Liquid Bridges Between Contacting Balls

The problem studied is that of a rotationally symmetric liquid bridge between two contacting balls of equal radius, with the same contact angle with both balls, and in the absence of gravity. The bridge surface must be of constant mean curvature, hence a Delaunay surface. If the contact angle is less than \({\frac{\pi}{2}}\) , existence of a rotationally symmetric bridge is shown for a large range of the relevant parameter, giving unduloidal, catenoidal, and nodoidal bridges. If the contact angle is greater than or equal to \({\frac{\pi}{2}}\) , it is shown that no stable rotationally symmetric bridge which is symmetric across the perpendicular bisector of the line segment between the two centers of the balls exists. Existence therefore depends discontinuously on contact angle.     

Dynamic Contact Behavior of a Golf Ball during an Oblique Impact

The oblique impact between a golf ball and a rigid steel target was studied using a high-speed video camera. Video images recorded before and after the impact were used to determine the inbound velocity v _i, rebound velocity v _r, inbound angle θ_i, rebound angle θ_r, and the coefficient of restitution e. The results showed that θ_r and e decreased as v _i increased. The maximum compression ratio η_c, contact time t _c, average angular velocity , and tangential velocity , along the target were determined from images obtained during the impact. The images demonstrated that η_c increased with v _i while t _c decreased. In addition, and increased almost linearly as v _i increased. A rigid body model was used to estimate the final angular velocity ω* and tangential velocity ν_t* at the end of the impact; these results were then compared with experimental data.     

Vorticity and its rate of change just downstream of a curved shock

A theory is developed for the vorticity and its substantial derivative just downstream of a curved shock wave, the resulting formulas are exact, algebraic, and explicit. Analysis is for a cylinder-wedge or sphere-cone body, at zero incidence, whose downstream half-angle is θ_b. Derived formulas directly depend only on the ratio of specific heats, γ, the freestream Mach number, M ₁, the local slope and curvature of the shock, and the dimensionality parameter, σ, which is zero for a two-dimensional shock and unity for an axisymmetric shock. In turn, the slope and curvature depend on γ, M ₁, and θ_b. Numerical results are provided for a bow shock in which θ_b is 5°, 10°, or 15°, M ₁ is 2, 4, or 6, and γ = 1.4. There is little dependence on the half angle but a strong dependence on the freestream Mach number and on dimensionality. For vorticity and its substantial derivative, the dimensionality dependence gradually decreases with increasing Mach number. In comparison to the two-dimensional case, an axisymmetric shock generates considerable vorticity in a region relatively close to the symmetry axis. Moreover, the magnitude of the vorticity, in this region, is further enhanced in the flow downstream of the shock. This dimensionality difference in vorticity and its substantial derivative is attributed to the three-dimensional relief effect in an axisymmetric flow.

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The micropolar fluid model for blood flow through a tapered artery with a stenosis

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.     

Measurement of the relaxation time in Darcy flow

The inertia of a liquid flowing through a porous medium is normally ignored, but if the acceleration is great, it may be important. The relaxation time, defined so that it alone accounts for the inertia, has been determined experimentally with a simple oscillator. A U-Tube is provided with a porous plug and filled with a liquid. During pendulation of the liquid, the frequency and the damping define the relaxation time. The measured value of the relaxation time is about 10 times the theoretical estimate derived from Navier-Stokes equation.Symbols E modulus of elasticity - E _D dissipated energy - E _k kinetic energy - g acceleration of gravity - G pressure gradient - h height - K ₀ permeability - L length of porous plug - n porosity - P dissipated power - pressure - R half the tube length - R _c radius of the tube bend - r radial coordinate - r _o radius of the tube - s coordinate along a streamline in the tube - t time - v flux per unit area - it relaxation time - , auxiliary variables - , v dynamic and kinematic viscosity - , velocity potential for inviscid flow and gravity potential - dissipation function - displacement of the liquid - , _o frequency of damped and undamped oscillations     

Axisymmetric spreading of a thin liquid drop with suction or blowing at the horizontal base

The axisymmetric spreading under gravity of a thin liquid drop on a horizontal plane with suction or blowing of fluid at the base is considered. The thickness of the liquid drop satisfies a non-linear diffusion equation with a source term. For a group invariant solution to exist the normal component of the fluid velocity at the base, v_n, must satisfy a first-order quasi-linear partial differential equation. The general form of the group invariant solution for the thickness of the liquid drop and for v_n is derived. Two particular solutions are considered. Each solution depends essentially on only one parameter which can be varied to yield a range of models. In the first solution, v_n is proportional to the thickness of the liquid drop. The base radius always increases even for suction. In the second solution, v_n is proportional to the gradient of the thickness of the liquid drop. The thickness of the liquid drop always decreases even for blowing. A special case is the solution with no spreading or contraction at the base which may have application in ink-jet printing.     

Experimental investigations of steady and oscillating annular liquid curtains with different surface tensions

Experiments were performed on laminar, vertical, annular, liquid curtains to study the dynamics of steady curtains, and the onset and frequency of oscillating curtains. The experiments were conducted to observe the effects of inertia and pressure on liquid curtains with different surface tensions. For steady curtains, convergence lengths were measured as functions of Froude number and pressure differential for three different surface tensions. The factors causing the onset of oscillations in a pressurized curtain were observed and the frequency of the internal pressure fluctuations were measured for various Froude numbers and two surface tensions.List of symbols b local thickness of curtain sheet - b ₀ initial thickness of curtain or nozzle gap thickness (0.5 mm) - C _P pressure coefficient - Fr Froude number (V ₀ ² /g R ₀) - g gravitational acceleration - g gravitational acceleration - L convergence length of curtain - L ^* dimensionless convergence length (L/R ₀) - N _c convergence number (g ² R ₀ ² b ₀ /2v ₀ ² ) - P _e pressure outside the curtain (ambient) - P _i pressure inside the curtain - P pressure differential (P _i– P _e) - P _cr pressure differential at which curtain begins to oscillate - R local radius of curvature in the horizontal plane - R ₀ initial curtain radius or radius of nozzle exit (50 mm) - r _v local radius of curvature in the vertical plane - V local liquid velocity - V ₀ initial liquid velocity - V ^* dimensionless local liquid velocity (V/V ₀) - z axial distance from the nozzle - z ^* dimensionless axial distance from the nozzel (z/R ₀) - s differential length of curtain - differential angle in the horizontal plane - angle between the direction of the surface tension force in the vertical plane and the direction of r _v - deangle between the direction of the surface tension force in the horizontal plane and the direction of R - angle between r _vand R in the vertical plane - ₀ nozzle exit angle (zero degrees) - surface tension of liquid - liquid density (1.0 gm/cm³)     

Geometric properties of two phase flow in geothermal reservoirs

The two phase flow equations frequently used in geothermal engineering ignore capillary pressure, which results in a singular system of equations. Analysis of these equations reveals three mechanisms for altering saturation: local boiling, the spatial dependence of flowing enthalpy due to the convective transport of fluid, and counterflow. A scalar function is associated with each of these three mechanims. At each point in space, flows are essentially two dimensional, with gravity establishing a vertical hierarchy, in that volumetric, energy and mass fluxes can never point below a lower member in this triple. With increasing liquid saturation, the characteristics associated with the saturation equation move up from below this grouping of directions, and eventually may even point above volumetric fluxes. Finally, weak shocks and the associated entropy condition are considered. The characteristics of the saturation equation coincide with the velocity of extremely weak shocks, and saturation increases with the passage of a weak shock, provided the magnitude of the characteristic speed increases with saturation.Notation C_l liquid heat capacity - C_m rock heat capacity - C_v vapour heat capacity - G counterflow energy flux - h flowing enthalpy - hl liquid enthalpy - h_v vapour enthalpy - k permeability - k downward vector - P pressure - S liquid saturation - T temperature - dT/dP derivative at saturation - z vertical coordinate - l liquid viscosity - v vapour viscosity - Pl liquid density - _m rock density - _v vapour density - porosity     

Behavior of liquid menisci formed during the extraction of a vertical rod from the free surface of a liquid contained in a finite basin (Part 1)

Many studies involving the shapes and stability of liquid menisci formed during the extraction of a vertical rod from a liquid basin (rod‐in‐free‐surface problem) have been reported in the literature. However, the vast majority of these were conducted under the assumptions that the radius of the basin (R) is infinite and that, at its extremity, both the slope and curvature of the liquid surface are zero. Recently, a few studies involving finite basins have been reported; however, these were conducted under the assumption that the displaced volume of the liquid in the basin is prescribed. In this study, a parametric finite element method was employed to determine the behavior (shape and stability) of liquid menisci formed during the extraction of a vertical rod with circular cross‐section from a liquid contained in a circular basin with finite radius. The plots presented in this paper enable investigators to predict the critical extraction height (a priori) as a function of the radius ratio (R/r) and Bond number (β₀=ρgr²/γ) for the case where the contact angle (θ₂) at the outer extremity of the basin is 90^°. Theoretical and experimental results obtained for arbitrary values of θ₂ will be presented in a Part 2 paper. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of liquid-crystal thermometry to drop temperature measurements

A technique has been developed that enables remote sensing of the temperatures of liquid drops in a medium of an immiscible, transparent liquid with the aid of dispersing microcapsules of thermochromic liquid crystal in each drop under illumination by either a planar floodlight or a light sheet which cuts the drop at a meridian. Based on appropriate hue-temperature calibrations made with an isothermal, stationary drop/medium system, one can analyze spatial and time variations of temperature within drops in motion under transient convective heating (or cooling) from the medium.List of Symbols B tristimulus blue component - D drop diameter - G tristimulus green component - H hue angle - h ₀ constant term in the expression for H - H _m mean value of H over drop surface - h vertical coordinate fixed onto test column - R tristimulus red component - Re drop Reynolds number, UD/v _c - r, g, b chromaticity coordinates - r drop radius - s penetration depth of light into drop - T temperature - T _d instantaneous drop temperature - T _d0 initial drop temperature - T _c continuous-phase temperature - U velocity of rise of drop - z vertical coordinate laid on drop - v _c kinematic viscosity of continuous phase - angle of lighting measured from camera axis - _s local view angle (azimuth) - polar angle     

Computational evaluation of ship manoeuvring performance based on scale model tests

Summary A brief review of the most important existing mathematical models for predicting the manoeuvring performance of a ship at the design stage is presented. A model based on the derivation of the hydrodynamic coefficients from force measurements on scale models is used to develop a computer program for the evaluation of the ship performance in some standard manoeuvres such as turning circle and zig-zag manoeuvres.

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Sommario Viene presentata una breve descrizione delle metodologie attuali più seguite per la identificazione di un modello matematico atto alla previsione delle caratteristiche di manovrabilità di una nave. Utilizzando coefficienti idrodinamici ricavati da prove su modelli in scala si è sviluppato un codice di calcolo che consente di ottenere la risposta della nave in alcune manovre standard quali quelle di evoluzione e zig-zag.

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Symbols G Center of gravity - g Acceleration due to gravity - I _ZZ Moment of inertia aboutz-axis - i _EP Effective moment of inertia about propeller axis - L Length between perpendiculars - m Ship mass - N Hydrodynamic moment aboutz-axis - n Rate of revolutions of propeller - O Origin of shipbound coordinate system - Q Propeller torque - Q _E Engine torque - q _F Engine fuel rate - R _T Total hull resistance - r Rate of turn aboutz-axis (yaw rate) - U Along-track velocity of0 - u, v Components ofU alongx, y-axes - X, Y Hydrodynamic forces alongx, y-axes - x,y,z Shipbound coordinate axes - x _G ,y _G ,z _G Coordinate of center of gravity in the shipbound system - x _o,y ₀,z ₀ Coordinate of 0 in the earthbound system, Fig. 1 - Drift angle - Rudder angle - Characteristic time - Heading angle Presented at the II Convegno AIMETA di Meccanica Computazionale, Rome, June 2–5, 1987.     

Modeling of bubble detachment in reduced gravity under the influence of electric fields and experimental verification

A simple model for predicting bubble volume and shape at detachment in reduced gravity under the influence of electric fields is described in the paper. The model is based on relatively simple thermodynamic arguments and relies on and combines several models described in the literature. It accounts for the level of gravity and the magnitude of the electric field. For certain conditions of bubble development the properties of the bubble source are also considered. Computations were carried out for a uniform unperturbed electric field for a range of model parameters, and the significance of model assumptions and simplifications is discussed for the particular method of bubble formation. Experiments were conducted in terrestrial conditions and reduced gravity (during parabolic flights in NASAs KC-135 aircraft) by injecting air bubbles through an orifice into the electrically insulating working fluid, PF5052. Bubble shapes visualized experimentally were compared with model predictions. Measured data and model predictions show good agreement. The results suggest that the model can provide quick engineering estimates concerning bubble formation for a range of conditions (both for formation at an orifice and boiling) and such a model reduces the need for complex and expensive numerical simulations for certain applications. a Major axis of spheroid (m) - a _m Measured bubble height (m) - b Minor axis of spheroid (m) - b _m Measured bubble width (m) - A, B, C, F Parameters of the Kumar-Kuloor model - a/b Computed aspect ratio - a _m /b _m Measured aspect ratio - D Orifice diameter (m) - E Magnitude of the electric field (V/m) - g Gravitational acceleration (m/s²) - g _t Terrestrial gravity (g _t = 9.81 m/s²) - N _w Electrical Weber number - p Pressure (Pa) - Q Volume flow rate (m³/s) - r Radius of the spherical bubble (m) - R Radius of curvature at the tip of the bubble (m) - t Time (s) - t Time interval (s) - T Temperature (°C) - U Electrical potential (V) - u Velocity (m/s) - V Volume (m³) - x, y Dimensionless coordinates of the Cartesian coordinate system - x, y Scaled coordinates, Cheng-Chaddock model - X, Y Dimensional coordinates of the Cartesian coordinate system - Characteristic wave number (m^–1) - Eötvös number - Absolute dielectric permittivity (F/m) - Contact angle (deg.) - Gibbs free energy (J) - Surface tension (N/m) - Dynamic viscosity (Pa s) - Density (kg/m³) - cr Critical value - d Detachment - eq Equilibrium - g Gas - K Refers to the Kumar-Kuloor model - l Liquid - m Measured value - t Terrestrial     

Advection of axisymmetric interfaces by the volume-of-fluid method

A criterion is proposed for the advection of axisymmetric interfaces. The location of an interface is followed by a volume-tracking technique wherein a volume fraction parameter is assigned to each of the cells in a Eulerian grid system. The interface is discretized into a set of line segments fitted at the boundary of every pair of neighbouring computational cells. The orientation of a line segment is obtained by inspecting the volume fractions of two neighbouring cells. The volume fractions are then advected using the velocity components at the boundary of the two cells. The following advection criterion is proposed: for advection in the axial direction the axial velocity u is assumed constant in the vicinity of each cell face; for advection in the radial direction the radial velocity v times the radial distance r is assumed constant in the vicinity of each cell face, i.e. r^βv = const., where β = 0 for Cartesian and β = 1 for axisymmetric systems. The above criterion is used to develop an algorithm for the advection of axisymmetric interfaces which is referred to as the ‘axisymmetric flux line segment model for advection and interface reconstruction’ or A-FLAIR.     

Loss of real characteristics for models of three-phase flow in a porous medium

In this paper we examine the generalized Buckley-Leverett equations governing threephase immiscible, incompressible flow in a porous medium, in the absence of gravitational and diffusive/dispersive effects. We consider the effect of the relative permeability models on the characteristic speeds in the flow. Using a simple idea from projective geometry, we show that under reasonable assumptions on the relative permeabilities there must be at least one point in the saturation triangle at which the characteristic speeds are equal. In general, there is a small region in the saturation triangle where the characteristic speeds are complex. This is demonstrated with the numerical results at the end of the paper.Symbols and Notation a, b, c, d entries of Jacobian matrix - A, B, C, D coefficients in Taylor expansion of _t, _v, _a - det J determinant of matrix J - dev J deviator of matrix J - J Jacobian matrix - L linear term in Taylor expansion for J near (s _v, s_a) = (0, 1) - m slope of r ₊ - p pressure - r± eigenvectors of Jacobian matrix - R real line - S intersection of saturation triangle with circle of radius centered at (1, 0) - S intersection of saturation triangle with circle of radius centered at (0, 1) - s _l, s_v, s_a saturations of phases (liquid, vapor, aqua) - tr J trace of matrix J - v _l , v _v , v _a phase flow rates (Darcy velocities) - v _T total flow rate - X, Y, Z entries of dev J - smooth closed curve inside saturation triangle - saturation triangle - _l, _v, _a phase density times gravitational acceleration times resevoir dip angle - K total permeability - _l, _v, _a three-phase relative permeabilities - _lv>, _la liquid phase relative permeabilities from two-phase data - _l, _v, _a mobilities of phases - _T total mobility - _l Corey mobility - _l, _v, _a phase viscosities - _± eigenvalues of Jacobian matrix - porosity Supported in part by National Science Foundation grant No. DMS-8701348, by Air Force Office of Scientific Research grant No. AFOSR-87-0283, and by Army Research Office grant No. DAAL03-88-K-0080.This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.     

Natural convection in partially heated vertical channels

A numerical analysis has been performed on laminar natural convection of air in open vertical channels partially heated at uniform wall temperature (UWT) or at uniform heat flux (UHF). The governing equations have been solved by means of a finite difference technique. Results showing axial velocity and temperature developments as well as heat transfer performances and correlations between non-dimensional groups, are presented.

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Natürliche Konvektion in teilweise erwärmten vertikalen Kanälen

Zusammenfassung Eine numerische Analyse wurde über die natürliche Luftkonvektion in vertikalen, mit gleichmäßiger Wandtemperatur (UWT) oder mit gleichmäßigem Wärmestrom (UHF) teilweise erwärmten Kanälen durchgeführt. Die analytischen Gleichungen des Problems wurden mit der Finit-Differenzen-Technik gelöst, und es werden Ergebnisse hinsichtlich der Geschwindigkeits- und Temperaturverteilungen im Inneren des Kanals sowie der thermischen Leistung des Systems aufgeführt.

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Nomenclature a thermal diffusivity of the fluid - c _p specific heat (at constant pressure) of the fluid - g acceleration due to gravity - Gr =[·g·S ³ ·(T₁-T₀)]/v²,Grashof number (UWT case) - Gr =[-g-S ⁴ -q ₁]/(v ²·k), Grashof number (UHF case) - Gr ^* =(S/H) Gr, modified Grashof number - H overall channel height - I, J X andY coordinate indexes - k thermal conductivity of the fluid - Nu mean Nusselt number of the channel - p difference between pressure inside the channel and pressureoutside, at the same heightx - P dimensionless difference pressure - Pr Prandtl number - q specific heat flux - q ₁ specific heat flux from heated plates (UHF case) - Q heat flux (per unit length in thez-direction) from walls - S channel width - T temperature - T _w reference wall temperature - T _o fluid temperature at the inlet section - T ₁ heated plates temperature (UWT case) - u, axial and transverse velocity of the fluid - u _o axial velocity of the fluid at the inlet section - U, V dimensionless axial and transverse velocity - U _o dimensionless axial velocity at the inlet section - x, y axial and transverse coordinate - X, Y dimensionless axial and transverse coordinate - X =H/(S·Gr), dimensionless overall channel height - thermal expansion coefficient of the fluid - dimensionless temperature - v kinematic viscosity of the fluid - density of the fluid     

Three-segment electrodiffusion probe for velocity measurements

A cylindrical electrodiffusion probe for the measurement of liquid velocity vectors in the plane perpendicular to its axis was developed as an analogue to the triple-split film thermoanemometer. The geometry of the probe enables high directional resolution in the whole range of 360°. The total mass transfer of the probe was well correlated by the relation Sh = 0.76 Sc ^0.33 Re ^0.47.List of symbols A _kj , B _kj Fourier coefficient - c [mol/m³] depolarizer concentration - te]D [m²/s] diffusion coefficient of species - d [m] diameter of probe - f [1/s] frequency of vortex formation - h [mol/m²s] coefficient of mass transfer - I _k normalized current of K-th segment - i [A] total current - i _k [A] current of K-th segment - Re Reynolds number, u d/v - Sc Schmidt number, v/D - Sh Sherwood number, h d/c D - Sr Strouhal number, f d/v - v [m/s] free stream velocity - [°] flow angle, i.e. angle between approaching stream and reference direction of probe - v [m²/s] kinematic viscosity     

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China     

Identification of the Physical Parameters Used in the Thermo-Hygro-Mechanical Model

This paper describes different methods used to identify a large number of physical parameters of the thermo-hygro-mechanical coupling model. This model is developed on the basis of mechanics of porous media and deals with the prediction of response of a structure submitted to thermal, hygrometric and mechanical loading. The aim of this work is mainly to propose some experimental methods for the determination of physical parameters used previously in the model such as hygrometric parameters (liquid Biot's coefficient b _l , vapour and liquid permeability _v, _l and tangent capillary modulus N _ll). Thermal parameters such as thermal conductivity (), specific heat (C) and the thermo-hydrous expansion coefficient ( _i ^p ) have been identified using some works published previously. The different physical parameters were identified in the case of cement mortar without taking into account the influence of hysteresis.     

Heat transfer in a thin layer of a viscous heavy noncompressible liquid under wavy flow conditions

The article describes a method for calculating the flow of heat through a wavy boundary separating a layer of liquid from a layer of gas, under the assumption that the viscosity and heat-transfer coefficients are constant, and that a constant temperature of the fixed wall and a constant temperature of the gas flow are given. A study is made of the equations of motion and thermal conductivity (without taking the dissipation energy into account) in the approximations of the theory of the boundary layer; the left-hand sides of these equations are replaced by their averaged values over the layer. These equations, after linearization, are used to determine the velocity and temperature distributions. The qualitative aspect of heat transfer in a thin layer of viscous liquid, under regular-wavy flow conditions, is examined. Particular attention is paid to the effect of the surface tension coefficient on the flow of heat through the interface.Notation x, y coordinates of a liquid particle - t time - v and u coordinates of the velocity vector of the liquid - p pressure in the liquid - c_v, , T,, andv heat capacity, thermal conductivity coefficient, temperature, density, and viscosity of the liquid, respectively - g acceleration due to gravity - surface-tension coefficient - c phase velocity of the waves at the interface - T_w wall temperature - h₀ thickness of the liquid layer - u₀ velocity of the liquid over the layer Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 147–151, July–August, 1970.     

A method for overcoming the surface tension time step constraint in multiphase flows II

A method for overcoming the surface tension time step constraint is presented. The algorithm presented in this work is an improvement on the work presented by Sussman and Ohta (SIAM J Sci Comput 2009). In this work, the method of Sussman and Ohta is extended in order to treat problems with contact angle dynamics. Furthermore, this work presents a more efficient method for computing volume‐preserving motion by mean curvature than the method presented previously. The new method is tested on the following four 2D problems: (1) 3D axisymmetric (r?z) surface tension driven zero gravity droplet oscillation, (2) measurement of the magnitude of parasitic currents for a droplet on a substrate initialized in static equilibrium, (3) relaxation of a 2D droplet on a substrate to static shape, and (3) relaxation of a 2D bubble on a substrate to static shape. Copyright © 2011 John Wiley & Sons, Ltd.