Small Surface Tension Research Articles

Study on the electrostatic shedding and crushing characteristics of ethanol and diesel droplets

The study of electrostatic shedding and crushing characteristics of droplets is the basis of understanding electrostatic atomization, and the study of its shedding and crushing behavior in electrostatic field is conducted. Micropump drive is used to control the flow rate, electrostatic generation device to form a stable electric field, light lighting and high-speed camera to obtain the dynamic behavior of shedding and crushing process, and use digital image processing technology to extract the process parameters. The results show that: when the capillary tube diameter and flow are unchanged, when the electric field voltage is low, the droplet deviates and falls off, the diesel droplet is smaller than the ethanol; when the electric field voltage is moderate, the droplet is closed or deformed into wave strip; only when the flow rate increases and the electric field voltage is large, the average particle size of ethanol is smaller than diesel, indicating that the electrostatic atomization effect of ethanol with small surface tension is significantly better than that of diesel oil.

Bubble nucleation in the two-flavor quark-meson model* *Supported in part by the National Natural Science Foundation of China (NSFC) (11675048)

We investigate the dynamics of a first-order quark-hadron transition via homogeneous thermal nucleation in the two-flavor quark-meson model. The contribution of the fermionic vacuum loop in the effective thermodynamics potential and phase diagram, together with the location of the critical endpoint (CEP), is obtained in the temperature and chemical potential plane. For weak and strong first-order phase transitions, by taking the temperature as a variable, the critical bubble profiles, evolutions of the surface tension, and saddle-point action in the presence of a nucleation bubble are numerically calculated in detail when fixing the chemical potentials at and . Our results show that the system could be trapped in the metastable state for a long time as long as the temperature is between the metastable region characterized by the up and low spinodal lines. Moreover, the surface tension at criticality will rise to approximately when the chemical potential is very high. Such a small surface tension value would favor a mixed phase in the cores of compact stars and may have an important implication in astrophysics.

Lattice Boltzmann modelling of multicomponent and multiphase flow with high density ratio

Thermodynamic consistency is a key factor in heat and mass transfer simulation. A modified lattice Boltzmann pseudopotential model with the ability to simulate multiphase and multicomponent flow with a large density and viscosity ratio is proposed. Relative to a model using the exact difference method, a better thermodynamic consistency is obtained through introducing an improved external force term, a multi-relaxation-time collision operator, and a scaling coefficient k of the equation of state. The coefficient of scale k = 0.1 is preferred due to its better thermodynamic consistency, lower spurious current and a smaller surface tension. The inter-particle interaction strength has little influence over the thermodynamic consistency due to its limited contributions to the surface tension. With the model, the bubble dissolution under pressure is investigated and Henry’s law is validated.

Research on Fuel atomization technology in aero engine

Recently, fuel combustion-related performances of aero engines are increasingly demanding, and their combustion quality directly affects their power, economy and emission characteristics, and a series of key performance indicators. The fuel atomization is the key link to determine the combustion condition. Therefore, this paper clarifies the mechanism of fuel atomization in aero-engines, studies the characteristics and methods of fuel atomization in aero-engines, and analyzes the influencing factors in the this process. The results indicate that lower fuel viscosity, smaller surface tension and appropriate temperature pressure, nozzle geometry, etc. can better enhance the fuel atomization performance. Herein, good atomization effect is the premise of efficient combustion, and it is important for energy saving and environmental protection. For the future development of engines, the rational organization of combustion is essential to improve their performance.

On the structure of parasitic gravity-capillary standing waves in the small surface tension limit

We present new numerical solutions for nonlinear standing water waves when the effects of both gravity and surface tension are considered. For small values of the surface tension parameter, solutions are shown to exhibit highly oscillatory capillary waves (parasitic ripples), which are both time- and space-periodic, and which lie on the surface of an underlying gravity-driven standing wave. Our numerical scheme combines a time-dependent conformal mapping together with a shooting method, for which the residual is minimised by Newton iteration. Previous numerical investigations typically clustered gridpoints near the wave crest, and thus lacked the fine detail across the domain required to capture this phenomenon of small-scale parasitic ripples. The amplitude of these ripples is shown to be exponentially small in the zero surface tension limit, and their behaviour is linked to (or explains) the generation of an elaborate bifurcation structure.

Impact of fuel properties on the transition of liquid-gas interface dynamics under supercritical pressure

Fuel injection dynamics transition from two-phase theory to single-phase dense fluid dynamics are a crucial phenomenon that markedly affects the mixing process and subsequent combustion under diesel engine-relevant conditions. As the significant effect of fuel properties on the timescale and mechanism of this transition remains elusive yet, this work focuses on the impact of fuel properties on the transition to single-phase dense fluid at supercritical pressure. The detailed thermodynamic structure of non-continuum gas-liquid interfaces at supercritical pressures was constructed through gradient theory, and its evolution was analyzed. The driving mechanism of transition from spray to single-phase dense fluid was discussed. The influences of fuel properties on the timescale and mechanism of breakdown of the two-phase theory were investigated through the comparison of three different alkanes. Theoretical analysis suggests that the transition from spray to single-phase dense fluid is jointly promoted by the thickening interface, the diminished surface tension, and the shorter molecular mean free path. The gas-liquid interface of lighter-alkane/nitrogen binary systems is more inclined to evolve into the continuum length-scale regime. The cause is a combination of two aspects: (1) smaller thermodynamic potential energy density difference ω¯(ϱM)−ω¯s and smaller interfacial tangential pressure across lighter alkanes/nitrogen interfaces lead to broader interfaces and smaller surface tension, (2) the more volatile nature of lighter alkanes results in shorter molecular mean free path. The minimum reduced pressure required for gas-liquid interfaces to reach critical mixing states is lower for lighter and more volatile alkanes at the same reduced temperature. From a time-scale perspective, the non-continuum gas-liquid interfaces evolve into the continuum length scale regime later for heavier alkanes. This suggests that the transition to the diffusive mixing mechanism occurs further downstream for heavier alkane sprays. A conceptual diagram was presented to illustrate the effect of fuel properties on the transition.

Analytical theory for a droplet squeezing through a circular pore in creeping flows under constant pressures

We derived equations and closed-form solutions of transit time for a viscous droplet squeezing through a small circular pore with a finite length at microscale under constant pressures. Our analyses were motivated by the vital processes of biological cells squeezing through small pores in blood vessels and sinusoids and droplets squeezing through pores in microfluidics. First, we derived ordinary differential equations (ODEs) of a droplet squeezing through a circular pore by combining Sampson flow, Poiseuille flow, and Young–Laplace equations and took into account the lubrication layer between the droplet and the pore wall. Second, for droplets wetting the wall with small surface tension, we derived the closed-form solutions of transit time. For droplets with finite surface tension, we solved the original ODEs numerically to predict the transit time. After validations against experiments and finite element simulations, we studied the effects of pressure, viscosity, pore/droplet dimensions, and surface tension on the transit time. We found that the transit time is inversely linearly proportional to pressure when the surface tension is low compared to the critical surface tension for preventing the droplet to pass and becomes nonlinear when it approaches the critical tension. Remarkably, we showed that when a fixed percentage of surface tension to critical tension is applied, the transit time is always inversely linearly proportional to pressure, and the dependence of transit time on surface tension is nonmonotonic. Our results provided a quick way of quantitative calculations of transit time for designing droplet microfluidics and understanding cells passing through constrictions.

Deciphering surface tension effects of double cavitation bubbles interaction: A lattice Boltzmann study

A modified double distribution function thermal lattice Boltzmann method is employed to study the influences of surface tension on the interaction between two equal-sized and two unequal-sized bubbles. The entire evolution process of the laser- or spark-produced bubble, including the inception, growth and collapse stage, is realised by considering a temperature that is equal to or higher than the critical temperature, and the effects of the flow and temperature fields on each other are also considered. Based on the Rayleigh–Plesset (R–P) equation and considering the effects of the adjacent bubble, a thermal effect term is incorporated, and this modified R–P equation can predict the radius evolution process for the two equal-sized and the two unequal-sized cavitation bubbles while considering the thermal effect. For the strong interaction mode of the two equal-sized cavitation bubbles, the large surface tension prevents the dramatic distortion of the bubbles, leading to an overall movement of the cavitation bubble under the influence of the Bjerknes force and resulting in an easier coalescence, which significantly reduces the interval distance for the strong film mode than that of the small surface tension. However, for the two unequal-sized bubbles, since non-equilibrium force is present on both sides of the liquid film, the small bubble will be pushed away from the symmetry axis, leading to a difficult coalescence, which will consequently decrease the interval distance for the coalescence mode. Furthermore, an external source term is utilized to achieve the tuneable surface tension and an additional stress term is introduced on the pressure tensor as Gc46κψ∇∇ψ; thus, the inertia model can accurately predict the film thinning process with κ=0. Moreover, a modified inertia model is proposed for the thinning process of the film between two unequal-sized bubbles, which was shown to be accurate for κ=0.

Understanding the desalination performance of seawater passing through the lamellar BN membranes: Effect of interlayer spacing and concentration

Due to its smaller surface tension and greater wetting degree, BN-based membranes have exhibited promising application prospect in water treatment and seawater desalination. In this work, boron nitride nanosheets were employed to establish lamellar BN membranes layer by layer. By using non-equilibrium molecular dynamics simulations (NEMD), we evaluated the influence of interlayer spacing on the desalination performance of BN membranes. We also evaluated the relationship between the water permeability and the concentration of the feed solution. The simulation results showed that the water permeability of BN membrane first decreased and then increased with the interlayer spacing, it reached the minimum at the interlayer spacing of 1.1 nm, with a turning point at the same time. This is due to the strong interaction between water molecules and BN. What’s more, with the increase of the concentration of the feed solution, the hindering effect of ions on the transport of water molecules gradually decreases, the difference between water permeability in systems with different interlayer spacing decreases gradually.

Simulations of Bubble Formation and Oscillation Behavior in Micro-Leakage Measurement System

In the process of measuring micro-leakage based on the bubble method, the physical parameters of the liquid phase have a great impact on the formation and movement of bubbles, thus affecting the measurement accuracy of the system. Therefore, it is of great significance to study the physical parameters of the liquid phase. At present, it is difficult to independently study the parameters of the liquid phase by experimental methods. In this paper, based on the Cahn-Hilliard phase field model, a gas-liquid two-phase flow model for the expression of leakage is established to independently study the influence of different physical parameters on the formation and movement of bubbles in the measuring system. Firstly, the effects of liquid medium density, dynamic viscosity coefficient and surface tension on the initial shape (aspect ratio), the generation period and the shape oscillation of bubbles after they leave the nozzle are analyzed. Then, an experimental platform for visualization of bubbles in two-phase flow based on machine vision is built, through which the morphological parameters of bubbles in the liquid phase can be obtained in real time. Finally, the results of visualization experiment and numerical simulation are compared. The results show that the initial aspect ratio error of bubbles obtained by visual experiment and numerical simulation is 1.8%, and the average oscillation period error is 12.3%. The results are basically consistent, which proves the rationality and correctness of the mathematical model established. It is found that the liquid with larger dynamic viscosity coefficient μ and density ρ and smaller surface tension σ can be selected as the liquid medium of the measurement system. It is more conducive to the accurate expression of micro-leakage in the measurement system, and the bubble shape can quickly reach a stable state. It provides theoretical support for improving the accuracy and stability of the micro-leakage measurement system.

Effect of Antimony on Wetting Behavior and Interfacial Reaction between Zinc Liquid and X80 Steel

The wetting behavior of molten Zn and Zn-Sb alloy and X80 steel in a high vacuum environment was studied by the modified sessile drop method. The wetting morphology and interface structure were analyzed by scanning electron microscope and energy dispersive spectrometer. The results show when the content of Sb in Zn-Sb alloy increases from 0.0 wt. % to 1.0 wt. %, the initial contact angle between the droplet and the substrate decreases from 102.8° to 82.5°, and the equilibrium contact angle also decreases from 57.4° to 41.4°. Sb element in the Zn-Sb alloy can reduce the contact angle and improve the wettability due to its smaller surface tension. The spreading process of Zn-Sb alloys on X80 steel can be divided into rapid adsorption, reaction control, steady-state equilibrium stages, and Zn-Sb alloys with different mass fractions have the same spreading kinetics. The volatilized Zn element in the Zn-Sb alloy will reduce the oxide film on the surface of the substrate, making it easier for the Zn-Sb droplet to wet the steel plate and induce the formation of a precursor film. The formation mechanism of the precursor film is the subcutaneous penetration mechanism.

Investigation on interfacial properties of conventional and functional modified TiO2/water nanofluids

The interfacial properties of conventional and functional modified nanofluids, including tension and contact angle, are investigated experimentally. The conventional nanofluids are prepared by mixing pure TiO2 nanoparticles into water containing surfactants, and the functional modified nanofluids are prepared by adding 3-aminpropyltriethoxysilane (APTS) or γ-glycidoxypropyltrimethoxysilane (GPTMS) treated nanoparticles into water. The results show that the surface tension of both conventional and functional modified nanofluids shows a decreasing trend with the elevating nanoparticle concentration and temperature. The surface roughness of copper plates as well as the nanoparticle loading would both have obvious effects on the contact angle. The surface tension and contact angle of conventional nanofluids decrease with the increasing surfactant concentration. Among all tested samples, the APTS modified nanofluids have larger surface tension and contact angle, which indicates a poorer wettability. The sodium dodecyl sulfate (SDS) added nanofluids have better wettability, in which smaller surface tension and contact angle are found.

Solid particles moving parallel to a deformable liquid–liquid interface in a micro-channel: migration forces

This work focuses on the dynamics of a train of solid particles, separated by a distance $L$ , flowing near a deformable interface formed by two co-flowing immiscible fluids in a microchannel of height $h$ . Our study includes a systematic analysis of the influence of the governing parameters (fluids viscosity ratio, interface and particle positions, Reynolds $Re$ and capillary $Ca$ numbers and the inter-particle distance $L$ ) on the hydrodynamic force $f$ exerted on the particle. In the pure inertial regime with non-deformable interfaces $Ca=0$ , the particle is driven towards the wall (interface) when the particle is close to the interface (wall). Up to three neutral equilibrium positions $f=0$ , two of them stable, are found in this limit. The contrary is obtained in the pure capillary regime $Re=0$ . In this limit, we also carried out an asymptotic analysis in the distinguished limits of very large and very small surface tension. In the latter case, the amplitude of the interface deformation induced by the particle is large, comparable to its diameter, but its influence is limited to a small region upstream and downstream of the particle. In the limit of very large surface tension, the amplitude of the interface deformation is small but the presence of the particle modifies the shape of the interface in a region of length $2\lambda$ , much larger than the particle diameter $d$ . The parameter $\lambda$ , introduces an additional characteristic length that determines the asymptotic behaviour of the flow properties in the limit of large surface tension.

Effect of ionic emulsifiers on the properties of emulsified asphalts: An experimental and simulation study

The incorporation of emulsifiers into asphalt binder has significant advantages on decreasing mixing temperature, improving construction environment and saving energy. In this study, the effects of ionic emulsifiers on the service performances of emulsified asphalts were investigated by laboratory experiments and molecular dynamic (MD) simulation. To this aim, cationic stearyl trimethyl ammoium chloride (STAC) and anionic sodium dodecylbenzene sulfonate (SDBS) were selected. The effects of these two ionic emulsifiers on the stability and rheological response of emulsified asphalts were investigated via the surface tension, storage stability and dynamic shear rheology tests. Furthermore, the binary model of emulsifier/asphalt and the ternary model of water/emulsifier/asphalt were constructed, and a series of indices such as interaction energy, roughness, relative concentration distribution, mean square displacement (MSD) were analyzed to explain the performance differences of various emulsified asphalt from molecular perspective. The experimental results showed that the influence of STAC on stability and rheological properties of emulsified asphalt was more considerable by comparison to that of SDBS. The smaller surface tension could be detected for STAC emulsified asphalt considering the stronger hydrophilicity of STAC. Moreover, compared to SDBS, STAC significantly improved the deformation resistance and elastic recovery of emulsified asphalt. It was concluded from MD simulation that the adsorption system formed by STAC was more stable. Both of experimental and simulation results provide insight into understand the contribution of ionic emulsifiers to the stability and rheological properties of emulsified asphalts.

Exponential asymptotics for steady parasitic capillary ripples on steep gravity waves

In this paper, we develop an asymptotic theory for steadily travelling gravity–capillary waves under the small-surface tension limit. In an accompanying work (Shelton et al., J. Fluid Mech., vol. 922, 2021) it was demonstrated that solutions associated with a perturbation about a leading-order gravity wave (a Stokes wave) contain surface-tension-driven parasitic ripples with an exponentially small amplitude. Thus, a naive Poincaré expansion is insufficient for their description. Here, we develop specialised methodologies in exponential asymptotics for derivation of the parasitic ripples on periodic domains. The ripples are shown to arise in conjunction with Stokes lines and the Stokes phenomenon. The resultant analysis associates the production of parasitic ripples to the complex-valued singularities associated with the crest of a steep Stokes wave. A solvability condition is derived, showing that solutions of this type do not exist at certain values of the Bond number. The asymptotic results are compared with full numerical solutions and show excellent agreement. The work provides corrections and insight of a seminal theory on parasitic capillary waves first proposed by Longuet-Higgins (J. Fluid Mech., vol. 16, issue 1, 1963, pp. 138–159).

Numerical investigation on the performance of gas-lift pump with large density ratio of liquid to gas

Heavy liquid metals such as sodium and liquid lead-bismuth eutectic (LBE) have excellent heat transfer capability and receive increasing attention as the primary coolant in fast reactors and accelerator driven systems (ADS). In ADS system, coolant system is designed as natural circulation, to simplify the primary system, improve the compactness of reactors and most important of all is to increase the inherent safety of reactor. Because the electromagnetic pump that drives the flow of liquid metal is eliminated in the coolant natural circulation system. In such situation, gas-lift technique named gas-lift pump could be adopted to enhance the coolant natural circulation capacity. The open research on the performance of gas-lift liquid metal pump is much less than that of air- lift water pump. The physical properties of large density ratio of liquid to gas, small kinematic viscosity and high surface tension of liquid metal is believed to have effects on the performance of gas-lift liquid metal pump. The present paper carries out some preliminary numerical simulation work on the two-phase flow characteristics of argon-liquid LBE in the up-riser tube and the performance of gas-lift liquid metal pump. Eulerian-Eulerian two-fluid model is used to describe the two-phase flow. Some interphase momentum transfer models from literature are used to account for the interfacial momentum transfer between liquid and gas phases. SST k-ω model with mixture treatment is used to compute the turbulence parameters of the homogeneous mixing phase in the present study. The influence of such parameters as argon injection superficial velocity, submergence ratio and diameter of up-riser tube on the discharged LBE mass flow rate and pressure drop of gas-lift pump are checked. The results could be helpful for the design of the gas-lift liquid metal pump.

Foaming of Binary Mixtures: Link with the Nonlinear Behavior of Surface Tension in Asymmetric Mixtures.

The lifetimes of single bubbles or foams that are formed in mixtures of liquids can be several orders of magnitude larger than the ones formed in pure liquids. We recently demonstrated that this enhanced stability results from differences between bulk and interfacial concentrations in the mixture, which induce a thickness dependence of the surface tension in liquid films, and thus a stabilizing Marangoni effect. Concentration differences may be associated with nonlinear variations of surface tension with composition and we further investigate their link with foamability of binary mixtures. We show that, for asymmetric binary mixtures, that is, made of molecules of very different sizes, strong nonlinearities in surface tension can be measured, that are associated with large foam lifetimes. When the molecules that occupy the largest surface areas have the smallest surface tension, the surface tension of the mixture varies sublinearly with composition, reflecting an enrichment in this species at the interface with air, as classically reported in the literature. In contrast, when they exhibit the largest surface tension, superlinear variations of surface tension are observed, despite a similar enrichment. We discuss these variations in light of a simple thermodynamic model for ideal mixtures and we demonstrate why foam stability is enhanced for both sublinear and superlinear surface tension variations, thus, shedding new light on foamability without added surfactants.

Evaporation of R1234yf, R1234ze(E) and R1234ze(Z) on Cu surface: A molecular dynamics study

Understanding the interface phase transition behavior of the working fluid helps to improve the energy conversion efficiency of a thermodynamic cycle. In this study, the evaporation behaviors of R1234yf, R1234ze(E) and R1234ze(Z) liquid film on the solid surface are performed using molecular dynamics simulation. The results suggest the evaporation rate and heat flux almost remain constant in the steady state. And during this period, the evaporation rate and heat flux of R1234yf is the largest among the studied systems. Meanwhile, the total thermal resistance of R1234ze(Z) system is greater than that of R1234ze(E) and R1234yf. The Kapitza resistance between solid and liquid accounts for only a small part of the total thermal resistance. The main reason for the difference of the total thermal resistance is the large difference of evaporation resistance at the liquid–vapor interface. Furthermore, the largest liquid–vapor interface area gives R1234yf the largest surface area for heat and mass transfer, thus enhancing the performance of evaporation. Besides, R1234yf has the smallest surface tension, followed by R1234ze(E) and R1234ze(Z). And the self-diffusion coefficient of R1234yf is the greatest. R1234yf also has the smallest interaction energy between liquid molecules. Therefore, the R1234yf liquid molecule is easy to escape from the liquid–vapor interface among the studied systems.

Solitary waves in a Whitham equation with small surface tension

AbstractUsing a nonlocal version of the center‐manifold theorem and a normal form reduction, we prove the existence of small‐amplitude generalized solitary‐wave solutions and modulated solitary‐wave solutions to the steady gravity‐capillary Whitham equation with weak surface tension. Through the application of the center‐manifold theorem, the nonlocal equation for the solitary wave profiles is reduced to a four‐dimensional system of ODEs inheriting reversibility. Along particular parameter curves, relating directly to the classical gravity‐capillary water wave problem, the associated linear operator is seen to undergo either a reversible bifurcation or a reversible bifurcation. Through a normal form transformation, the reduced system of ODEs along each relevant parameter curve is seen to be well approximated by a truncated system retaining only second‐order or third‐order terms. These truncated systems relate directly to systems obtained in the study of the full gravity‐capillary water wave equation and, as such, the existence of generalized and modulated solitary waves for the truncated systems is guaranteed by classical works, and they are readily seen to persist as solutions of the gravity‐capillary Whitham equation due to reversibility. Consequently, this work illuminates further connections between the gravity‐capillary Whitham equation and the full two‐dimensional gravity‐capillary water wave problem.

Stable Up-Down Quark Matter Nuggets, Quark Star Crusts, and a New Family of White Dwarfs

The possible existence of stable up-down quark matter (udQM) was recently proposed, and it was shown that the properties of udQM stars are consistent with various pulsar observations. In this work we investigate the stability of udQM nuggets and found at certain size those objects are more stable than others if a large symmetry energy and a small surface tension were adopted. In such cases, a crust made of udQM nuggets exists in quark stars. A new family of white dwarfs comprised entirely of udQM nuggets and electrons were also obtained, where the maximum mass approaches to the Chandrasekhar limit.