Liquid Surface Tension Research Articles

High-Temperature Measurements on Viscosity and Surface Tension of the Ionic Liquid 1-Ethyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide ([EMIM][NTf2]) up to 473 K

In the present study, the viscosity and surface tension of the commercial low-viscosity ionic liquid (IL) 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)-imide ([EMIM][NTf2]) were determined by a combination of surface light scattering (SLS) and the pendant-drop (PD) method between (303 and 473) K. Both methods operating at thermodynamic equilibrium were applied inside the same measurement cell at identical experimental conditions under an argon atmosphere at 0.1 MPa. For SLS measurements performed in the temperature range from (303 to 323) K, the overdamped behavior of the surface fluctuations allowed access to the viscosity with an expanded uncertainty of 2.3 % using the surface tensions determined via the PD method with an uncertainty of 2 % as input quantities. Above 323 K up to 473 K, the oscillatory behavior of the probed surface fluctuations by SLS enabled a simultaneous determination of viscosity and surface tension with average expanded uncertainties of (4 and 3) %, respectively. Multiple repetition measurements by both methods have been conducted at 323 K after experiments at larger temperatures up to 473 K, and the consistency of their results could indicate a sound thermal stability of the IL sample. The mutual agreement of the surface tension results from SLS and the PD method between (353 and 473) K demonstrates that both techniques analyze the very same IL surface. For both properties, the results from this work agree well with the majority of experimental data reported in the literature typically up to 353 K. In summary, the viscosity and surface tension results presented in this study contribute to an improved data landscape for this particular IL and ILs in general at elevated temperatures.

Collapsing and Splashing Dynamics of Single Laser-Induced Cavitation Bubbles within Droplets

In the present paper, the cavitation bubble dynamics model for a single bubble oscillating within a droplet is improved based on the classical Rayleigh–Plesset bubble dynamics equation and the effects of liquid surface tension and viscosity are both considered. In the aspect of the experiment, the collapsing dynamic process of a bubble within a droplet is carried out by building a high-speed photography experimental platform. In addition, the numerical solution of the dynamic equation for the collapse time of the bubble within the droplet is also carried out. The findings are given as follows: (1) The bubble dynamic equation considering liquid surface tension and viscosity of bubble within droplet is proposed. (2) The surface of liquid droplets induced by the bubble motion could be divided into three modes: no splashing, scattered splashing, composite splash consisting of scattered and flaky splash. (3) The bubble interface during the first collapsing stage could be divided into three types: spherical, conical, and fungiform. (4) The numerical solution shows an accurate prediction of the bubble collapse time within the droplet especially under the condition of medium radius ratio.

Wetting model of rough solid surfaces and the effect of aggregate properties on epoxy resin binder-aggregate interface wetting

In order to study the effect of aggregate characteristics on the wetting of epoxy resin binder-aggregate interface, based on the Wenzel model and Cassie model, this paper established a new wetting model of the irregular rough surface. The model regularizes the rough solid surface and can calculate the wetting depth and apparent contact angle between different irregular rough solids and liquids. The texture parameters of aggregates, the surface tension of test liquids and the contact angles of different liquids-aggregates were tested by laser confocal tester and optical contact angle measuring instrument. It was found that the surface texture parameters of different aggregates were quite different. The relative error between the apparent contact angle calculated by the prediction model and the contact angle measured by the test was less than 15 %, indicating that the prediction model had excellent prediction effect. Through the analysis of the wetting model, it is found that the surface tension of the test liquid, the lithology of the solid aggregate, the surface roughness and the texture structure are the important control parameters affecting the wetting. The surface morphology of rough solid can be designed by changing the resolution k and depth H of micropores, so as to control the wettability of solid aggregate surface and epoxy resin aggregate.

CFD-VOF-DPM numerical simulation of enhanced boiling heat transfer characteristics of microencapsulated phase change material slurry

Two-dimensional (2D) computational fluid dynamics (CFD) simulations of water-based microencapsulated phase change material suspension (MPCMS) on the flow boiling in a gas–liquid–solid flow system was performed with volume of fluid (VOF) method and discrete particle model (DPM). The Lagrangian particles were linked to the Eulerian phases through the interchange terms such as the drag force in the respective momentum equations. Influences of particle properties including mass fraction and core phase transition temperature, fluid properties including liquid surface tension force and viscosity, detachment time and rise velocity of gas bubbles and particle entrainment in the gas–liquid–solid flow under ambient conditions were numerically investigated. The effects of particles on bubble nucleation, growth and rupture during boiling were studied by visualization. The results show that MPCM can enhance the boiling heat transfer ability of the base liquid. The maximum heat transfer enhancement rate of MPCMS (28 °C) is 4.8%, the maximum heat transfer enhancement rate of MPCMS (90 °C) is 5.1%, the maximum heat transfer enhancement rate of MPCMS (110 °C) can reach 6.7%. MPCM can promote the formation of new bubbles and the rupture of large bubbles, reduce the departure diameter of bubbles, and enhance the boiling heat transfer capacity of the base liquid. The MPCM with core phase change temperature higher than the boiling temperature of base fluid has the best enhancement effect. Through the combination of numerical simulation methods such as VOF and DPM, the complex phase transition heat transfer process of gas-liquid-solid particle coupling of latent thermal functional thermal fluid can be accurately simulated. The work lays a foundation for further explorations on the gas–liquid–solid flows and possible industry applications.

Transferable united atom model for carbohydrates with explicit water: Glucose and sucrose

Understanding the role that molecular interactions have in aqueous solutions of carbohydrates is important in several technological applications, such as in the pharmaceutical industry. It is developed a force field for glucose and sucrose from a united atom model of methanol and ethanol parameterized with explicit water. The simulation results of liquid density, dielectric constant, surface tension, self-diffusion coefficient and shear-viscosity of glucose and sucrose in aqueous solutions are in excellent agreement with experimental data. The model improves the results of several all atoms models evaluated in this work. The surface tension increases with concentration of both carbohydrates because the molecules are dissolved within the liquid. It is also developed an all atoms model of glucose where dielectric constant is increased by changing the Lennard-Jones parameters. That model predicts that glucose is adsorbed at the liquid-vapor interface decreasing the surface tension as the concentration increases but the transport properties are not well reproduced. It is shown that the dielectric constant depends linearly on the molecular dipole moment of a mixture. The dihedral distribution on the hydroxymethyl group has a small effect on thermodynamic and transport properties. The systems are homogeneous and no evidence of phase separation is observed in the range of studied concentrations.

Surface tension and viscosity of binary ionic liquid mixtures from high vacuum up to pressures of 10 MPa

In the present study, we investigated the surface tension and viscosity of binary ionic liquid (IL) mixtures at or close to saturation conditions from high vacuum conditions up to elevated pressures. We studied four different mixtures of 1,3-bis(2-(2-methoxyethoxy)ethyl)imida-zolium iodide ([(mPEG2)2Im]I) and 1-methyl-3-octylimidazolium hexafluorophosphate ([C8C1Im][PF6]) with [C8C1Im][PF6] mole contents between (4.6 and 49.8) mol%. Argon (Ar) gas of relatively low solubility was used to vary the applied pressure between (0.1 and 10) MPa. For temperatures from (303 to 363) K, the surface tension obtained by the pendant-drop (PD) method was used to determine the saturated liquid viscosity from surface light scattering (SLS). These studies are complemented by additional PD measurements under ultraclean high vacuum (HV) conditions in a second setup. At about 0.1 MPa, the surface tension and viscosity of the IL mixtures show negative deviations from a linear mixing rule based on the molar bulk composition, which is more pronounced at lower temperatures. The surface tension values at 0.1 MPa and under HV agree with each other and lie closer to the values of [C8C1Im][PF6] that has a distinctly lower surface tension than [(mPEG2)2Im]I and is surface-active. For the equimolar IL mixture at 303 K, an increase in the pressure up to 10 MPa has a negligible influence on the viscosity, while it causes a distinct reduction in the surface tension compared to the value at 0.1 MPa. The pressure-dependent relative change for the viscosity of the ternary mixtures of the two ILs and Ar corresponds well to the mean values of the positive and negative relative changes observed for the two binary [(mPEG2)2Im]I-Ar and [C8C1Im][PF6]-Ar subsystems, respectively. For the surface tension, the absolute changes at a given pressure are very similar regardless of the IL bulk composition, suggesting a similar weak Ar enrichment at the gas–liquid interface.

Excellent Liquid Unidirectional Transport Inner Tilted‐Sector Arrayed Tubes

AbstractLiquid unidirectional transport exhibits critical applications from water harvesting to microfluidics. Despite extensive progress, implementation of liquid unidirectional transport that is not subjected to the liquid surface tension and injecting velocity also remains a great challenge. Here, a tilted‐sector arrayed tube for excellent liquid unidirectional transport is proposed that applies to a vast width domain of liquid surface tension and injecting velocity. In addition, the transport direction is abnormally against the tilted direction of structure, in stark contrast to the traditional understanding that is along tilted direction. This excellent and unique liquid unidirectional transport is caused by synergistic effects of tilted sectors and tube structures, which induce a unique 3D liquid propagation mode as well as a large Laplace pressure asymmetry between the front and rear sides of the liquid. Moreover, the antigravity climbing, circuit isolating, and chemical reaction controlling can be achieved based on the excellent liquid unidirectional transport. It is envisioned that the design can be extensively applied in microfluidics, lab‐on‐a‐chip devices, and biochemistry microreactors.

Production of nano-scale cellulose nanocrystal powder via electrospray drying (ESD) for sustainable composites

This research introduces the use of electrospray drying (ESD) using the electro-hydro dynamic atomization (EHDA) mechanism to produce dry nano-scale cellulose nanocrystal (CNC) powder from a 3 wt% aqueous suspension. The nano-scale CNC suspensions being mostly water are energy intensive to dry. Gas atomization in convection spray drying (SD) produces micron-scale CNC powder during dehydration. The ESD mechanism utilizes coulomb repulsion to overcome the suspension’s liquid surface tension and produces ultra-fine droplets. The droplets dehydrate after falling a fixed distance at atmospheric temperature and pressure, leaving nano-scale powder CNCs. Drying CNCs in suspension occurred after reducing the liquid’s surface tension by mixing 40% (wt) ethanol and 60 (wt) de-ionized (DI) water. The suspension feed rate was optimized at 6 µL min−1 and four syringes were employed to increase CNC powder production rates. Particle dimensions, observed by scanning electron microscopy (SEM) and measured by image analysis software, ranged from 40 to 1200 nm in length and 10–500 nm in width. Up to 80% of the sprayed CNCs in suspension were recovered from a parallel plate collector and contained ~ 5 wt% water content. Adding 0.5 wt% nano-scale powder CNCs in the poly-lactic acid (PLA) tensile strength by 10.3% and elastic modulus by 9.9%. The tensile yield strength and elastic modulus of nano-scale CNC/PLA composite specimens were 62.5 MPa and 3.66 GPa, respectively. For comparison, 0.5 wt% SD micron scale CNC/PLA composite only increased strength 5.1 and stiffness 1.3% at the same processing conditions.Graphical abstract

Liquid temperature gradient estimation for screen channel liquid acquisition device bubble point tests in liquid nitrogen

The LAD screen utilizes surface tension forces in microgravity environments to allow liquid to flow through the screen while blocking vapor ingestion up to a certain pressure differential across the screen. The limiting pressure differential of LAD screen operation prior to bubble breakthrough is known as the bubble point pressure (ΔPBP). Previous cryogenic ΔPBP studies have identified how noncondensable pressurization decreases the interface temperature within the pores of a LAD screen via evaporative cooling and how autogenous pressurization increases the interface temperature within a LAD screen via condensation heating. The temperature gradient in the liquid side boundary layer near the screen caused by these effects has not been previously quantified. This study provides an order of magnitude analysis to show how certain variables can influence the liquid side temperature gradient during ΔPBP tests in liquid nitrogen (LN2) using noncondensable pressurization. Furthermore, cryogenic LN2ΔPBP data is taken for a 325x2300 Dutch Twill and 200x600 Dutch Twill screen with liquid side temperature measurements collected at varying distances away from the screen using dewar pressures ranging from ∼0-8psig (∼101.3-156.5kPa absolute). It has been shown that measuring the liquid screen side temperature 1/8″ (3.2 mm) away from the screen can result in a liquid side surface tension value that is ∼10-12.5% lower than the actual surface tension value at the interface for GHe tests in LN2. An empirical correlation is provided based on experimental temperature gradient data to correct historical and future ΔPBP data for the liquid screen side diode placement.

Improvements in the surface tension measurement using the capillary rise method and its application to water under external magnetic fields

Using a micro ruler and charge-coupled device image acquisition system, we have improved the capillary rise method for an easy, quick and accurate measurement of liquid surface tension. We have determined and assessed the surface tension coefficients and temperature characteristics of purified water, ethylene glycol and anhydrous ethanol. Our results demonstrate low uncertainties for stable liquids and good linearity with temperature, with a measuring percentage deviation of less than 0.1% at 20 °C for purified water. Furthermore, we exposed purified water to a series of external magnetic fields ranging from 0 to 5 T for 40 min, followed by a withdrawal of fields for 5 min and observed a drop peak of surface tension at 1.0 T and a saturating transition at approximately 1.2 T. Furthermore, we found that the surface tension coefficients rapidly decrease with increasing magnetic fields from 0 to 1.0 T, increase rapidly from 1.0 to 1.2 T and then increase slowly at fields higher than 1.2 T. The maximum reduction of surface tension affected by external fields is approximately 11%. These magnetic behaviours of water surface tension have scientific significance in the study of water molecular liquids and their potential applications in water treatments.

Microwave‐Assisted Fabrication of Superamphiphobic Surfaces on Aluminum Substrates

The field of superamphiphobic surface fabrication has evolved rapidly in the last decade; however, research on important issues such as sustainability and green chemistry procedures is still scarce. Herein, a simple method of microwave irradiation (MW) to minimize energy consumption during the preparation of superamphiphobic aluminum (Al) surfaces is reported. Al substrates are first etched in diluted HCl solutions to generate a microstructure and then irradiated in a commercial microwave unit for several time intervals, temperatures, and pressures. The surfaces are then coated with different compounds, and the wettability is tested with high and very‐low surface tension liquids. Optical profilometry and scanning electron microscopy images show that the density of hierarchical micro‐nanostructures increases with MW time, temperature, and pressure. At 170 °C and 7.9 bar, the surfaces present a high density of structures and re‐entrant topographies. The obtained coatings display excellent repellence to liquids with surface tensions as low as 27.5 mN m−1. X‐ray photoelectron spectroscopy data show the importance of efficient surface functionalization for the production of superamphiphobicity in Al substrates. The results show that MW irradiation of Al substrates can be a green and efficient method for fabricating superamphiphobic surfaces.

Thermophysical properties of the liquid organic hydrogen carrier system based on diphenylmethane with the byproducts fluorene or perhydrofluorene

Fluorene (H0-F) and perhydrofluorene (H12-F) represent process-related byproducts formed by a dehydrocyclization step in the liquid organic hydrogen carrier (LOHC) system based on diphenylmethane (H0-DPM) and dicyclohexylmethane (H12-DPM). The influence of these byproducts on the liquid viscosity, surface tension, and liquid density of the DPM-based system was experimentally determined by studying three dehydrogenated binary mixtures with H0-F mole fractions of 0.05, 0.10, and 0.20 as well as one hydrogenated binary mixture with an H12-F mole fraction of 0.10 close to 0.1 MPa from (283–573) K. The densities increase with increasing share of H0-F or H12-F by around 1% per added byproduct mole fraction of 0.1. For the surface tension, an increase relative to the values of H0-DPM or H12-DPM by up to 6% is found. The addition of H0-F to H0-DPM or H12-F to H12-DPM yields a relative increase in viscosity by up to 9% at the lowest temperature studied.

Impact of surface tension on the barrier performance of gowns and coveralls

Health care workers and laboratory workers who are routinely exposed to potentially life-threatening infectious diseases should wear protective clothing when anticipating contact with infectious materials. The most critical property ofprotective clothing is its ability to prevent liquids and viruses from passing through the garment. There are a number of potentially infectious liquids that workers may be exposed to during routine tasks. Each liquid has different physical and chemical properties that affect penetration. However, the current test methods use a limited number of liquids for classifying the barrier performance. The impact of the surface tension of the challenge liquid on the penetration resistance of gowns and coveralls was investigated in this study. Eight isolation gowns and 2 coveralls were tested in accordance with American Association of Textile Chemists and Colorists 42 and American Association of Textile Chemists and Colorists 127 test methods, which were modified to incorporate the substitute challenge liquids. Although current standard test methods only use water to categorize the liquid penetration resistance of minimal to moderate barrier performance gowns, a significant difference in the penetration was found when simulated body fluids were used. The results suggest that safety professionals and wearers should consider the varying barrier performance of personal protective equipment with different liquids and the use limitations when selecting them for the required tasks. Furthermore, standard development organizations should consider multiple challenge liquids when classifying protective clothing for health care settings.

Effects of liquid surface tension on gas capillaries and capillary forces at superamphiphobic surfaces

The formation of a bridging gas capillary between superhydrophobic surfaces in water gives rise to strongly attractive interactions ranging up to several micrometers on separation. However, most liquids used in materials research are oil-based or contain surfactants. Superamphiphobic surfaces repel both water and low-surface-tension liquids. To control the interactions between a superamphiphobic surface and a particle, it needs to be resolved whether and how gas capillaries form in non-polar and low-surface-tension liquids. Such insight will aid advanced functional materials development. Here, we combine laser scanning confocal imaging and colloidal probe atomic force microscopy to elucidate the interaction between a superamphiphobic surface and a hydrophobic microparticle in three liquids with different surface tensions: water (73 mN m−1), ethylene glycol (48 mN m−1) and hexadecane (27 mN m−1). We show that bridging gas capillaries are formed in all three liquids. Force-distance curves between the superamphiphobic surface and the particle reveal strong attractive interactions, where the range and magnitude decrease with liquid surface tension. Comparison of free energy calculations based on the capillary menisci shapes and the force measurements suggest that under our dynamic measurements the gas pressure in the capillary is slightly below ambient.

Bioinspired Synergy Strategies Empower Small‐Scale Robots with Higher Performance

Small‐scale robots need to be agile to perform various tasks in complex environments and the design faces great challenges with limited size and power consumption. However, the advent of advanced functional materials, compliant structures/mechanisms, and flexible fabrication techniques has brought new evolution directions to robotics. These technologies enrich the robots' actuation strategies, improving their performance of small robots while simplifying the complexity of the system and thus making it possible to be applied in diverse scenarios, such as disaster rescue, medical, and environmental exploration. In nature, small organisms have shown numerous efficient survival strategies. They can easily achieve locomotion tasks with low energy consumption. For example, dragonflies complete long flights with the help of wind, and stenus (one kind of rove beetle) uses the surface tension of liquids to dodge prey quickly. Insects are usually considered to be agile, efficient, and intelligent, which is the same requirement as for small robots. Yet the corresponding bioinspired design strategies bring new opportunities and challenges to the development of small‐scale robots. Herein, the development trends of small‐scale robots are analyzed and discussed, and several potential bioinspired synergy strategies are induced, which may be useful for the future design of insect‐level soft robots.

Regimes of the length of a laminar liquid jet fragmented by a gas co-flow

Atomization occurs when a high-speed gas jet breaks a low-speed liquid jet coaxial to it, forming a spray via the production of ligaments, sheets, and drops. This mechanism has received a lot of attention and different fragmentation regimes have been identified qualitatively using imaging in the vicinity of the nozzle’s exit plane, as a proxy for the change of underlying break-up mechanisms. As the Weber number increases, i.e. as the gas aerodynamic stresses become larger with respect to the liquid surface tension, the liquid–gas interface suffers from instabilities that are governed by either capillarity, shear, or acceleration (or a combination of these). Several fragmentation regimes, in the low Weber number range, are typically deemed undesirable for applications such as propulsion or additive manufacturing, but no quantitative regime map is readily available. Using back-lit high-speed imaging in a multiscale approach, coaxial two-fluid fragmentation is studied in a broad range of gas Weber numbers that spans five fragmentation regimes. A fixed laminar liquid injection rate is maintained while the gas jet exit velocity is varied widely. The liquid core length, i.e. the extent of the liquid jet that is still fully connected to the nozzle, is an important metric of fragmentation, but most research has been focused on its average value in the bag break-up and fiber-type atomization regimes. The scaling laws of the first three statistical moments, the minimum value, and the correlation time of the liquid core length are reported across fragmentation regimes. The changes in scaling laws appear to be good indicators for several of the transitions explored.

Simulation of droplet bouncing on flexible substrate in 2D and 3D with WC-TL SPH method

Droplet impacts on super-hydrophobic surfaces play an important role in many fields. Previous studies have focused on rigid substrates and ignored the effect of substrate deformation. Simulating droplet impacts on a flexible substrate is a challenge to numerical methods due to the coupling of free surface, elasticity, large deformation and surface tension. In this study, a fully meshfree model of fluid–solid interaction is developed based on the smoothed particle hydrodynamics (SPH) method. The liquid droplet is modeled by the weakly compressible (WC) SPH method, and the flexible substrate is modeled by the total Lagrangian (TL) SPH method. Liquid surface tension is modeled by the continuum surface force (CSF) method through reconstructing the free surface of the droplet. The surface geometry reconstruction process is given for both 2D and 3D cases, enabling the model to simulate the bouncing of droplets in both 2D and 3D cases. Furthermore, in order to reduce the computational cost of 3D simulation, the TL-SPH model combined with shell theory established the TL-SPH-shell model, thus achieving the simulation of 3D droplet impact on thin plates. For verification and testing, the established WC-TL SPH model is used to simulate the process of droplet impact on various substrates, including fixed-fixed and curved beams, micro-pillar substrates, and cantilever beams. The results show that the spreading, retraction and bouncing processes of the droplets interact with the deformation and recovery of the flexible substrate, accompanied by large deformation and dynamic characteristics, which can be effectively simulated by the model.

Decrease in the Surface Tension of Nanobubble Dispersion in Water: Results of Surface Excess of Bulk Nanobubbles at Interfaces

The effect of nanobubbles (NBs) on the surface tension of liquid was investigated by three methods of different measuring principles, pendant drop (PD), Wilhelmy, and du Noüy methods, over a wide range of number concentration of bulk NBs (BNBs). In all of the three methods, the surface tension decreased in proportion to the number concentration of BNBs and the proportional constant was different among the three methods. Such behavior was inferred to be caused by the surface excess of BNBs at the gas-liquid or solid-liquid interface. In the PD method, the hydrophobic interaction between BNBs and air around a drop seems to cause the surface excess of BNBs along the surface of water drops. It brings about a subtle change in its profile, resulting in the decrease in surface tension, which takes a time of hundreds of seconds. Meanwhile, in the Wilhelmy and du Noüy methods, electrostatic attractive force between BNBs and a plate or ring is a likely cause of surface excess at the solid-liquid interface, resulting in the instantaneous decrease in surface tension. This study also provides a practical methodology of comparison for surface tension of NB dispersion: surface tension shall be compared among different samples with the same measurement method. Especially in the PD method, retention time of droplets before measurement shall be the same among samples.

Effects of SDS surface-active agents on hydrodynamics and oxygen mass transfer in a square bubble column reactor: Experimental and CFD modeling study

This work examined experimentally and numerically the effects of sodium dodecyl sulfate (SDS) surfactant agent on mass transfer coefficients kLaL and kL in a high-aspect square bubble column reactor. To this end, SDS aqueous solutions at concentrations between 5 ppm and 30 ppm were prepared. Superficial gas velocity was varied from 0.74 cm.s−1 to 9.44 cm.s−1 covering all flow regimes to analyze the interaction between different phases and the effect of liquid surface tension on gas-liquid interfaces. Experimental data indicated that the presence of the SDS in the liquid phase augmented the overall gas holdup up to 25% at a constant gas velocity (Ug = 7.3 cm.s−1) in the transition regime, which is due to the role of SDS in bubble interactions. The impact of SDS addition on the mass transfer is twofold. Firstly, it reduced kL because the SDS molecules migrate towards the bubble-liquid interface thanks to the lower O2 diffusivity in water, thus hindering the O2 transfer from one phase to the other. Secondly, it increased aL owing to the inhibition of bubbles coalescence and, therefore, the lower mean bubble size. Among these two effects, the latter is prevailing, which led to an increase in kLaL in contaminated systems. In the second part of this work, a population balance model (PBM) was coupled with a computational fluid dynamics (CFD) model based on large-eddy simulation (LES) to analyze the effect of both tap water and SDS contaminated systems on the breakage phenomena, local flow pattern, and the resulting hydrodynamics and mass transfer features in the reactor. Ultimately, experiments and numerical simulations agreed well in terms of global gas holdup and kLaL coefficient. In particular, the transition points in the case of the SDS media (except for foam formation) provided the model with adequate PBM definitions for the dispersed phase.

Semi-empirical model for the liquid fuel film formed by an oblique jet impinging on a curved wall

The operating conditions and the properties of the liquid have great effects on the shape and size of the liquid film and eventually affect the efficiencies of the atomization of alternative fuels, liquid jet impingement cooling, and equipment cleaning processes. The shape and size of the liquid film are dominated by the distance from the stagnation point to the liquid film edge(rmax). In this study, after deducing the thickness profile and the theoretical rather than the numerical solution of the initial velocity profile of the liquid film, a set of semi-empirical models about the shape, size of the liquid film, and the width of the raised zone formed by an oblique jet impinging on curved walls have been developed. In order to validate the theoretical model, a corresponding experiment has been developed, in which the jet velocities, impingement angles, liquid viscosity, surface tension, and radius of curvature have been included. The comparisons showed the theoretical results are in good agreement with the experimental data. The error for the location of the inner and outer border lines are less than 14.9% and 13.5%, respectively, except for the location in the upstream part of the film. And the effects of jet velocity, impingement angle, surface tension, dynamic viscosity, and radius of curvature were also theoretically discussed. The outer border line of the liquid film is dominated by the impingement angle and the impingement velocity, which affect the rmax exponentially and linearly, respectively. And the liquid viscosity and surface tension coefficient also affect the rmax approximately linearly. But the effects of the liquid viscosity and surface tension coefficient on the rmax are much less than the impingement velocity. The radius of curvature has little effect on the outer border lines and width of the raised zone when gravity is ignored.