Free surface cusps

A Monte Carlo (MC) study is performed to evaluate the surface tension $$\gamma $$ of spherical membranes that may be regarded as the models of the lipid layers. We use the canonical surface model defined on the self-avoiding triangulated lattices. The surface tension $$\gamma $$ is calculated by keeping the total surface area A constant during the MC simulations. In the evaluation of $$\gamma $$ , we use A instead of the projected area $$A_p$$ , which is unknown due to the fluctuation of the spherical surface without boundary. The pressure difference $${\varDelta }p $$ between the inner and the outer sides of the surface is also calculated by maintaining the enclosed volume constant. Using $${\varDelta }p $$ and the Laplace formula, we obtain the tension, which is considered to be equal to the frame tension $$\tau $$ conjugate to $$A_p$$ , and check whether or not $$\gamma $$ is consistent with $$\tau $$ . We find reasonable consistency between $$\gamma $$ and $$\tau $$ in the region of sufficiently large bending rigidity $$\kappa $$ or sufficiently large A / N. It is also found that $$\tau $$ becomes constant in the limit of $$A{/}N\rightarrow \infty $$ both in the tethered and fluid surfaces.

Characterization of two-phase displacement mechanisms in porous media by capillary and viscous forces estimation using the lattice Boltzmann simulations

A classical problem of the dynamics of the free surface of an ideal incompressible fluid with infinite depth has been considered. It has been found that the regime of motion of the fluid where the pressure is a quadratic function of the velocity components is possible in the absence of external forces and capillarity. It has been shown that equations of plane potential flow for this situation are linearized in conformal variables and are then easily solved analytically. The found solution includes an arbitrary function specifying the initial shape of the surface of the fluid. The developed approach makes it possible for the first time to locally describe the formation of various singularities on the surface of the fluid—bubbles, drops, and cusps.

Elastocapillarity has attracted increasing interest in recent years due to its important roles in many industrial applications. In this work, we derive a thermodynamically consistent continuum model for the dynamics of two immiscible fluids on a thin and inextensible elastic sheet in two dimensions. With the sheet being modelled by a deformable curve with the Wilmore energy and local inextensibility constraint, we derive a two-phase hydrodynamics model with the interfacial and boundary conditions consistent with the second law of thermodynamics. In particular, the boundary conditions on the sheet and at the moving contact line take the form of force balances involving the fluid stress, surface tensions, the sheet bending force and sheet tension, as well as friction forces arising from the slip of fluids on the sheet. The resulting model obeys an energy dissipation law. To demonstrate its capability of modelling complex elastocapillary interactions, we consider two applications: (1) the relaxation dynamics of a droplet on an elastic sheet and (2) the transport of a droplet driven by bendotaxis in a channel bounded by elastic sheets. Numerical solutions for the coupled fluid–sheet dynamics are obtained using the finite element method. The detailed information provided by the full hydrodynamics model allows us to better understand the dynamical processes as compared to other simplified models that were used in previous work.

We consider a model for the flow of two immiscible fluids in a two‐dimensional thin strip of varying width. This represents an idealization of a pore in a porous medium. The interface separating the fluids forms a freely moving interface in contact with the wall and is driven by the fluid flow and surface tension. The contact‐line model incorporates Navier‐slip boundary conditions and a dynamic and possibly hysteretic contact angle law. We assume a scale separation between the typical width and the length of the thin strip. Based on asymptotic expansions, we derive effective models for the two‐phase flow. These models form a system of differential algebraic equations for the interface position and the total flux. The result is Darcy‐type equations for the flow, combined with a capillary pressure–saturation relationship involving dynamic effects. Finally, we provide some numerical examples to show the effect of a varying wall width, of the viscosity ratio, of the slip boundary condition as well as of having a dynamic contact angle law.

The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of two superposed semi-infinite Rivlin-Ericksen viscoelastic dielectric fluids streaming through porous media in the presence of suspended particles is investigated in three dimensions. The method of multiple scales is used to derive a nonlinear Schrodinger equation with complex coefficients. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. The limiting cases of linear results recovered the previous studies. For the nonlinear two-dimensional case, we found that the system is always unstable and this instability decreases by increasing the medium permeability, the surface tension, and the porosity of the porous medium; while it increases by increasing fluid velocities, viscosities, viscoelasticities, electric field, and number densities of particles. Also, in the nonlinear three-dimensional case, we found that the medium permeability and the porosity of the porous medium have stabilizing effects, and the fluid velocities, viscoelasticities, surface tension, and electric field have destabilizing effects; while the number densities of particles and viscosities have no effect on the stability of the system. In the latter case, the dimension has different effects depending on increasing various parameters individually.

The present simulation study investigates the effects of ambient pressure oscillation on cylindrical liquid jet sprays, using the volume of fluid method. The research is motivated by combustion instability in combustion engines, where strong harmonic pressure oscillation can damage internal structures. Oscillating pressure modulates not only the fuel mass flow rate but also the ambient gas density and liquid surface tension, and in liquid sprays, the ambient fluid density and surface tension can have substantial effects on spray breakup. In order to investigate the multiple property changes with ambient pressure oscillation, therefore, a new solver in OpenFOAM is developed. In the solver, liquid mass flow rate, ambient gas density, and liquid surface tension change simultaneously as a result of pressure oscillation. Simulations were conducted at a Reynolds number of 2000 and Weber number over 2000, conditions that are conducive to primary breakup in laminar flows. The simulations show that oscillations in ambient pressure significantly strengthen the surface instability of the liquid ligament, which depends on the surface tension–pressure coefficient, the mean pressure, and the amplitude of oscillation.

In many engineering applications, including coating and lubrication operations, analyzing the temperature behavior of thin film flows on a vertically upward-moving tube is crucial to improving predictive models. This paper examines a steady third-grade fluid film flow with a surface tension gradient on a vertical tube. The mechanisms responsible for the fluid motion are upward tube motion, gravity, and surface tension gradient. This analysis focuses on heat transfer and stagnant ring dynamics. The formulated highly nonlinear ordinary differential equations are solved using the Adomian decomposition method. The conditions for stagnant rings and uniform film thickness are attained and discussed. The inverse capillary number C, Stokes number St, Deborah number De, and Brinkman number Br emerged as flow control parameters. The temperature of the fluid film rises with an increase in the C, St, De, and Br, whereas it decreases with an increase in thermal diffusion rate. The radius of stagnant rings tends to shrink by the increase in C, St, and De. When the value of De is high, third-grade fluid behaves like solids; only free drainage happens with smaller radius stagnant rings and high temperatures. A comparison between Newtonian and third-grade fluids regarding surface tension, velocity, temperature, stationary rings, and fluid film thickness is also provided.

Optically induced rotation relies on dynamic optical forces acting on microscopic particles via spatiotemporal light modulation, angular momentum transfer, or recoil forces. However, rotating macroscopic particles using light fields with intensity, polarization, or phase variations is challenging, especially underwater, due to the low torque of electromagnetic fields. This study demonstrates stable optical trapping and switchable light‐induced rotation of millimeter‐scale liquid marbles (LMs) in a uniform, time‐invariant DC magnetic field. These LMs, composed of self‐assembled ferrofluid droplets encapsulated by superhydrophobic particles with high photothermal conversion efficiency, float on a fluid surface and are stably trapped via controlled surface tension forces. Light‐induced photothermal interactions within the magneto‐optical field generate significant angular momentum, driving rotation through the Kelvin body force—resulting from a thermo‐magnetic gradient—and surface tension forces. This enables optically induced rotation of magnetically trapped coupled LMs, with angular velocity tunable via magnetic and optical field strength, fluid viscosity, and surface tension. Torques exceeding 170 nN·µm are achieved with a 200 mW CW laser, modulating underwater optical transmission at 1–4 Hz. This approach advances reversible optical torque generation and optical communication in fluidic systems. Additionally, ultrasonic waves modulate rotation by altering the nonequilibrium force distribution within ferrofluid LMs.

Oil drops placed on surfactant laden water surface exhibit a transition from surface tension driven to surface tension gradient driven spreading as a function of surfactant concentration. Interestingly, this transition occurs at the critical micellar concentration irrespective of surfactant chemistry demonstrating a connection between fluid flows and shuttling of surfactant between the bulk and the interface.

Owing to challenges encountered by mesh-based CFD methods when simulating large material deformation, a number of meshfree methods have been presented. The optimized transportation meshfree method is a newly developed meshfree method, but it inherits the advantage of the finite element method in boundary treatment and thus having great potential applications in surface tension effect simulation. By adding the surface tension potential into the Lagrangian, the resulting generalized force acts on fluid surfaces exactly. The axial symmetry treatment is also discussed. By simulating several benchmark cases such as two- and three-dimensional Poiseuille flow, static and vibrating drop and drop deformation, the advantages like precision and convergence of the optimized transportation meshfree method in simulating surface tension effect are verified.

ABSTRACTWe report a study of the surface morphology and microstructure of Si epitaxial layers grown by MBE on (001) Si at temperatures at which epitaxy breakdown is observed. For films grown in the 400 - 450 °C temperature range the epitaxy breakdown is very sluggish and characterized by a columnar growth and the formation of surface cusps. We have used atomic force microscopy to study the shape, size and distribution of those surface cusps. Surface cusps are of square shape with sides predominantly oriented along <110> directions and are typically of 50 nm size and 5 nm depth. The cusps can be very regular in size and their surface density (typically of 109-1010 cm-2) is dependent on the growth temperature. The epitaxial Si in this temperature regime exhibits a residual strain of the order of -5 × 10−5 in the growth direction. Photoluminescence (PL) from cusped Si films is characterized by a broad PL at low energy possibly due to impurities incorporation at low growth temperatures. We have observed that Ge self-assembled dots can be grown on cusped surfaces. Large area AFM measurements reveal that surface cusps are “decorated” by clusters of large dome-like Ge dots, while a lower density of smaller dome and pyramid shape islands are seen away from the cusps.

In the present study, an adjustable coefficient is introduced in order to make the pseudo-potential multiphase model more flexible for the simulation of a wide range of surface tensions. This coefficient can be utilized for different density ratios without any limitation. First, the effect of this coefficient is evaluated by the Laplace test. Then, density and pressure profiles along the interface are plotted which indicate that the major influence of the surface tension coefficient is localized along the interface. In other words, no negative influence is observed either for the density of two phases or for their pressures elsewhere. Hence, using the proposed surface tension coefficient, it is now possible to adjust the surface tension in multiphase Lattice Boltzmann flow simulations in a wider range. However, as the surface tension coefficient increases to increase the value of the fluid surface tension, the maximum spurious velocity might increase.

: We achieved a serious progress in numerical simulation of surface waves on free surface of 3D deep fluid in presence of gravity and surface tension. We obtained important results in the theory of 2D fluid with a free surface. We performed a numerical calculation of the Kolmogorov constant in the theory of turbulence of ideal fuid in one loop approximation in Clebsh variables.

The free surface of a viscous fluid is a source of convective flow (Marangoni convection) if its surface tension is distributed non-uniformly. Such non-uniformity arises from the dependence of the surface tension on a scalar quantity, either surfactant concentration or temperature. The surface-tension-induced velocity redistributes the scalar forming a closed-loop interaction. It is shown that under the assumptions of (i) small Reynolds number and (ii) vanishing diffusivity this nonlinear process is described by a single self-consistent two-dimensional evolution equation for the scalar field at the free surface that can be derived from the three-dimensional basic equations without approximation. The formulation of this equation for a particular system requires only the knowledge of the closure law, which expresses the surface velocity as a linear functional of the active scalar at the free surface. We explicitly derive these closure laws for various systems with a planar non-deflecting surface and infinite horizontal extent, including an infinitely deep fluid, a fluid with finite depth, a rotating fluid, and an electrically conducting fluid under the influence of a magnetic field. For the canonical problem of an infinitely deep layer we demonstrate that the dynamics of singular (point-like) surfactant or temperature distributions can be further reduced to a system of ordinary differential equations, equivalent to point-vortex dynamics in two-dimensional perfect fluids. We further show, using numerical simulations, that the dynamical evolution of initially smooth scalar fields leads in general to a finite-time singularity. The present theory provides a rational framework for a simplified modelling of strongly nonlinear Marangoni convection in high-Prandtl-number fluids or systems with high Schmidt number.