is, however, more for a nozzle hole than for a plain hole. Correlations to estimate drop diameter for both types of holes are presented. [ABSTRACT FROM AUTHOR]

Direct Numerical Simulations have been performed to study the droplet spreading behaviour on a spherical surface. A coupled immersed boundary and volume of fluid method is used to represent the gas-liquid-solid interactions. The contact area of the droplet on the surface is recorded in order to fit the initial spreading with a power-law representation, using the contact-angle and interface curvature as fitting parameters. Small viscous droplets are used to reduce interfacial oscillations as well as low drop velocities to reduce impact forces. A decrease of spreading area with increasing curvature is observed. Moreover, the model shows good agreement compared to equilibrium states. A strong contact-angle dependence is found for the pre-factor of the power law, which is expected, and a linear decrease was found in the exponent for increasing curvature of the surface. Unlabelled Image • The spreading dynamics change with increasing surface curvature. • Two spreading regimes become apparent at increased curvatures and make the fitting of the power law impossible. • Due to the reduced spreading area for increased curvatures, droplet oscillations are more pronounced. • Less viscous spreading occurs at higher surface curvatures. [ABSTRACT FROM AUTHOR]

Highlights • The aspect ratio of drops continuously increases with the increase in Weber number. • Increased viscosity of the drop fluid damps the velocity gradient inside the drop. • The shape of a drop is either prolate or spherical at the incipience of pinch-off. • A non-spherical drop oscillates while falling through a surrounding medium. • The oscillatory motion of the drops is damped by viscosity. Abstract Present study focuses on the shape of a drop during pinch-off and how the shape of a drop is affected by the flow parameters and different physical properties of the fluids. Both experimental and numerical investigations are performed to unveil the mechanism of non-spherical drop formation and the oscillatory motion of a drop after pinch-off. Numerical simulations are performed over a wide range of density ratios (0.001–0.9) and viscosity ratios (0.01–10) ranging from a gas-liquid system to a liquid-liquid system. The deformation of a drop at the incipience of pinch-off depends on the internal stress distribution within the drop. A larger velocity gradient inside the drop culminates in a stronger shear force within the drop leading to a non-spherical drop during pinch-off. We reveal that the shape of a drop remains either in prolate or in spherical form during pinch-off. A drop undergoes prolate-oblate-prolate oscillation while falling through the surrounding medium. The oscillatory motion is generated due to the local capillary pressure that develops across the drop surface because of the deformed shape of the drop after pinch-off. Present investigation reveals that the deformation of the drop because of the downward pull generated near the pinching region makes the drop shape non-spherical after pinch-off and initiates the oscillatory motion of the drop. The oscillation of a drop reduces substantially at higher relative strength of the viscous force. [ABSTRACT FROM AUTHOR]

Evaporation of a drop, though a simple everyday observation, provides a fascinating subject for study. Various issues interact here, such as dynamics of the contact line, evaporation-induced phase transitions, and formation of patterns. The explanation of the rich variety of patterns formed is not only an academic challenge, but also a problem of practical importance, as applications are growing in medical diagnosis and improvement of coating/printing technology. The multi-scale aspect of the problem is emphasized in this review. The specific fundamental problem to be solved, related to the system is the investigation of the mass transfer processes, the formation and evolution of phase fronts and the identification of mechanisms of pattern formation. To understand these problems, we introduce the important forces and interactions involved in these processes, and highlight the evaporation-driven phase transitions and flows in the drop. We focus on how the deposited patterns are related to and tuned by important factors, for instance substrate properties and contents of the drop. In addition, the formation of crust and crack patterns are discussed. The simulation and modeling methods, which are often utilized in this topic, are also reviewed. Finally, we summarize the applications of drop evaporation and suggest several potential directions for future research in this area. Exploiting the full potential of this topic in basic science research and applications needs involvement and interaction between scientists and engineers from disciplines of physics, chemistry, biology, medicine and other related fields. [ABSTRACT FROM AUTHOR]

Highlights • The interaction of drops in various arrangements is studied using the VOF method. • Regime maps on the observed interaction scenarios are presented. • Breakup times of secondary drops are compared to data available for single drops. • Flow and material properties significantly influence interaction phenomena. • A method for the modelling of dense spray regions is suggested. Abstract A Volume of Fluid (VOF) method is applied to study the interaction between two liquid drops with the same initial diameter in uniform flow. Various arrangements of the drops are studied, based on two parameters, namely the initial separation distance and the angle between the line connecting the centres of the drops and the free-stream direction. Initial separation distances of 1.5–5 drop diameters, and angles between β = 0 ∘ and 90° are considered. Simulations for a Weber number of W e = 20 , two Reynolds numbers R e = 20 and 50, and density and viscosity ratios in the range ρ * = 20 –80 and μ * = 0.5 –50 are performed. The movement of the secondary drop with respect to the primary drop, and estimates on the time required for the breakup of the secondary drop as compared to those observed for single drops are evaluated. It is found that the drops collide only in cases corresponding to the shortest initial displacements, while in others they deform and break up independently, similarly or identically to single drops. The same behaviour is reflected in the time required for breakup. Cases where the drops behave independently show breakup times close to those observed for single drops. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Temperature and velocity fields of the droplets are heterogeneous and unsteady. • Heating time for droplet of a salt solution at the 100–500 °C reached 3–18 s. • Velocity of the convection varies inside range 0.3–4 mm/s. • Heating rate of the salt solution droplets more than for the water droplets. • Differences of evaporation rates for salt solution and water droplets reaches 1.45 times. Abstract Salt solutions are widely used in many industrial technologies, including those associated with high heat fluxes. The main constraint to the introduction of many promising high-temperature gas-vapor technologies with using salt solutions is that the mechanisms of interrelated processes of heat and mass transfer and phase transformations of such solutions under intense heating have not been sufficiently studied yet. In most modern devices, blocks and setups, intensive convective heating is realized both through gas and liquid media. As a result, the study of these processes under high-temperature convective heating is topical. The most significant results may be obtained by using the low-inertia non-contact measurement methods. This article presents the results of experimental studies of the processes of heating of drops of typical salt solutions (LiBr, CaCl 2 , LiCl, NaCl) placed in the flow of heated air on the holder. The temperature range was chosen from 20 °C to 600 °C to cover a large group of gas–vapor technologies, primarily evaporation (boilout) and burning (burnout) of impurities from water. Thus, the main attention was paid to the study of convective heat exchange of drops of salt solutions with a heated gas medium. The optical method Planar Laser Induced Fluorescence (PLIF) was used to control the temperature field of the droplet. The convection velocity in the droplet was registered using the optical method of Micro Particle Image Velocimetry (Micro PIV). The main attention was paid to the effects of crystallization, processes of heating and evaporation of droplets, taking into account different properties and component composition of salt solutions. The influence of these factors and processes is shown at different heat-up temperatures. The differences in the rates of heating and evaporation of salt solution drops under intense convection heating have been established. Recommendations on the application of research results for the development of promising gas–vapor technologies have been formulated. [ABSTRACT FROM AUTHOR]

Highlights • Simulations of accelerated rising of drops agree with experimental data. • Numerical results capture the oscillatory regime for low Weber number drops. • The interplay of shape oscillations and velocity fluctuations is explained. • The simulations disclosed that symmetry breaks cause the double-threaded wakes. Graphical abstract Abstract The present work addresses the numerical simulation of rising droplets with clean interface. An interface-tracking methodology was applied to simulate the particular behavior of water-immersed toluene drops. The obtained transient velocity profiles were compared with experimental data, confirming the methodology's capability to represent this two-phase flow. Numerical simulations enable scrutinizing many flow details which are not accessible experimentally. In this regard, the elements linked to the velocity oscillatory behavior of droplet sizes between diameters of 2.2 and 3 mm are discussed. It could be verified that velocity oscillations were directly related to variations in shape, internal circulation and flow separation. Simulations indicated that three-dimensional shape asymmetries are associated with vorticity accumulation in preferential regions of the drop, which disturb the internal circulation pattern. In the oscillatory size range, flow separation causes periodic vortex detachment, enabling formation of a double-thread wake. Evaluation of non-dimensional parameters further disclosed the relation of the transitory behavior and steady state drop shape. [ABSTRACT FROM AUTHOR]

Mass transfer around spherical bubbles, drops, and solid particles in uniaxial and biaxial nonlinear extensional creeping flows at large Peclet numbers is the subject of this theoretical report. The fluid mechanics problem is governed by the viscosity ratio (λ) and the nonlinear intensity of the flow (E). The flow outside such bodies reveals a different picture than the linear case (E = 0) such as separating surfaces or closed circulations. There is a range: −1.04 < E < 0 (bubbles and drops) and −0.490 < E < 0 (particles) where the mass transfer rate is lower than the linear case. Outside these ranges, the mass transfer rate is higher than the linear case and in general it increases as |E| increases. Same mass transfer rates are expected in uniaxial and biaxial flows, except in the presence of external closed circulations where the biaxial flow overcomes the uniaxial flow. © 2018 American Institute of Chemical Engineers AIChE J, 65: 398–408, 2019 [ABSTRACT FROM AUTHOR]

The properties and shapes of drops attached to fibers are important for understanding the movements of drops on fibers in applications such as coalescing filters. One of the features of the shape of a drop attached to a cylindrical fiber is an inflection in the curvature of the drop profile near the contact line between the drop and the fiber surface. Depending on the drop volume, the point of inflection may occur very close to the drop-fiber contact line, and the angle at the inflection point could mistakenly be interpreted as the intrinsic contact angle. Measurement of the angle at the inflection point improves the characterization of the drop profile for a drop-on-fiber system. Many studies provide methods that apply droplet geometric symmetry to extract the profile of drops on flat surfaces. However, none of these methods can be easily applied to drops on fibers due to the curvature of the fiber surface and its effect on the shape of the drop. In the case of drops on fibers, drop properties such as drop length, thickness, inflection angle and volume are useful to obtain the wetting properties of the fiber surfaces without knowing the liquid properties. To determine inflection angles and volumes of axisymmetric barrel-shaped droplets on fibers from 2D images of droplets profiles a polynomial fitting method for fibers (PFMF) was applied. The strategy employed detects the location of the droplet boundary, fits a polynomial to the boundary, and calculates the inflection angle and the volume of the droplet. Volume measurements using the PFMF were consistent with calculations from Surface Evolver™ program. Using the PFMF, a new correlation was generated for a shape factor characterizing the asymmetry of barrel-shaped droplets as a function of liquid properties, fiber radius, and droplet volume. [ABSTRACT FROM AUTHOR]

Investigation of the physical phenomena involved in blood interactions with real surfaces present new exciting challenges. The fluid mechanical properties of such a fluid is singular due its non-Newtonian and complex behaviour, depending on the surrounding ambient conditions and the donor/victim's blood biological properties. The fundamental research on the topic remains fairly recent; although it finds applications in fields such as forensic science, with bloodstain pattern analysis, or biomedical science with the prospect of disease detection from dried blood droplets. In this paper, we review the understanding that has been achieved by interpreting blood wetting, spreading and drying when in contact, ex-vivo, with non-coated surfaces. Ultimately, we highlight the applications with the most up to date research, future perspectives, and the need of advancing further in this topic for the benefit of researchers, engineers, bloodstain pattern analysts, and medical practitioners. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation of deformation and breakup of a solidifying liquid drop pendant from a cold solid surface by an axisymmetric front-tracking method combined with an interpolation technique for enforcing the no-slip velocity boundary at the solid–fluid interface. Many dimensionless parameters such as the Prandtl number Pr , the Stefan number St , the Rayleigh number Ra , the Ohnesorge number Oh and the Bond number Bo are varied to reveal their effects on the process. Numerical results show that depending on the flow conditions, the liquid drop can break up while solidifying. Starting from non-breakup, increasing Bo (from 1.0 to 3.5) or Pr (from 0.01 to 3.16) causes the solidifying drop to break up into liquid drops that fall away from the solid surface. The transition from non-breakup to breakup also appears when decreasing St from 1.0 to 0.01, Ra from 1000 to 50, or Oh from 0.316 to 0.01. In addition, the effects of these parameters on the solidification time and the height of the solidified products are investigated. Moreover, the effects of volume change (in terms of the solid-to-liquid density ratio) upon solidification and the tri-junction (in terms of the growth angle) are introduced. We also present a phase diagram of Bo versus St that shows the region of the non-breakup-to-breakup transition. [ABSTRACT FROM AUTHOR]

We report that the addition of a small amount of cellulose nanofibers (CNFs) into an aqueous dispersion of colloidal particles suppresses the coffee-ring effect when the dispersion dries on a solid substrate, as revealed by the computational analysis of experimental time-series images and by particle image velocimetry. The addition of CNFs is much more effective than the increase of colloidal particle concentration at the same weight percentage; it is also more environment friendly than the use of typical molecular surfactants. This finding is promising for the fabrication of metamaterials from colloidal dispersions and for ink printing in electronics, where CNFs can also serve as a substrate for flexible devices. [ABSTRACT FROM AUTHOR]

The results of detailed, three-dimensional numerical simulations of fixed spherical drops in a uniform flow are presented. The fluid dynamics outside and inside of the drops as well as the internal problem of mass (or heat) transfer are studied. Liquid drops in both a liquid and a gaseous ambient phase are considered. Special emphasis is put on the investigation of different modes of internal circulation. At low Reynolds numbers of the inner fluid, the flow field inside the drop resembles the well known Hill’s vortex solution. However, at higher internal Reynolds numbers, stable steady or quasi-steady alternative modes of internal circulation are found. As these modes are not cylindrical symmetric around the streamwise axis, the often applied assumption of a two-dimensional, axisymmetric flow field is not justified in these cases. Thus, major discrepancies to previous numerical studies are obtained. However, it is shown that experimental results support our findings. For liquid drops surrounded by a liquid, a major influence of the state of internal circulation on the drag is discovered, whereas the drag is nearly unaltered in the case of a liquid drop in gas. Concerning the internal problem of mass/heat transfer, the various internal flow modes show different characteristics. At low internal Peclet numbers, higher Sherwood numbers are reached for the Hill’s vortex-like cases, whereas at higher Peclet numbers, the transfer is faster for the alternative modes. For cases with a Hill’s vortex-like solution, asymptotic Sherwood numbers for very high Peclet numbers of around 20 are found, whereas no upper limit for cases with alternative modes can be determined. In the present study a maximum internal Sherwood number of 130 is reached, more than six times the maximum value for a case with a Hill’s vortex-like internal solution. [ABSTRACT FROM AUTHOR]

Three-dimensional numerical simulations of the interaction between two drops rising in a thermally stable stratified fluid are presented. The governing equations are solved using a finite-volume/front-tracking method. The influence of stratification on the dynamics of two drops moving in line and side by side is studied. For the case of nearly spherical drops ascending side by side, drops remain in the horizontal alignment during the interaction; but the rate of separation, after their initial collision, decreases for stronger stratifications. We demonstrate that, in contrast to the case of a homogeneous fluid, two drops moving in tandem in a strongly stratified fluid retain their in-line configuration. [ABSTRACT FROM AUTHOR]

The objective of this work is to propose a mathematical expression for the instantaneous velocity of falling water droplets in air and traveled height versus time. In addition, changes in terminal velocity depending on terminal height are studied. For very small spherical drops, having very low Reynolds number and obeying Stokes law for the drag force, the instantaneous velocity u of the drop with time is a well-known result. From the expression of that speed, it is easy to get the drop height h versus time. By eliminating the time, the displacement h of the droplet as a function of the velocity u is obtained. In the present work, the latter was extended to larger drops. The values predicted by the mathematical equation obtained from the combination of theory and experiment (semi empirical equation) are compared with well known experimental data . The results show good agreement between the values predicted and the experimental data. [ABSTRACT FROM AUTHOR]

The transfer of mass between a slender drop and a liquid in an axisymmetric extensional flow, at zero Peclet numbers, is theoretically studied. We allow the external flow to have a small (but not zero) amount of inertia. The problem is governed by three dimensionless parameters: the capillary number (Ca >> 1), the viscosity ratio ( λ << 1) and the external Reynolds number (Re << 1). It is shown that the shape of the drop is, at first approximation, a slender spindle suggesting the usage of the bispherical coordinate system. Applying the method presented by Szegö and Pyne, for the electrostatic capacity of a spindle, an analytical solution containing conal functions is obtained. The results show that, as the capillary number or the Reynolds number increase, the drop becomes thinner and longer, the surface area increases, resulting in larger mass transfer rates, with the capillary number being the most influential parameter. [ABSTRACT FROM AUTHOR]

This work is centered upon the thermal transients taking place during the evaporation of a spherical drop of a pure liquid suspended in a gaseous environment. Based on mass and energy conservation equations, a so-called complete model is developed considering quasi-steady diffusive and Stefan convective transports in the non-isothermal gas phase, and unsteady conduction in the liquid drop. A simplified version of the complete model, the so-called quasi-homogeneous model, is developed using an asymptotic analysis in the limit of small thermal homogenization time in the drop compared to the total drop evaporation time. The models enable highlighting the role of two dimensionless numbers, R and H , characterizing the two thermal transients of the problem: the thermal relaxation transient of the drop interfacial temperature and the thermal homogenization transient of the drop. The values of these two dimensionless numbers are provided for several liquids and their dependence on the evaporation conditions is discussed. It is shown that, when an accurate evaluation of the drop evaporation time is required by the considered application, the use of a fully quasi-steady model should be restricted to systems presenting small values of R compared to one (at least an order of magnitude smaller) and H < 1 . For other systems, it appears necessary to use the complete model or the quasi-homogeneous model. A simple formula is proposed to evaluate the relative difference between the drop evaporation times predicted by the complete model and by the fully quasi-steady model. When an accurate evaluation of the time evolution of the drop temperature field is required by the considered application, it appears to be necessary to use the complete model, whatever the system considered in this work. Indeed, the thermal transients can generally take an important part of the drop evaporation time and large temperature gradients can develop in the drop. The use of the complete model reveals that three different types of dynamics can be observed when a drop evaporates, depending on the relative values of three temperatures: the initial drop temperature, the dew point temperature of the gas far from the drop and the established interfacial temperature ( i.e. the drop interfacial temperature calculated using a fully quasi-steady model). [ABSTRACT FROM AUTHOR]

We describe the first method to control, in a single microfluidic device, the generation, fusion, and mixing of pico- to nanoliter water-in-oil drops using a straightforward LED light stimulus. This is achieved by implementing a photosensitive surfactant in the water phases of a novel dual flow-focusing microfluidic configuration. UV illumination at 365 nm enables dynamic switch of the flow behavior between a stable dual jet regime (−UV) and a stable dual drop regime (+UV), thus allowing us to generate on-demand two distinct populations of water drops. These drops are fused and mixed downstream inside expansion chambers, offering both a dynamic control by light stimulation and a controllable degree of fusion and mixing by the positions of chambers. The mixing inside the fused drops is found to be much faster than diffusion due to the chaotic advection inside the moving drops. [ABSTRACT FROM AUTHOR]

We study the formation of nanoliter-sized droplets in a microfluidic system composed of a T-junction in PEEK and tubing in Teflon. This system, practical for a ‘plug and play’ set-up, is designed for droplet-based experiments of crystallization with a statistical approach. Hence the aim is to generate hundreds of droplets identical in size and composition and spatially homogeneous. Therefore, parameters of control are droplet size and frequency. However, the geometry of the T-junction is not perfect and, moreover, its channels are circular, as opposed to the planar geometries with rectangular cross-sections that are usually used. However, based on 3D experiments and 2D simulations, we observe the same regimes of droplet generation in circular channels as in planar geometries, and with the same stability. Therefore, we refer to velocities instead of flow rates to characterize the system. Then we define operating range in terms of droplet size and frequency through empirical relations using total velocity, velocity ratio and capillary number, to ensure homogeneous droplets in channels of 500 µm and 1 mm diameters. [ABSTRACT FROM AUTHOR]

The movement behavior of glycerol–water mixtures as sessile drops on a tilted PTFE incline is investigated here. The slip angles found showed complex relationships in relation to the mixture composition. Since the drop was found to breach its front contact line first, the levels of contact angle hysteresis did not have corresponding trends with the slip angles. However, the ratios of the drop lengths (at the point of detachment against that at equilibrium) had corresponding trends with the slip angle. The drop elongated in a two-stage manner as it was tilted progressively. Since this could not be ascribed to a sudden change in the gravitational force acting, it implied that the drop extended first as a single body before attempting to split into two. In considering the energetics involved, the change in the solid–liquid area was mainly used by the drop to adjust to the energy supplied by gravity. Comparative experiments done with drop compression and extension on the same surface eliminated the contribution from specific characteristics associated with the liquid and solid, and inaccuracies in the contact angle measurement method used. Turbidity measurements indicate the viability of using higher glycerol content to improve thermal stability of bovine serum albumin. The findings have important implications on the manner of how heat and mass transfer occurs for drops on inclines for biochemical applications. [ABSTRACT FROM AUTHOR]

Measurements of the drop velocity in the absence of mass transfer, for two liquid-liquid systems in a rotating liquid–liquid extractor unit have been carried out using a high-speed video camera. The drop velocity was measured as function of rotational speed, radius and physical properties. These velocities were compared with those predicted from the equation of motion for the drop and it was found that the contribution of the history integral was important in predicting drop velocity. [ABSTRACT FROM AUTHOR]

This paper reports – for ambient conditions – experimentally determined surface regression rates of acoustically levitated acetone/water drops as a function of the mixture composition at the drop boundary. The fluid levitated as a drop was a mixture of acetone and water with vapor pressures of 24.5 kPa and 3.17 kPa, respectively, at ambient conditions. As expected the acetone evaporated faster from the acetone/water drop than water. Already small quantities of acetone in the mixture significantly increased the surface regression rate of the drop. Temporally and spatially resolved composition profiles were measured along a line through the drops using one-dimensional Raman spectroscopy. Shadowgraphs of the evaporating drops were acquired, from which the drop shrinkage was derived. Due to the good spatial (120 μm) and temporal (1 s) resolution of the one-dimensional Raman experiment the evolution of the radial composition profiles through the drop could be followed showing that the diffusion-process inside the drop plays an important role in the binary evaporation process. [ABSTRACT FROM AUTHOR]

A drop of water subjected to a pulsed electric field in emulsified oil undergoes periodic stretching vibration, which is very effective for promoting the coalescence of the emulsified drops. In this study, the forces that act on a single water drop during its vibration in a pulsed electric field are analysed, and a dynamics model of the vibration of the drop is developed. The expression of the model indicates that the vibration can be described as a non-linear parametric excitation vibration, and comparison of the model predictions with experimental results reveals a good similarity. In addition, a first-order approximation of the predictions of the model is used to obtain the waveforms of the vibration, and the peak of the amplitude–frequency curve reveals the occurrence of resonance. This affords a basis for determining the optimal demulsification frequency of the emulsified oil in the pulsed electric field. [ABSTRACT FROM AUTHOR]

Determination of effective transport properties of droplet-hydrogel composites is essential for various applications. The transport of ions through a droplet-hydrogel composite subjected to an electric field is theoretically studied as an initial step toward quantifying the effective transport properties of droplet-hydrogel composites. A three-phase electrokinetic model is used to derive the microscale characteristics of the polyelectrolyte hydrogel, and the droplet is considered an incompressible Newtonian fluid. The droplet-hydrogel interface is modeled as a surface, which encloses the interior fluid. The surface has the thickness of zero and the electrostatic potential ζ. Standard averaging procedures are used to derive the effective governing equation for the current density that captures the macroscopic behavior. The results show that the polymer boundary condition has a modulating impact on the electrical conductivity, and the influence of the boundary condition decreases as the interior fluid viscosity increases. At the limit of the polymer's no-slip boundary condition, the interior and exterior fluids' viscosities, Brinkman screening length, and ionic strength have a significant impact on the conductivity. Interestingly, it should be possible to determine the ζ-potential for a droplet-hydrogel composite from measurements of the electrical conductivity with the aid of the formula derived for the conductivity. Finally, the theoretical study for determining the response of droplet-hydrogel composites to an imposed pressure gradient is undertaken, and it is found that the polymer boundary condition has a modulating impact on the response. [ABSTRACT FROM AUTHOR]

In this paper, a new comprehensive analysis of a suspended drop of a pure liquid evaporating into air is presented. Based on mass and energy conservation equations, a quasi-steady model is developed including diffusive and convective transports, and considering the non-isothermia of the gas phase. The main original feature of this simple analytical model lies in the consideration of the local dependence of the physico-chemical properties of the gas on the gas temperature, which has a significant influence on the evaporation process at high temperatures. The influence of the atmospheric conditions on the interfacial evaporation flux, molar fraction and temperature is investigated. Simplified versions of the model are developed to highlight the key mechanisms governing the evaporation process. For the conditions considered in this work, the convective transport appears to be opposed to the evaporation process leading to a decrease of the evaporation flux. However, this effect is relatively limited, the Péclet numbers happening to be small. In addition, the gas isothermia assumption never appears to be valid here, even at room temperature, due to the large temperature gradient that develops in the gas phase. These two conclusions are explained by the fact that heat transfer from the gas to the liquid appears to be the step limiting the evaporation process. Regardless of the complexity of the developed model, yet excluding extremely small droplets, the square of the drop radius decreases linearly over time ( R 2 law). The assumptions of the model are rigorously discussed and general criteria are established, independently of the liquid–gas couple considered. [ABSTRACT FROM AUTHOR]

This work focused on the influence of energy spectrum distribution on drop breakage in turbulent flows. An improved breakage model in terms of general energy spectrum function was presented. It can be coupled with available forms of energy spectrum and can be applied to the wider operating conditions such as the wider size range of drops. Unlike previous work that only considered the inertia subrange spectrum, this work simulated the breakage in the framework of wide energy spectrum and accounted for the necessity of considering the wide energy spectrum distribution. The improved model coupled with wide energy spectrum function can theoretically explain the recent experimental phenomena observed by Maaß and Kraume, 2012. Determination of breakage rates using single drop experiments. Chem. Eng. Sci. 70, 146-164. That is, breakage frequency increases to a maximum and then decreases with increasing parent drop size. This is because the non-monotone energy spectrum function can distinguish three spectrum ranges, i.e., containing-energy range, inertia subrange and dissipation range, and the treatment that parent drop size always falls in the inertia subrange is no longer required in this work. While when only the energy spectrum of inertia subrange is applied to the whole size range of eddies, the predicted breakage frequency monotonously increases with parent drop diameter. Therefore, the energy spectrum distribution has a crucial influence on the evolution of the breakage frequency with parent drop size. [ABSTRACT FROM AUTHOR]

Mixing in droplets is an essential task in a variety of microfluidic systems. Inspired by electrokinetic mixing, electric field-induced hydrodynamic flow inside a charged droplet embedded in an unbounded polyelectrolyte hydrogel is investigated theoretically. In this study, the polyelectrolyte hydrogel is modeled as a soft, and electrically charged porous solid saturated with a salted Newtonian fluid, and the droplet is considered an incompressible Newtonian fluid. The droplet-hydrogel interface is modeled as a surface, which is located at the plane of shear, with the electrostatic potential $$\zeta $$ . The fluid inside the droplet attains a finite velocity owing to hydrodynamic coupling with the electroosmotic flow arising from the droplet and polymer charge. The fluid velocity inside the droplet is linearly proportional to the electroosmotic flow velocity in the charged gel and the electroosmotic flow velocity beyond the electrical double layer of a charged interface. It is found that the polymer boundary condition at the droplet surface and the viscosities of the fluids inside and outside the droplet significantly modulate the interior fluid flow. The ionic strength and the permeability of the polymer network impact the flow differently depending on whether the flow arises from the droplet or polymer charge. Finally, the displacement of a charged droplet embedded in a gel under the influence of an external electric field is undertaken. This work is motivated by experimental attempts, which can register sub-nanometer-scale inclusion displacements in hydrogels, to advance electrical microrheology as a diagnostic tool for probing inclusion-hydrogel interfaces. In the absence of polymer charge, a close connection is found between the electrical response of a charged droplet when it is immobilized in an uncharged incompressible gel and when it is dispersed in a Newtonian electrolyte. [ABSTRACT FROM AUTHOR]

This study was concerned with the interaction between a gaseous dispersion of fine particles travelling in the horizontal direction and discrete drops of water falling vertically through the dispersion. A simple analytical model of the particle–drop collision was developed to describe the particle recovery by the drops as a function of the water flux, covering two extremes of relative velocity between the particles and drops. The Discrete Element Method was used to validate the analytical model. Further validation of the model and insights were obtained through experimental studies. The physical process of wetting was observed to be important in influencing the tendency of particles to become engulfed by the drops of water, or to either adhere to the drops or by-pass the drops altogether. Hydrophilic particles were readily engulfed while hydrophobic particles, at best, adhered to the surface of the drop, or failed to attach. Moreover, the recovery of the hydrophilic silica particles was significantly higher than the recovery of hydrophobic coal particles, with the selectivity ratio approximately 1.5. Spherical ballotini particles were the most sensitive, with a notable increase in recovery when cleaned, and evidence of increased recovery with increasing particle size. The recovery of irregular shaped silica flour particles, however, was largely independent of the particle size. A similar result was observed for irregular coal particles, though the recoveries were all lower than relatively more hydrophilic ballotini or silica flour. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a focused beam reflectance method is used to investigate the evolution of dispersed droplets at various dispersed volume fractions for an Exxsol D80 mineral oil–water dispersion in a stirring tank. Two types of inversion experiments are compared, the direct and continuous mixing of the oil–water phases. The number density of the chord lengths and distributions are identified as the main parameters for comparison. The drop coalescence is dominant slightly before inversion, at which point the measured mean square weighted (Sqr-wt) chord length increases significantly. The way of mixing will also influence the effect of drop coalescence and result in different inversion processes. [Copyright &y& Elsevier]

A surface acoustic wave based drop-drop microextraction, in which an original position loop is used for stabilizing drops, is proposed. An interdigital transducer with 27.5 MHz center frequency was fabricated on a 128° yx-LiNbO3piezoelectric substrate for exciting surface acoustic wave. Mass transfer of extractive matter between two liquid phases was enhanced due to acoustic streaming caused by radiation of surface acoustic wave. An original position loop, which was used to prevent extraction liquid from movement along the surface of piezoelectric substrate, was fixed on the substrate with 1 mm gap. An ionic liquid and an organic dye (acid green-25) solution were used for extraction experiments. Results show that the extraction time is greatly decreased due to surface acoustic wave radiation, and extraction process can be finished within two minutes at 30.0 dBm RF signal power. [ABSTRACT FROM PUBLISHER]

Abstract: Terminal velocities and shapes of drops rising through vertical pipes in clean and fully-contaminated systems are measured by using a high-speed video camera and an image processing method. Silicon oils and glycerol water solutions are used for the dispersed and continuous phases, respectively. Triton X-100 is used for surfactant. Clean and contaminated drops take either spherical, spheroidal or deformed spheroidal shapes when the diameter ratio λ is less than a critical value, λC , whereas they take bullet shapes for λ > λC (Taylor drops). The applicability of available drag and Froude number correlations is examined through comparisons with the measured data. Effects of surfactant on the shape and terminal velocity of a Taylor drop are also discussed based on the experimental data and interface tracking simulations. The conclusions obtained are as follows: (1) drag and Froude number correlations proposed so far give reasonable estimations of the terminal velocities of clean drops at any λ, (2) the terminal velocities of contaminated drops are well evaluated by making the viscosity ratio μ * infinity in the drag correlation for clean drops in the viscous force dominant regime, (3) the effects of surfactant on the shape and terminal velocity of a Taylor drop become significant as the Eötvös number, EoD , decreases and μ * increases, and (4) the reduction in surface tension due to the addition of surfactant would be the cause of the increase in the terminal velocity and elongation of a contaminated Taylor drop. [Copyright &y& Elsevier]

Abstract: The spreading of a non-Newtonian liquid drop over a homogeneous rough surface is theoretically analyzed in the case of complete wetting. Using the energy approach, a relation is derived among the surface roughness, spreading rate of the drop and the contact angle. It is shown that non-Newtonian liquid drop spreads faster over rough surface than smooth surface. Further, it is observed that a shear thickening liquid (n >1) spreads with faster speed than a shear thinning liquid (n <1) over a rough surface. [Copyright &y& Elsevier]

The heat and mass transfer in the process of movement of water drops in a high-temperature gas medium was numerically investigated. The regimes and conditions of formation of the zone of mutual influence of two drops were determined on the basis of an analysis of the temperature and concentration fields of the water vapor in the neighborhood of the trajectory of movement of the drops. The times of existence (complete evaporation) of one and two drops as a result of their interaction with the high-temperature products of combustion of a typical condensed liquid substance were compared. It has been established that only in the case where the distance between the two drops is small is the intensity of evaporation of water from them substantially lower than that of a single drop. [ABSTRACT FROM AUTHOR]

Abstract: This work deals with the modeling of drop break-up in an inhomogeneous turbulent flow that develops downstream of a concentric restriction in a pipe. The proposed approach consists in coupling Euler–Lagrange simulations of the drop motion to an interface deformation model. First the turbulent flow downstream of the restriction is solved by means of direct numerical simulation. Single drop trajectories are then calculated from the instantaneous force balance acting on the drop within the turbulent field (one-way coupling). Concurrently, the interface deformation is computed assuming the drop to behave as a Rayleigh–Lamb type oscillator forced by the turbulent stress along its trajectory. Criterion for break-up is based upon a critical value of drop deformation. This model has been tested against experimental data. The flow conditions and fluids properties have been chosen to match those experimental investigations. Both turbulent flow statistics and break-up probability calculations are in good agreement with experimental data, strengthening the relevance of this approach for modeling break-up in complex unsteady flow. [Copyright &y& Elsevier]

Abstract: The derivation of for the mass transfer coefficient of carbon dioxide absorption into water droplets formed by controlled breakup of capillary jet was based on turbulent flow equations. This derivation was re-examined, taking into account the fact that the data used were in fact in the laminar flow regime. An alternative derivation and correlation is presented. [Copyright &y& Elsevier]

Abstract: The disintegration of liquid by rotary cups has been investigated experimentally. The mechanism of direct drop formation and ligament formation in a rotary cup was studied using photos taken by a high-speed camera. Two kinds of liquids and three kinds of cups were used in the experiment. In the study, we found that three different types of disintegration formation occur as the angular speed increases in a given flow rate. The equations have been derived theoretically for calculating diameter of liquid drop produced by direct drop formation and ligament formation and the dimensionless equations obtained from the experimental results are applicable for calculating diameter of drops in a wide range of operating conditions. In the process of disintegration by ligament formation, the diameter of liquid drop is determined by the diameter of tail end of ligament, which was constant in diameter. The transition equations from direct drop formation to ligament formation and ligament formation to sheet formation arranged by three dimensionless parameters and compared with various experimental results. The transition equations fit quite well in the trend shown by the experimental date and they are applicable in a particular range of We, i.e. 103

Abstract: The evaporation of sessile drops is central to a number of important processes, including printing, washing and coating. In this paper, the evaporation of water sessile droplets on hydrophobised silicon wafers and Teflon was analysed from theoretical and experimental perspectives. The contact angle, volume and base radius of the water droplets as a function of time were determined using tensiometry. The theoretical analysis showed different evaporative flux phenomena for acute and obtuse contact angles. The non-linear evolution of residual droplet volume, contact angle and base radius are solved and depend on the hydrophobicity of the solid surface and droplet dimension. Good agreement between the theoretical and experimental results was observed during pinning and depinning stages of evaporation. It was shown that the surface roughness, hydrophobicity and the contact angle hysteresis significantly influenced the evaporation of sessile drops and need to be considered when quantifying the evaporation process. [Copyright &y& Elsevier]

Abstract: In this work, the interfacial phenomena of a single hanging drop have been observed and captured by a Schlieren optical system. The extraction fractions at different hanging times were determined. For the system without surfactant, the Marangoni effect induced by interphase mass transfer of a solute displays regular convection patterns. The addition of surfactants changed the mode of interfacial instability significantly but in different ways: SDS enhanced the mass transfer and Triton X-100 reduced the extraction fraction. [Copyright &y& Elsevier]

Abstract: High-pressure homogenizers (HPHs) are used to create sub-micron emulsions in low-viscosity fluids. As the flow in a real HPH is very extreme, with gaps ranging from 10 to 100μm and high velocities, it is almost impossible to visualize the drop break-up process. In this study a plastic scale model of a HPH was made, allowing the visualization of drop deformation and break-up. Great care was taken to keep the relevant dimensionless numbers constant during the scaling-up. The experimental data were interpreted in terms of theoretical drop break-up theory. It was found that both viscous and inviscid mechanisms can deform the drop. When a drop is exposed to a high-energy eddy, the deformation process proceeds rapidly. The deformed drop offers very little resistance to the eddies surrounding it, and it is drawn out, coiled and finally broken up into smaller droplets of various sizes. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents experimental data on droplet entrainment from a wetted wire (stainless steel diameter ) exposed to a gas cross flow using nitrogen as the gas phase and n-decane as the liquid phase. The system pressure ranged from 600 to 1600kPa and the gas flow from 30 to 100NL/min (estimated from 6 to 35m/s). The selected binary system has a surface tension of 23mN/m at 23°C. High speed photography was used to gather the droplet and film data from the experiments. The resulting droplet mean diameter was compared with droplet entrainment data for annular flow. [Copyright &y& Elsevier]

Abstract: The solvent extraction features mass transfer between drops and the surrounding immiscible liquid. Previous study indicated that drop formation plays an important role in extraction because 10–50% of total mass transfer occurs in this stage. It is necessary to have thorough understanding about the mechanism of mass transfer between the drop phase and continuous phase during drop formation. In this work, the level set approach was adopted to capture the interface, and unsteady mass transfer during drop formation was formulated and numerically simulated in an axisymmetric cylindrical coordinate system by solving the fluid motion coupled with mass transfer equations. Drop formation time and mass transfer parameters from the numerical simulation were compared with experimental data in the MIBK–acetic acid–water solvent extraction system. The numerical predictions were found in good agreement with the experimental measurements. [Copyright &y& Elsevier]

Abstract: The optimization, design and choice of separation technology and the internals of a gas–liquid scrubber are highly dependent on the size of the liquid droplets to be removed. The majority of the liquid entrainment correlations for two-phase flow systems only provide information about the net mass transfer between the phases and not much data are available regarding the drop size distribution of entrained, low surface tension liquids (e.g. hydrocarbons) at working pressures higher than atmospheric. This paper provides a data set with new results for liquid entrainment of a mixture of Exxsol D60TM as the liquid phase and nitrogen as the gas phase, with the system''s pressure ranging from 900 to 1600kPa. The corresponding surface tensions were 24.0–24.3mN/m. The paper also reports results of a study on the additional drop size distribution information and provides a correlation that can be taken into consideration in suitable mathematical frameworks in order to increase the level of detail in describing multiphase systems. Further on, a new correlation for the mean droplet diameter was obtained by improving the numerical fitting of data sets which include lower surface tension systems. [Copyright &y& Elsevier]

Abstract: A comparison and analysis of results from multicomponent droplet vaporization simulations at low temperatures using well-mixed and diffusion-limited models are presented. An approach combining elements of continuous and discrete multicomponent mixture description is proposed to model mixtures such as gasoline–ethanol blends, where a pure substance is mixed with a continuous mixture. The rates of heat and mass transfer between the droplet and its environment are evaluated under the assumption that the fluid properties are constant in the gas film surrounding the droplet. The liquid phase is modelled according to three different assumptions: a well-mixed model where temperature and composition are uniform, a combined model where mass transfer is limited by diffusion, but temperature is uniform and a fully diffusion-limited model with respect to both composition and temperature. Results show that the difference between the predictions of a fully diffusion-limited model and that of the combined model increases as temperature is reduced. It is shown that diffusion-limited heat transfer has an appreciable impact on droplet lifetime. The application of an electronic database of experimentally determined fluid properties allowed a partial validation of the accuracy of the chosen empirical correlations. [ABSTRACT FROM AUTHOR]