Absence Of Surface Tension Research Articles

Ablation and molten layer flow simulation for plate model of SiO2f/SiO2 composite material using particle method

In this paper, the moving particle semi-implicit method (MPS) is extended from calculating free mobility to simulating the extremely viscous and temperature-dependent molten layer flow of SiO2f/SiO2 composite material under aerodynamic heating conditions, which includes strong heating and shear of incoming flow. A method for applying heat flux and airflow shear, based on the conceptual particle approach, has been established. Heat transfer, melting, solidification, and evaporation behaviors are considered, with temperature-dependent viscosity variations also accounted for. The ablative regression of the plate model is verified using experimental results of the SiO2f/SiO2 composite material, and results from convergence analysis demonstrate the accuracy of the space step size selection. Surface morphology analysis through three-dimensional computation indicates that the extended particle method also accurately describes the surface morphology of SiO2f/SiO2 composite material under aerodynamic heating conditions. Thus, the extended particle method accurately simulates both the ablation process and the surface morphology of the SiO2f/SiO2 composite material. The influences of acceleration and surface tension are discussed. Ablative recession, when subject to acceleration, is smaller than that observed in its absence. When exposed to surface tension, the liquid layer tends to form a spherical shape, and the particles behave as a cohesive unit, resulting in smaller ablative recession than in the absence of surface tension.

Holding water in a sieve—stable droplets without surface tension

Our understanding of supercritical fluids has seen exciting advances over the last decades, often in direct contradiction to established textbook knowledge. Rather than being structureless, we now know that distinct supercritical liquid and gaseous states can be distinguished and that a higher order phase transition - pseudo boiling - occurs between supercritical liquid and gaseous states across the Widom line. Observed droplets and sharp interfaces at supercritical pressures are interpreted as evidence of surface tension due to phase equilibria in mixtures, given the lack of a supercritical liquid-vapor phase equilibrium in pure fluids. However, here we introduce an alternative physical mechanism that unexpectedly causes a sharpening of interfacial density gradients in absence of surface tension: thermal gradient induced interfaces (TGIIF). We show from first principles and simulations that, unlike in gases or liquids, stable droplets, bubbles, and planar interfaces can exist without surface tension. These results challenge and generalize our understanding of what droplets and phase interfaces are, and uncover yet another unexpected behavior of supercritical fluids. TGIIF provide a new physical mechanism that could be used to tailor and optimize fuel injection or heat transfer processes in high-pressure power systems.

Evolution of waves in liquid films on moving substrates

Accurate and computationally accessible models of liquid film flows allow for optimizing coating processes, such as hot-dip galvanization and vertical slot-die coating. This paper extends a classic three-dimensional integral boundary layer model for falling liquid films (FFs) to account for a moving substrate (MS). We analyze the stability of the liquid films on vertically moving substrates in a linear and in a nonlinear setting. In the linear analysis, we derive the dispersion relation and the temporal growth rates of an infinitesimal disturbance using normal modes and linearized governing equations. In the nonlinear analysis, we consider disturbances of finite size and numerically compute their evolution using the set of nonlinear equations in which surface tension has been removed. We present the region of (linear) stability of both FF and MS configurations, and we place the operating conditions of an industrial galvanizing line in these maps. A wide range of flow conditions was analyzed and shown to be stable according to linear and nonlinear stability analyses. Moreover, the nonlinear analysis, carried out in the absence of surface tension, reveals a nonlinear stabilizing mechanism for the interface dynamics of a liquid film dragged by an upward-moving substrate.

Supercritical CO2 assisted synthesis of SBA-15 supported amino acid ionic liquid for CO2 cycloaddition under cocatalyst/metal/solvent-free conditions

Heterogenization of homogeneous catalysts without the loss of activity is still a huge challenge. Herein, homogeneous [HTMG][His][I] amino acid ionic liquid (IL), consisting of 1,1,3,3-tetramethylguanidine cation, histidine anion and iodine anion, were introduced into the pore channels of SBA-15 substrate with the assistance of supercritical CO2 (scCO2) media. Due to its low viscosity, high diffusivity and absence of surface tension, scCO2 enabled [HTMG][His][I] to highly disperse in SBA-15 pore channels. Surprisingly, [HTMG][His][I]/SBA-15 heterogeneous catalyst displayed higher CO2 cycloaddition activity (95% propylene carbonate yield) than equivalent molar pristine [HTMG][His][I] homogeneous catalyst (69% propylene carbonate yield) under the identical conditions. The significantly enhanced activity was resulted from the synergistic effect of [HTMG][His][I] and SBA-15 support. Moreover, [HTMG][His][I]/SBA-15 performed outstanding universality of various epoxides and reusability. This work developed a promising strategy to heterogenization of homogeneous IL catalyst assisted by scCO2 as synthetic media and provided an efficient catalyst for CO2 conversion.

The effect of surface tension on the adhesion performance of nanoscale fibrillary structures——a theoretical prediction

The last decade witnesses the thorough investigation of bio-inspired nanoscale fibrillary structures with strong adhesion to stiff substrates. In the present study, we explore the effect of surface tension on the adhesion behavior of a rigid nanoscale fiber and an elastic substrate. With the existence of surface tension, we reconsider the optimal shape of the fiber, critical condition for spontaneous adhesion, saturation of adhesion strength and flaw-tolerant capability. The results indicate that the critical fiber radius for spontaneous adhesion and threshold value for crack size can be significantly enhanced due to surface tension. Meanwhile, the adhesion strength can approach the maximum value faster with fiber radius decreasing ascribed to surface tension, compared with the situation with the absence of surface tension. These conclusions present an inspiration for the optimization of adhesion strength of fibrillary surfaces.

High Spots for the Ice-Fishing Problem with Surface Tension

In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (``the ice'') with a hole. We investigate the ice-fishing problem including the effects of surface tension on the free surface. The dimensionless number that describes the effect of surface tension is called the Bond number. For holes that are infinite parallel strips or circular holes, we transform the problem to an equivalent eigenvalue integro-differential equation on an interval and expand in the appropriate basis (Legendre and radial polynomials, respectively). We use computational methods to demonstrate that the high spot, i.e., the maximal elevation of the fundamental sloshing profile, for the ice-fishing problem is in the interior of the free surface for large Bond numbers, but for a sufficiently small Bond number the high spot is on the boundary of the free surface. While several papers have proven high spot results in the absence of surface tension as it depends on the shape of the container, to the best of our knowledge, this is the first study investigating the effects of surface tension on the location of the high spot.

Colloidal exchange flow in ducts

Buoyancy-driven exchange flow, i.e. drainage of a heavy colloidal suspension by an immiscible light pure fluid in a vertical duct, is studied analytically. A lubrication model is developed for two-dimensional channel and axisymmetric pipe geometries. The outcome transport equations are solved numerically to capture the effect of important governing dimensionless parameters: Péclet number, precursor film thickness, Reynolds number, mixtures’ viscosity ratio, initial volume fraction of hard-sphere particles, particles concentration within the precursor film, and capillary number. Recent study of colloidal film flow over a flat surface reveals interface thinning over time due to diffusion impact on suspension viscosity. However, the current model suggests that there is no such thinning phenomenon observed for colloidal flows within confined geometry unless in the absence of surface tension. The extent of the mixed particle zone along the duct grows as the Péclet number is decreased. Precursor film thickness is found to decrease the capillary ridge height forming at heavy suspension front. Either an increase in the Reynolds number or a decrease in light-to-heavy-fluid viscosity ratio extends the interpenetration rate of mixtures. As the bulk volume fraction of particles is increased close to 50 %, interesting secondary fronts emerge within the flow that coincide with the range where the diffusion coefficient is minimized. The heavy suspension layer drains slightly faster when the gradient in particle concentration between the bulk and precursor film regions is maximum. Finally, the non-monotonic impact of surface tension on the extent of mixtures’ exchange zone is uncovered via simulations conducted at various capillary numbers.

Steady circular hydraulic jump on a rotating disk

The paper deals with the steady axially symmetric flow of a viscous liquid layer over a rotating disk. The liquid is fed near the axis of rotation and spreads due to inertia and the centrifugal force. The viscous shallow-water approach gives a system of ordinary differential equations governing the flow. We consider inertia, gravity, centrifugal and Coriolis forces and estimate the effect of surface tension. We found four qualitatively different flow regimes. Transition through these regimes shows the continuous evolution of the flow structure from a hydraulic jump on a static disk to a monotonic thickness decrease on a fast rotating one. We show that, in the absence of surface tension, the intensity of the jump gradually vanishes at a finite distance from the axis of rotation while the angular velocity increases. The surface tension decreases the jump radius and destroys the steady solution for a certain range of parameters.

Kelvin wake pattern at small Froude numbers

Abstract

The use of the Gurtin-Murdoch theory for modeling mechanical processes in composites with two-dimensional reinforcements

This paper explores the possibility of using the Gurtin-Murdoch theory of material surface for modeling mechanical processes in nanomaterials reinforced by two-dimensional flexible and extensible nanoplatelets. In accordance with the theory, reinforcement is modeled by a vanishing thickness prestressed membrane embedded in an isotropic elastic matrix material. The governing equations for the model are reviewed with a detailed discussion of the conditions at the membrane tips. Plane strain assumption is made and with the purpose of representing the displacements in the bulk material, a single layer elastic potential is employed, with the density representing the jump in tractions across the membrane. Expressions for the remaining elastic fields are provided in terms of complex integral representations. The case of a rectilinear membrane of finite length is considered in detail. Numerical solution for this case is based on the use of approximations that automatically incorporate the membrane-tip conditions into the resulting system of boundary integral equations. Numerical examples illustrate the influence of governing dimensionless parameters and present simulations of the local elastic fields in the materials under study. Additionally, it is shown that, in absence of surface tension, the problem considered here is related to that of a membrane type elastic inhomogeneity embedded into a homogeneous elastic medium.

Controlled Release Utilizing Initiated Chemical Vapor Deposited (iCVD) of Polymeric Nanolayers.

This review will focus on the controlled release of pharmaceuticals and other organic molecules utilizing polymeric nanolayers grown by initiated chemical vapor deposited (iCVD). The iCVD layers are able conform to the geometry of the underlying substrate, facilitating release from one- and two-dimensional nanostructures with high surface area. The reactors for iCVD film growth can be customized for specific substrate geometries and scaled to large overall dimensions. The absence of surface tension in vapor deposition processes allows the synthesis of pinhole-free layers, even for iCVD layers <10 nm thick. Such ultrathin layers also provide rapid transport of the drug across the polymeric layer. The mild conditions of the iCVD process avoid damage to the drug which is being encapsulated. Smart release is enabled by iCVD hydrogels which are responsive to pH, temperature, or light. Biodegradable iCVD layers have also be demonstrated for drug release.

Effect of variation in density on the stability of bilinear shear currents with a free surface

We perform the stability analysis for a free surface fluid current modeled as two finite layers of constant vorticity, under the action of gravity and absence of surface tension. In the same spirit as Taylor [“Effect of variation in density on the stability of superposed streams of fluid,” Proc. R. Soc. London, Ser. A 132, 499 (1931)], a geometrical approach to the problem is proposed, which allows us to present simple analytical criteria under which the flow is stable. A strong destabilizing effect of stratification in density is perceived when the results are compared with those obtained for the physical setting where the vorticity interface is also a density interface separating two immiscible fluids with constant densities. In contrast with the homogeneous case, the stratified bilinear shear current is mostly unstable and can only be stabilized when the background current in the upper layer is constant.

Poisson brackets for the dynamically coupled system of a free boundary and a neutrally buoyant rigid body in a body-fixed frame

The fully coupled dynamic interaction problem of the free surface of an incompressible fluid and a rigid body beneath it, in an inviscid, irrotational framework and in the absence of surface tension, is considered. Evolution equations of the global momenta of the body+fluid system are derived. It is then shown that, under fairly general assumptions, these evolution equations combined with the evolution equation of the free-surface, referred to a body-fixed frame, is a Hamiltonian system. The Poisson brackets of the system are the sum of the canonical Zakharov bracket and the non-canonical Lie-Poisson bracket. Variations are performed consistent with the mixed Dirichlet-Neumann problem governing the system.

Modified Babenko’s Equation For Periodic Gravity Waves On Water Of Finite Depth

Summary A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko’s equation considered in Kuznetsov and Dinvay (Water Waves, 1, 2019). Both operators in the proposed equation are nonlinear and depend on the parameter equal to the mean depth of water, whereas each solution defines a parametric representation for a symmetric free surface profile. The latter is a component of a solution of the two-dimensional, nonlinear problem describing steady waves propagating in the absence of surface tension. Bifurcation curves (including a branching one) are obtained numerically for solutions of the new equation; they are compared with known results.

Babenko’s Equation for Periodic Gravity Waves on Water of Finite Depth: Derivation and Numerical Solution

The nonlinear two-dimensional problem describing periodic steady gravity waves on water of finite depth is considered in the absence of surface tension. It is reduced to a single pseudo-differential operator equation (Babenko’s equation), which is investigated analytically and numerically. This equation has the same form as the equation for waves on infinitely deep water; the latter had been proposed by Babenko and studied in detail by Buffoni, Dancer and Toland. Instead of the $$2 \pi $$ -periodic Hilbert transform $${\mathcal {C}}$$ used in the equation for deep water, the equation obtained here contains a certain operator $${\mathcal {B}}_r$$ , which is the sum of $${\mathcal {C}}$$ and a compact operator depending on a parameter related to the depth of water. Numerical computations are based on an equivalent form of Babenko’s equation derived by virtue of the spectral decomposition of the operator $${\mathcal {B}}_r \mathrm {d}/ \mathrm {d}t$$ . Bifurcation curves and wave profiles of the extreme form are obtained numerically.

Stability analysis of a thin film on a rotating cylinder with low airflow

This paper studies the operating conditions of a novel pesticide applicator, by analyzing the stability of a thin film on a rotating horizontal cylinder in the presence of low airflow. The analysis shows that the film is destabilized by the airflow, with a few notable further findings. First, when the airflow coincides with the angular velocity at the underside of the cylinder, the film becomes unstable at smaller wind speeds compared to airflow anti-parallel to the angular velocity. Second, in the absence of surface tension, the thin film model does not have a stable stationary state. The solution settles into an oscillatory state instead. Finally, an analytical solution is presented for the special case where the initial condition is a uniform film thickness. When surface tension is included in this analysis, the temporal terms decay when the stability condition is satisfied. Some of the modes decay very slowly, as confirmed by the multiple time scale analysis.

Revisiting the linear stability analysis and absolute–convective transition of two fluid core annular flow

Numerous experimental, numerical and theoretical studies have shown that core annular flows can be unstable. This instability can be convective or absolute in different situations: miscible fluids with matched density but different viscosities, creeping flow of two immiscible fluids or buoyant flow along a fibre. The analysis of the linear stability of the flow equation of two fluids injected in a co-current and concentric manner into a cylindrical tube leads to a rather complex eigenvalue problem. Until now, all analytical solution to this problem has involved strong assumptions (e.g. lack of inertia) or approximations (e.g. developments at long or short wavelengths) even for axisymmetric disturbances. However, in this latter case, following C. Pekeris, who obtained, almost seventy years ago, an elegant explicit solution for the dispersion relationship of the flow of a single fluid, we derive an explicit solution for the more general case of two immiscible fluids of different viscosity, density and inertia separated by a straight interface. This formulation is well adapted to commercial software. First, we review the creeping flow limit (zero Reynolds number) of two immiscible fluids as it is used in microfluidics. Secondly, we consider the case of two fluids of different viscosities but of the same density in the absence of surface tension and also without diffusion (i.e. miscible fluids with infinite Schmidt number). In both cases, we study the transition from convective to absolute instability according to the different control parameters.

Surface tension-pressure superposition principle for anisotropic shrinkage of an ellipsoidal pore in viscous sintering

The shrinkage of a spherical pore is a classical model of the final stage of sintering; however, closed pores observed in real sintering have irregular shapes, which can be approximated as ellipsoids in many cases. In this study, we used the finite element simulation to evaluate the anisotropic shrinkage of a non-spherical pore. The shape evolution was expressed as the superposition of the deformation of a pore driven by surface tension and the deformation of a void driven by remote pressure in the absence of surface tension. By using this superposition principle, we can predict the shape evolution of any spheroidal pore, which is affected by the initial aspect ratio, the remote pressure, and the gas pressure inside the pore. We analyzed the role of sintering stress tensor on the anisotropic shrinkage also.

Asymptotic decay and non-rupture of viscous sheets

For a nonlinear system of coupled PDEs, that describes evolution of a viscous thin liquid sheet and takes account of surface tension at the free surface, we show exponential (H^1,,L^2) asymptotic decay to the flat profile of its solutions considered with general initial data. Additionally, by transforming the system to Lagrangian coordinates we show that the minimal thickness of the sheet stays positive for all times. This result proves the conjecture formally accepted in the physical literature (cf. Eggers and Fontelos in Singularities: formation, structure, and propagation. Cambridge Texts in Applied Mathematics, Cambridge, 2015), that a viscous sheet cannot rupture in finite time in the absence of external forcing. Moreover, in the absence of surface tension we find a special class of initial data for which the Lagrangian solution exhibits L^2-exponential decay to the flat profile.

Three-dimensional computational model of multiphase flow driven by a bed of active cilia

Micro-scale physiological fluid propulsion is often accomplished with arrays of beating cilia. It is well-known that cilia can spontaneously coordinate their beat patterns to form metachronal waves. While it is generally agreed upon that metachronal waves arise largely due to hydrodynamic coupling, their effects on fluid propulsion are not thoroughly explored. There are presently complex, nonlinear models where cilia motion mimics their internal mechanisms; however these models are often computationally challenging and expensive to perform. We therefore present a simplified computational model of a cilia array with the ability to spontaneously produce metachronal waves. Each cilium is modeled as a one-dimensional elastic structure immersed in a stratified, two-fluid configuration. This model is used to simulate in vitro artificial cilia. Our model treats the upper fluid as a high-viscosity Newtonian fluid. Our model shows that, in the presence of surface tension between the lower and upper fluid layers, the fluid velocity component perpendicular to the interface is suppressed. This suppression prevents the interface from deforming, leading to increased fluid flow along the cilia array and enhancing fluid transport. Conversely, in the absence of surface tension, the fluid velocity component perpendicular to the interface is unsuppressed. The interface becomes severely deformed, enlarging the fluid interface area, thus potentially enhancing diffusive mixing. We finally present a phase-space plot of viscosity ratio against surface tension, showing conditions under which fluid transport or mixing is enhanced.