Contact Line Boundary Condition Research Articles

Stream function solutions for some contact line boundary conditions: Navier slip, super slip and the generalized Navier boundary condition

The stream function solution for the inner region Stokes flow, for a locally plane moving fluid interface near the triple point, is derived considering three different boundary conditions: the Navier slip boundary condition (NBC), the super-slip boundary condition and the generalized Navier boundary condition (GNBC). The NBC, incorporating a slip length parameter λ , is a well-known method for regularization in the context of the three-phase dynamic contact line problem. It is demonstrated that the velocity field solution under this boundary condition maintains a C 0 continuity at the contact line, resulting in a logarithmic divergence of the pressure at the contact line. By contrast, the super-slip boundary condition establishes a proportional relationship between the wall velocity and the normal derivative of the shear stress, leading to a C 1 velocity field. Furthermore, the GNBC, which introduces an uncompensated Young stress to drive the contact line, yields a C 2 velocity field. The dominant terms are explicitly derived, and the analytical approach presented here can be extended to other bi-harmonic problems as well.

Physics of a strongly oscillating axisymmetric air-water interface with a fixed boundary condition

A free-slip air-water interface with a fixed contact line boundary condition, when oscillating at certain frequencies with a large amplitude, can efficiently induce a fast-speed, far-propagating streaming jet. The extraordinary characters of the streaming jet can be employed to address engineering challenges across multiple disciplines.

Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model

In this paper, we present an efficient energy stable scheme to solve a phase field model incorporating contact line condition. Instead of the usually used Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field model with the static contact line boundary condition that coupled with incompressible Navier-Stokes equations with Navier boundary condition. The projection method is used to deal with the Navier-Stokes equa- tions and an auxiliary function is introduced for the non-convex Ginzburg-Landau bulk potential. We show that the scheme is linear, decoupled and energy stable. Moreover, we prove that fully discrete scheme is also energy stable. An efficient finite element spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed scheme is very efficient and accurate

Numerical simulation of bubble formation with a moving contact line using Local Front Reconstruction Method

The process of adiabatic bubble formation from an orifice plate occurs in various industrial applications. It is important to understand the dynamics of bubble formation and to develop numerical models to accurately predict the formation dynamics under various operating conditions. For the numerical models, an appropriate contact line boundary condition is necessary since this process may involve a moving contact line, which significantly affects the bubble departure size. In this paper, we extend the Local Front Reconstruction Method by incorporating contact angle dynamics. The predictions of the improved model are extensively verified and validated with experimental and numerical data available in the literature. The problem of three-dimensional bubble injection from an orifice into quiescent water using various volumetric flow rates is used to assess the numerical model under capillary dominant conditions and conditions where the interplay between inertial, viscous, surface tension, and buoyancy forces cause a complex interface deformation.

Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach

We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn--Hilliard equation with a dynamic moving contact line boundary condition. A crucial and challenging issue for solving this model numerically is the time marching problem, due to the high order, nonlinear, and coupled properties of the system. We solve this issue by developing two linear, second order accurate, and energy stable schemes based on the projection method for the Navier--Stokes equations, the invariant energy quadratization for the nonlinear gradient terms in the bulk and boundary, and a subtle implicit-explicit treatment for the stress and convective terms. The well-posedness of the semidiscretized system and the unconditional energy stabilities are proved. Various numerical results based on a spectral-Galerkin spatial discretization are presented to verify the accuracy and efficiency of the proposed schemes.

Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines

AbstractIn this paper, we present some efficient numerical schemes to solve a two-phase hydrodynamics coupled phase field model with moving contact line boundary conditions. The model is a nonlinear coupling system, which consists the Navier-Stokes equations with the general Navier Boundary conditions or degenerated Navier Boundary conditions, and the Allen-Cahn type phase field equations with dynamical contact line boundary condition or static contact line boundary condition. The proposed schemes are linear and unconditionally energy stable, where the energy stabilities are proved rigorously. Various numerical tests are performed to show the accuracy and efficiency thereafter.

Numerical approximations for a phase-field moving contact line model with variable densities and viscosities

We consider the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line boundary conditions. The model is a nonlinear, coupled system that consists of incompressible Navier–Stokes equations with the generalized Navier boundary condition, and the Cahn–Hilliard equations with moving contact line boundary conditions. By some subtle explicit–implicit treatments to nonlinear terms, we develop two efficient, unconditionally energy stable numerical schemes, in particular, a linear decoupled energy stable scheme for the system with static contact line condition, and a nonlinear energy stable scheme for the system with dynamic contact line condition. An efficient spectral-Galerkin spatial discretization is implemented to verify the accuracy and efficiency of proposed schemes. Various numerical results show that the proposed schemes are efficient and accurate.

Droplet spreading on rough surfaces: Tackling the contact line boundary condition

The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact line motion, is a controversial issue since the microscopic physics that gives rise to this displacement is still unknown. Here, a sharp interface, continuum-level, novel modeling approach, accounting for liquid/solid micro-scale interactions assembled in a disjoining pressure term, is presented. By following a unified conception (the model applies both to the liquid/solid and the liquid/ambient interfaces), the friction forces at the contact line, as well as the dynamic contact angle are derived implicitly as a result of the disjoining pressure and viscous effects interplay in the vicinity of the substrate’s intrinsic roughness. Previous hydrodynamic model limitations, of imposing the contact line boundary condition to an unknown number and reconfigurable contact lines, when modeling the spreading dynamics on textured substrates, are now overcome. The validity of our approach is tested against experimental data of a droplet impacting on a horizontal solid surface. The study of the early spreading stage on hierarchically structured and chemically patterned solid substrates reveal an inertial regime where the contact radius grows according to a universal power law, perfectly agreeing with recently published experimental findings.

Stability of Constrained Capillary Surfaces

A capillary surface is an interface between two fluids whose shape is determined primarily by surface tension. Sessile drops, liquid bridges, rivulets, and liquid drops on fibers are all examples of capillary shapes influenced by contact with a solid. Capillary shapes can reconfigure spontaneously or exhibit natural oscillations, reflecting static or dynamic instabilities, respectively. Both instabilities are related, and a review of static stability precedes the dynamic case. The focus of the dynamic case here is the hydrodynamic stability of capillary surfaces subject to constraints of (a) volume conservation, (b) contact-line boundary conditions, and (c) the geometry of the supporting surface.

Height functions for applying contact angles to 3D VOF simulations

AbstractA rigorous methodology is presented for applying a contact angle as a contact line boundary condition within a 3D volume‐of‐fluid‐based flow algorithm, based on the recently developed height function methodology that yields accurate interface normals and curvatures from volume fractions. We demonstrate that the approach yields accurate estimates of curvature and surface tension at a contact line, values that converge with spatial refinement. We then study the efficacy of this approach via examples of both static and dynamic contact line phenomena. Copyright © 2008 John Wiley & Sons, Ltd.

Numerical simulation of bubble formation on orifice plates with a moving contact line

The formation of bubbles on an orifice plate involves a moving contact line, especially in case of poor wetting conditions. The dynamics of the moving contact line and contact angle have a significant impact on the bubble departure size. Therefore, for the numerical simulation, an appropriate contact line boundary condition is essential for a correct prediction of the bubble formation. Numerical tests have been performed on two kinds of contact line models, one is a contact line velocity dependent model (Model-A, a commonly used model) and the other is a stick-slip model (Model-B). The calculation results using Model-A depend greatly on the prescribed maximum contact line velocity. With Model-B a parameter-independent prediction can be obtained provided that the mesh is sufficiently fine. The dynamic advancing and receding contact angles, which are two required inputs to both models, have a significant influence on the predicted bubble departure diameter, if the contact line moves beyond the inner rim of the orifice. The effect of wettability on the bubble departure size is realized via the variation of the maximum contact diameter. When the contact line sticks to a small region near the inner rim of the orifice, such as the bubble formation on a thin-walled nozzle, the effects of the contact angle and contact line models are negligible.

Modal analysis of liquid sloshing with different contact line boundary conditions using FEM

A finite element method (FEM) for liquid sloshing modal analysis is established. Surface tension and three kinds of contact line boundary conditions, namely, free-end, pin-end and wetting boundary conditions, are taken into account. Sloshing damping caused by energy dissipation at the wall, in the interior fluid and at the contact line is calculated. Numerical results are compared with the analytical values and measurements. For the pin-end and free-end boundary conditions the differences between numerical value and analytical value are small, and for the wetting boundary condition, because approximation is used, the differences are more significant.

Axisymmetric Surface Oscillations in a Cylindrical Container with Compensated Gravity

In this study the first mode of axisymmetric surface oscillations of a free liquid interface in a partly filled right circular cylinder under compensated gravity is investigated numerically. The situation is similar to a spacecraft that enters a ballistic flight at the end of thrust. A reorientation of the liquid of the free liquid surface toward the new equilibrium position takes place. The characteristics of this flow, such as the frequency and the damping, are governed by the behavior of the contact line. The investigations focus on the dependence on the contact line boundary condition, including contact angle variation, and on viscous effects. The effect on the natural frequency and the damping is considered. An analytical approximation for the frequency behavior for a frictionless liquid for a free and a fixed contact line condition is given. Further analytical approximations for the damping behavior in dependence on the contact angle and the Ohnesorge number are determined. The numerical results show very good agreement with experimental data.

Boundary conditions for contract lines in coextrusion flows

A bicomponent coextrusion process is modelled using a 3-D finite element formulation. The layer uniformity problem in coextrusion is addressed by examining the effects of the polymer melt/polymer melt/die wall contact line boundary condition. It has been observed that the less viscous polymer layer will tend to displace the more viscous polymer layer near the die wall. The behaviour of the contact lisle is considered to be either a “stick” or “slip” boundary condition. In the “stick” boundary condition, the contact line does not move from its original position after the two polymer layers meet, A slip boundary condition allows the contact line to move along the die wall. The calculated interfaces which result from different contact line assumptions are determined. Results show that if a “stick” boundary condition is appropriate for a given fluid/fluid/solid contact line, then a very thin entrained layer of the more viscous polymer melt will be trapped between the less viscous polymer melt and the die wall. Slip boundary conditions would allow complete displacement of the contact line along the die wall. Both slip and stick boundary conditions produce similar interface profiles far away from the die wall for small viscosity ratios. In certain eases, the displacement of the more viscous material by the less viscous material will cease and a static interface structure is produced regardless of die length. Experimental work with polycarbonate melts is compared with the numerical simulations.

Adsorption and capillary condensation at the contact line in change of phase heat transfer

A model based on adsorption and capillary condensation which describes the wetting characteristics of the contact line in change of phase heat transfer is proposed. A relationship between the equilibrium shape of a thin film at the contact line, superheat, and interfacial forces is derived for both zero and finite contact angle systems on “smooth” surfaces. Contact line boundary conditions which are a function of temperature, superheat and interfacial forces are presented. Homogeneous and heterogeneous nucleation at the minimum film boiling temperature is discussed.