Small Surface Tension Research Articles

Derivation and well-posedness of the extended Green-Naghdi equations for flat bottoms with surface tension

In this paper, we will derive the two-dimensional extended Green-Naghdi system {see Matsuno [Proc. R. Soc. A 472, 20160127 (2016)] for determination in a various way} for flat bottoms of order three with respect to the shallowness parameter μ. Then we consider the 1D extended Green-Naghdi equations taking into account the effect of small surface tension. We show that the construction of solution with a standard Picard iterative scheme can be accomplished in which the well-posedness in Xs=Hs+2(R)×Hs+2(R) for some s>32 of the new extended 1D system for a finite large time existence t=O(1ε) is demonstrated.

Simulation of GAP/HTPB phase behaviors in plasticizers and its application in composite solid propellant

Abstract Dissipative particle dynamics and molecular simulations were carried out to investigate the phase behaviors of glycidyl azide polymer (GAP)/hydroxyl-terminated polybutadiene (HTPB) polymer blend in dioctyl sebacate (DOS), and mixture of DOS and bis(2,2-dinitropropyl)formal/acetal (A3), respectively. The rheology of GAP/HTPB propellant slurry plasticized by A3/DOS was studied. First, single-phase aggregations of GAP and HTPB appear slightly in A3/DOS whereas it is conspicuous in DOS, which results from the small surface tension between the GAP/HTPB plasticized by A3/DOS and the weak thermal diffusion of this blend. Furthermore, with the plasticizing ratio (po/pl) increasing to 1.2, the GAP/HTPB propellant slurry plasticized by A3/DOS exhibits small viscosity and yield stress, and the Newtonian-like behavior of slurry improves its manufacturability. Finally, integral GAP/HTPB-based propellant can be obtained using A3/DOS as plasticizers.

Effects of xanthan gum on atomization and deposition characteristics in water and Silwet 408 aqueous solution

In order to investigate the effects of viscosity on spray formation and utilization of pesticide, different concentrations of xanthan gum (XG) were added into water and 0.1% Silwet 408 aqueous solution. Droplet size, relative span (RS), fan angle, length of breakup and maximum retention (Rm) were measured with the LU120-02 nozzle spraying under the pressure of 0.3 MPa. The dynamic spreading of the different solutions on maize leaves was tested using a 5 μL micro-injector. The results showed: VMD, RS, length of breakup and Rm went up as the increasing of XG concentration in the range of 0-0.5% with the same solution, while the fan angle of nozzle and spreading area on maize leaf showed the opposite tendency. Silwet 408 could reduce the surface tension of liquid, which could alter the dominant mode of spray formation and lead to earlier sheet breakup, especially in low viscosity solutions. Under the same concentration of XG the addition of Silwet 408 could reduce the RS of drop size spectrum but has no effect on VMD or fan angle. In water solution, there was no difference with different concentrations of XG in the spreading time on maize leaf. Besides, in the 0.1% Silwet 408 aqueous solution, the spraying time and area were several-fold of that in water with same XG concentration. Moreover, with the same XG concentration, the smaller surface tension liquid indicated lower Rm, and the difference was magnified as the concentration increases. This work has demonstrated that initial spray characteristics such as droplet size and RS, fan angle, length of breakup, Rm and spreading area can vary depending on the viscosity of spray liquids. Therefore, by transforming the viscosity of the spray liquid to adjust the droplet spectrum to reduce drift, increasing the Rm and spreading area to improve liquid utilization and reduce the usage of pesticides. Keywords: atomization, xanthan gum, spray, droplet size, breakup length, dynamic spreading DOI: 10.25165/j.ijabe.20181103.3802 Citation: Wang S L, He X K, Song J L, Wang S S, Jia X M, Ling Y. Effects of xanthan gum on atomization and deposition characteristics in water and Silwet 408 aqueous solution. Int J Agric & Biol Eng, 2018; 11(3): 29–34.

Mechanical properties of Sn63Pb37 components by fused coating technology

The fused coating process is a new material jetting additive manufacturing technology that proposes to solve the problem of high cost, low efficiency and high material requirements of laser-based process and electron beam process. The structure and operating principles of the fused coating machine are explained in this paper. Sn63Pb37 is taken as the experimental material because of its low melting temperature, small surface tension coefficient and high viscosity. Tensile test specimens were made both parallel and perpendicular to the forming trajectory. Tensile strengths were measured and the corresponding fractographies were observed. It is found that large plastic deformation has occurred before the fracture, and the plasticity of fused components that the tensile direction parallel to the forming trajectory, is higher. The densification degree of fused coating component is measured by the drainage method. The average value is up to 99.78% which indicates that the internal structure is indistinguishable from extruded Sn63Pb37. The Vickers hardness of the fused coated component and raw casted material were tested by 5 points respectively, the results showed that the average Vickers hardness of the fused coating component is 14.6% higher than the casted one.

On the deflection of a liquid jet by an air-cushioning layer

A hierarchy of models is formulated for the deflection of a thin two-dimensional liquid jet as it passes over a thin air-cushioning layer above a rigid flat impermeable substrate. We perform a systematic derivation of the leading-order equations of motion for the jet in the distinguished limit in which the air pressure jump, surface tension and gravity affect the displacement of the centreline of the jet, but not its thickness or velocity. We identify thereby the axial length scales for centreline deflection in regimes in which the air layer is dominated by viscous or inertial effects. The derived length scales and reduced equations aim to expand the suite of tools available for future analyses of the evolution of lamellae and ejecta in impact problems. Assuming that the jet is sufficiently long that tip and entry effects can be neglected, we demonstrate that the centreline of a constant-thickness jet moving with constant axial speed is destabilised by the air layer for sufficiently small surface tension. Expressions for the fastest-growing modes are obtained in both the viscous-dominated air and inertia-dominated air regimes. For a finite-length jet emanating from a nozzle, we show that, in one particular asymptotic limit, the evolution of the jet centreline is akin to the flapping of an unfurling flag above a thin air layer. We discuss the distinguished limit in which tip retraction can be neglected and perform numerical investigations into the resulting model. We show that the cushioning layer causes the jet centreline to bend, leading to rupture of the air layer. We discuss how our toolbox of models can be adapted and utilised in the context of recent experimental and numerical studies of splash dynamics.

Solution selection of axisymmetric Taylor bubbles

A finite difference scheme is proposed to solve the problem of axisymmetric Taylor bubbles rising at a constant velocity in a tube. A method to remove singularities from the numerical scheme is presented, allowing accurate computation of the bubbles with the inclusion of both gravity and surface tension. This paper confirms the long-held belief that the solution space of the axisymmetric Taylor bubble for small surface tension is qualitatively similar to that of the plane Taylor bubble. Furthermore, evidence suggesting that the solution selection mechanism associated with plane bubbles also occurs in the axisymmetric case is presented.

Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis

In this paper we study a free boundary problem modeling the growth of vascularized tumors. The model is a modification to the Byrne–Chaplain tumor model that has been intensively studied during the past two decades. The modification is made by replacing the Dirichlet boundary value condition with the Robin condition, which causes some new difficulties in making rigorous analysis of the model, particularly on existence and uniqueness of a radial stationary solution. In this paper we successfully solve this problem. We prove that this free boundary problem has a unique radial stationary solution which is asymptotically stable for large surface tension coefficient, whereas unstable for small surface tension coefficient. Tools used in this analysis are the geometric theory of abstract parabolic differential equations in Banach spaces and spectral analysis of the linearized operator.

Influence of droplet coalescence and breakup on the separation process in wave‐plate separators

AbstractThe purpose of this study is to investigate the numerical simulation method regarding the coalescence and breakup of droplets occurring during the gas‐liquid separation process and their influence on the separation efficiency and pressure drop. The Euler‐Lagrange method was used, and the discrete phase was simulated as an unsteady process. The results of the study indicate that numerical simulation results show better agreement with the experiment results when the coalescence and breakup model is taken into account. During the unsteady process, it was concluded that the simulation can meet the accuracy requirements as long as the Courant number of droplets is less than 1/3. The coalescence increases the droplet diameter, which improves the separation efficiency and reduces the pressure drop, whereas the opposite effect occurs with the breakup. Compared with other factors, the influence of the surface tension on the coalescence and breakup is more apparent, and droplets with a lower surface tension may be prone to coalescing or breaking. The coalescence occurs with a lower separation velocity, whereas breakup becomes predominant with higher separation velocity. The present research provides valuable suggestions on choosing strategies to improve the separation efficiency. For droplets with small surface tension, the separation velocity is restricted to not resulting breakup, and the separation efficiency can be improved by changing the shapes and spaces of the wave plate. In contrast, for droplets with large surface tension, increasing the velocity is an effective way to improve the separation efficiency.

Spreading dynamics of superposed liquid drops on a spinning disk

We have experimentally studied simultaneous spreading of superposed drops of two Newtonian liquids on top of a horizontal spinning disk using the flow visualization technique. An inner drop of high surface tension liquid is placed centrally on the disk followed by a drop of outer liquid (lower surface tension) placed exactly above that. The disk is then rotated at a desired speed for a range of volume ratios of two liquids. Such an arrangement of two superposed liquid drops does not affect the spreading behavior of the outer liquid but influences that of the inner liquid significantly. The drop spreads to a larger extent and breaks into more fingers (Nf) as compared to the case where the same liquid is spreading in the absence of outer liquid. The experimentally observed number of fingers is compared with the prediction using available theory for single liquid. It is found that the theory over-predicts the value of Nf for the inner liquid while it is covered by an outer liquid. We provide a theoretical justification for this observation using linear stability analysis. Our analysis demonstrates that for small but finite surface tension ratio of the two liquids, the presence of the outer interface reduces the value of the most unstable wave number which is equivalent to the decrease in the number of fingers observed experimentally. Finally, sustained rotation of the disk leads to the formation of droplets at the tip of the fingers traveling outwards.

The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom

The goal of this work is to investigate, analytically and numerically, the dynamics of gravity water waves with the effects of the small surface tension and the bottom topography taken into account. Using a third-order perturbative approach of the Boussinesq equation, we obtain a new third-order perturbed Korteweg-de Vries (KdV) equation which includes nonlinear, dispersive, nonlocal and mixed nonlinear-dispersive terms, describing shallow water waves with a non-flat bottom and the surface tension. We show by numerical simulations, for various bottom shapes, that this new third-order perturbed KdV equation can support the propagation of solitary waves, whose profiles strongly depend on the surface tension. In particular, we show that the instability observed in the numerical simulation can be suppressed by the inclusion of small surface tension.

Two cadmium(II) fluorous coordination compounds tuned by different bipyridines.

Fluorine is the most electronegative element and can be used as an excellent hydrogen-bond acceptor. Fluorous coordination compounds exhibit several advantageous properties, such as enhanced high thermal and oxidative stability, low polarity, weak intermolecular interactions and a small surface tension compared to hydrocarbons. C-H...F-C interactions, although weak, play a significant role in regulating the arrangement of the organic molecules in the crystalline state and stabilizing the secondary structure. Two cadmium(II) fluorous coordination compounds formed from 2,2'-bipyridine, 4,4'-bipyridine and pentafluorobenzoate ligands, namely catena-poly[[aqua(2,2'-bipyridine-κ2N,N')(2,3,4,5,6-pentafluorobenzoato-κO)cadmium(II)]-μ-2,3,4,5,6-pentafluorobenzoato-κ2O:O'], [Cd(C7F5O2)2(C10H8N2)(H2O)]n, (1), and catena-poly[[diaquabis(2,3,4,5,6-pentafluorobenzoato-κO)cadmium(II)]-μ-4,4'-bipyridine-κ2N:N'], [Cd(C7F5O2)2(C10H8N2)(H2O)2]n, (2), have been synthesized solvothermally and structurally characterized. Compound (1) shows a one-dimensional chain structure composed of Cd-O coordination bonds and is stabilized by π-π stacking and O-H...O hydrogen-bond interactions. Compound (2) displays a one-dimensional linear chain structure formed by Cd-N coordination interactions involving the 4,4'-bipyridine ligand. Adjacent one-dimensional chains are extended into two-dimensional sheets by O-H...O hydrogen bonds between the coordinated water molecules and adjacent carboxylate groups. Moreover, the chains are further linked by C-H...F-C interactions to afford a three-dimensional network. In both structures, hydrogen bonding involving the coordinated water molecules is a primary driving force in the formation of the supramolecular structures.

Nonlinearity of Finite-Amplitude Sloshing in Rectangular Containers

This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.

The vanishing surface tension limit for the Hele-Shaw problem

In this paper, we show the existence of solutions of the Hele-Shaw problem in two dimensions in the presence of surface tension and for a general class of initial data. The limit problem from nonzero to zero surface tension will also be investigated. In the case of injection and when volume conservation holds, for a sufficiently small surface tension, we prove the existence and uniqueness of perturbed solutions with nonzero surface tension near solutions with zero surface tension. We also show that solutions with nonzero surface tension exist up to a finite time before a possible singularity occurs in which solutions with zero surface tension are well defined. In addition, in the finite time interval, we prove that the solutions with nonzero surface tension approach the solutions with zero surface tension as the surface tension coefficient goes to zero. In the case of suction, for sufficiently small surface tension, we prove the existence of perturbed solutions near solutions with zero surface tension in any initially smooth domains. In this case, the local existence time depends on the surface tension coefficient.

A Robust Cu(OH)2 Nanoneedles Mesh with Tunable Wettability for Nonaqueous Multiphase Liquid Separation.

The separation of organic liquid mixtures is achieved by Cu(OH)2 nanoneedle-covered copper mesh based on the difference of the liquid surface tension. The as-prepared membrane allows the penetration of organic liquid with smaller surface tension and blocks the higher. Thus, the effective separation of these two organic liquids can be achieved.

Dynamics of internal jets in the merging of two droplets of unequal sizes

The head-on collision, merging and internal mixing dynamics of two unequal-sized droplets were experimentally studied and interpreted, using water, $n$-decane and $n$-tetradecane to identify the distinguishing effects of surface tension and liquid viscosity on the merging and mixing patterns. It is shown that, upon merging of water and $n$-decane droplets, mushroom-like jets of dissimilar characteristics develop within the merged mass for small and large values of the impact Weber number (We), and that such jets are not developed for intermediate values of We. Furthermore, such jet-like mixing patterns were not observed for droplets of $n$-tetradecane, which has smaller surface tension and larger viscosity as compared to water. A regime nomogram relating the Ohnesorge and symmetric Weber numbers is constructed, providing a unified interpretation of the internal mixing patterns. Numerical simulations based on an improved volume-of-fluid method and an adaptive mesh refinement algorithm provide auxiliary diagnoses of the flow fields and the observed phenomena.

Primer system for bonding conventional adhesives and coatings to silicone rubber

This research examines a novel, two-part primer system that allows almost any adhesive or coating to adhere strongly to silicone rubber. Based on cyanoacrylate, the system forms a thin coating that binds tightly to silicone and provides a porous, nanostructured surface to which adhesives and coatings can bond well. Crucial to the effectiveness of the primer layer is the solvent used in the second part of the primer system. The layer׳s polycyanoacrylate forms as a gel in the presence of that solvent and is subject to the solvent׳s chemical and physical influences. When the solvent has little affinity for the polycyanoacrylate, as well as a small surface tension, the gel is able to withstand capillary stresses exerted by the evaporating solvent and become a xerogel with extensive porosity and nanostructure.

Research on gas bubble merging through the lattice Boltzmann method

A numerical investigation of gas bubble merging in a liquid is carried out via the lattice Boltzmann method (LBM) in this work. The bubble merging process dependence on the bubble gap and the surface tension is obtained. It is found that the critical gap for bubble merging is smaller for smaller surface tension coefficients. Additionally, the merging velocity is computed to illustrate the merging process, which shows a rapid damping oscillation. The peak merging velocity value and the time taken to reach the peak velocity are found to be linear with the surface tension coefficient in a log-log coordinate system. The effects of fluid viscosity and the bubble gap on the merging velocity are also examined. Finally, the merging patterns for multiple bubbles are presented.

How does surface tension affect energy release rate of cracks loaded in Mode I?

The role of surface stress on fracture of elastic solids has been studied by two group of researchers with different conclusions. One group concludes that surface stress has no effect on energy release rate except that the singularity of the crack tip field is stronger than the usual inverse square root singularity dictated by linear elastic fracture mechanics. The other group concludes that the singularity of the stress field reduces to a logarithmic singularity, thus implying that the local energy release rate is zero. In this letter we resolve this paradox by examining the solution of a special case where surface stress is isotropic and independent of surface strain. We show that surface tension resists crack growth by lowering the applied energy release rate while retaining the inversely square root singularity of the elastic crack tip field. We demonstrate this idea by solving a perturbation problem where the capillary length is much smaller than the crack length. A closed form expression for the local energy release rate is obtained in the limit of small surface tension.

Computational fluid dynamic simulations on liquid film behaviors at flooding in an inclined pipe

The complex liquid film behaviors at flooding in an inclined pipe were investigated with computational fluid dynamic (CFD) approaches. The liquid film behaviors included the dynamic wave characteristics before flooding and the transition of flow pattern when flooding happened. The influences of the surface tension and liquid viscosity were specially analyzed. Comparisons of the calculated velocity at the onset of flooding with the available experimental results showed a good agreement. The calculations verify that the fluctuation frequency and the liquid film thickness are almost unaffected by the superficial gas velocity until the flooding is triggered due to the Kelvin–Helmholtz instability. When flooding triggered at the superficial liquid velocity larger than 0.15m·s−1, the interfacial wave developed to slug flow, while it developed to entrainment flow when it was smaller than 0.08m·s−1. The interfacial waves were more easily torn into tiny droplets with smaller surface tension, eventually evolving into the mist flow. When the liquid viscosity increases, the liquid film has a thicker holdup with more intensive fluctuations, and more likely developed to the slug flow.

Small membranes under negative surface tension.

We use computer simulations and a simple free energy model to study the response of a bilayer membrane to the application of a negative (compressive) mechanical tension. Such a tension destabilizes the long wavelength undulation modes of giant vesicles, but it can be sustained when small membranes and vesicles are considered. Our negative tension simulation results reveal two regimes-(i) a weak negative tension regime characterized by stretching-dominated elasticity and (ii) a strong negative tension regime featuring bending-dominated elastic behavior. This resembles the findings of the classic Evans and Rawicz micropipette aspiration experiment in giant unilamellar vesicles (GUVs) [E. Evans and W. Rawicz, Phys, Rev. Lett. 64, 2094 (1990)]. However, in GUVs the crossover between the two elasticity regimes occurs at a small positive surface tension, while in smaller membranes it takes place at a moderate negative tension. Another interesting observation concerning the response of a small membrane to negative surface tension is related to the relationship between the mechanical and fluctuation tensions, which are equal to each other for non-negative values. When the tension decreases to negative values, the fluctuation tension γ drops somewhat faster than the mechanical tension τ in the small negative tension regime, before it saturates (and becomes larger than τ) for large negative tensions. The bending modulus exhibits an "opposite" trend. It remains almost unchanged in the stretching-dominated elastic regime, and decreases in the bending-dominated regime. Both the amplitudes of the thermal height undulations and the projected area variations diverge at the onset of mechanical instability.