Collision of water drops with a plane water surface

The dependence of the outcome of the collision of uncharged water drops with a plane water surface on the impact angle , the velocity v₁ and the radius r₁ of the drops has been investigated experimentally. The impact parameters were varied over the intervals: v₁=0.40–1.05 m/sec, r₁=75–150m, and =16-85°. The method employed made it possible to avoid having to monitor the individual high-speed impact process. A stream of drops, produced in a vibrating reed type monodisperse droplet generator, was directed at the target. The impact parameters were measured by means of pulsed illumination. The results are expressed in the form of the dependence of the rebound probability and the coalescence coefficient E_S on the impact parameters. The existence of alternating conditional rebound-coalescence-rebound zones for different impact angles is established, together with a decrease in E_S with increase in r₁ and v₁. The data obtained generalize the results of previous experiments.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 165–168, May–June, 1990.     

Impact dynamics of surfactant laden drops: dynamic surface tension effects

We study the impact and subsequent retraction of aqueous surfactant-laden drops upon high-speed impact on hydrophobic surfaces. Without surfactants, a rapid expansion of the drop due to the fluid inertia is followed by a rapid retraction, due to the wetting incompatibility. With surfactants, the retraction can be partly or completely inhibited. We provide quantitative measurements showing that both the expansion and the retraction dynamics depend not only on the equilibrium surface tension (ST) but also on the dynamic tension of the surfactant solutions; the latter varies significantly between different surfactants.     

On the spreading radius of surface tension driven oil on deep water

The spread of a thin oil film by surface tension gradients from an oil source of unlimited mass on deep water is considered. A similarity solution for the velocity fields of the oil and water, the oil thickness and the rate at which each grow is obtained both for axisymmetric and the previously explored planar spreading. The dimensionless size of the spread, which is oil type independent, is shown to be 1.0754 and 1.4150 for axisymmetric and planar spreading respectively. It is further shown that the oil film equation of state, which relates surface tension to oil thickness, is unique to each oil or oil-surfactant mixture.     

Extrudate swell for a round jet with large surface tension

The problem of extrudate swell of a viscoelastic fluid from a round pipe is studied by the method of domain perturbations. The perturbation problems are solved by a finite-element method through second-order in the flow rate parameter ∈ for small flow rates. The analysis extends the work of Sturges on swelling in two-dimensional channels to round capillary tubes. In perturbation studies for small ∈, the rheology of the fluid may be expressed by three parameters, the viscosity and the two constants α₁ and α₂ appearing at order two in the expansion of the extra stress around zero shear. Surface tension has an important influence on the shape of the jet at low speeds. The shape of the surface on a round jet depends on α₁ and α₂, in the plane jet only on α₁. The analysis predicts that no matter what the constitutive equation may be, the jet will first contract if the radius of the pipe is sufficiently small. The contraction takes place in a length less than $\text{1}\text{10}$ the diameter of the jet and is followed by a swell. The contraction is usually small and may be hard to observe. There are five different contributions to the jet shape at second-order but only the viscoelastic ones persist as the pipe radius goes to zero.     

Cavity dynamics of water drop impact onto immiscible oil pool with different viscosity

Acta Mechanica Sinica - In this work, we numerically study the impact of a water droplet onto a deep oil pool. Two fluids are immiscible and the viscosity of the pool liquid is changed...     

Vaporization of single liquid drops in an immiscible liquid Part I: Forms and motions of vaporizing drops

Vaporization process of single drops of pentane or furan in an aqueous glycerol has been studied photographically in the region where the geometrically simple configuration and rectilinear motion of vaporizing two-phase bubbles are realized. The instantaneous velocity of rise of two-phase bubbles agreed approximately with Stokes' theory in the range Re < 1. The liquid-liquid interfacial area takes almost a constant value slightly higher than the initial surface area of the liquid drop in the range below 10% of the vaporization ratio, and then reduces gradually. The vaporization does not bring an effective increase of heat transfer area.     

Experimental investigation on splashing and nonlinear fingerlike instability of large water drops

The fluid physics of the splashing and spreading of a large-scale water drop is experimentally observed and investigated. New phenomena of drop impact that differ from the conventional Rayleigh–Taylor instability theory are reported. Our experimental data shows good agreement with previous work at low Weber number but the number of fingers or instabilities begins to deviate from the R–T equation of Allen at high Weber numbers. Also observed were multiple waves (or rings) on the spreading liquid surface induced from pressure bouncing (or pulsation) within the impacting liquid. The first ring is transformed into a radially ejecting spray whose initial speed is accelerated to a velocity of 4–5 times that of the impacting drop. This first ring is said to be “splashing,” and its structure is somewhat chaotic and turbulent, similar to a columnar liquid jet surrounded by neighboring gas jets at relatively high impact speed. At lower impact speeds, splashing occurs as a crown-shaped cylindrical sheet. A second spreading ring is observed that transforms into fingers in the circumferential direction during spreading. At higher Weber number, the spreading of a third ring follows that of the second. This third ring, induced by the pressure pulsation, overruns and has fewer fingers than the second, which is still in a transitional spreading stage. Several important relationships between the drop impact speed, the spray ejection speed of the first ring, and the number of fingers of the second and third rings are presented, based on data acquired during a set of drop impact experiments. Issues related to the traditional use of the R–T instability are also addressed.     

Collision between an ethanol drop and a water drop

The collision between a water drop and an ethanol drop was studied. In a binary collision between unlike miscible drops with a large surface tension difference, an unbalanced-surface-force (USF) deformation on the drop of larger surface tension, i.e., the water drop, occurs during the first stage of the collision. This deformation may squeeze out small satellites from the water drop at low-impact-parameter collisions or split the water drop at high-impact-parameter collisions. The later stages of the collision behavior, namely, coalescence and separation, resemble those of the drops of the smaller surface tension, i.e., the ethanol drop.     

Visualization of the impact of water drops on a hot surface: effect of drop velocity and surface inclination

The behaviour of one drop impinging on a hot surface by varying the surface temperature, the drop velocity and the position of the surface (horizontal and a inclined 45°) both at a temperature below and above the Leidenfrost temperature has been experimentally evaluated, estimating the temperature at which the drop rebounds. A large influence on the drop velocity has been evidenced. The inclination of the surface decreases the critical value of the temperature above which the surface is not rewetted.     

Two-dimensional third- and fifth-order nonlinear evolution equations for shallow water waves with surface tension

Nonlinear Dynamics - We derive two new two-dimensional third- and fifth-order nonlinear evolution equations that model a unidirectional wave motion in shallow water waves with surface tension....     

Upwind finite difference method for miscible oil and water displacement problem with moving boundary values

The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the twodimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal orderl2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.     

Evaporation of single liquid drops in an immiscible liquid at elevated pressures: equipment and preliminary results

This paper describes a piece of equipment which has been specially designed to permit the study of the evaporation of single liquid drops in an immiscible liquid at elevated pressures up to the order of 1 MPa. It is equipped with a piezoelectric discharger for yielding nucleation in each drop and with a dilatometer for detecting the change in volume of the drop in the course of evaporation succeeding the nucleation. Some preliminary results, obtained with the equipment, for n-pentane drops evaporating in a water medium at pressures up to 0.5 MPa (5 atm) are also presented.List of symbols C _D drag coefficient - D ₀ initial, equivalent spherical diameter of drop (= (6 V ₀/)^1/3) - H vertical position of two-phase bubble measured from the nozzle tip - H _t column height required for drop to vaporize completely - Nu Nusselt number related to instantaneous two-phase bubble diameter and thermal conductivity of the continuous phase - p ^* pressure at the nozzle tip - Pe Peclet number related to instantaneous diameter and rise velocity of two-phase bubble and to thermal diffusivity of the continuous phase - Re Reynolds number related to instantaneous diameter and rise velocity of two-phase bubble and to viscosity of the continuous phase - t time - t _v time required for drop to vaporize completely - T temperature in the bulk of the medium - T excess, assumed in theoretical model, of T above the temperature of two-phase bubble - T ₁ ^* excess of T above the saturation temperature of the dispersed-phase fluid corresponding to p ^* - T ₂ ^* excess of T above the temperature at which the sum of the saturated vapor pressures of the dispersed- and the continuous-phase fluids is equal to p ^* - V volume of two-phase bubble - V ₀ initial value of V     

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge–Kutta method of order 4.     

Thermal instability induced by buoyancy and surface tension with radiative transfer

The onset of steady, cellular convection in a horizontal fluid layer heated from below is considered taking into account the possibility of radiative heat transfer in addition to conduction and convection. The radiation is found to have a stabilizing effect even in the presence of surface tension. The effect of surface viscosity and surface deflexion are also discussed. The coupling between the surface tension and buoyancy becomes weaker as the radiative heat transfer rate is increased.     

Simple and efficient numerical methods for vortex sheet motion with surface tension

We present two simple and efficient explicit methods for the vortex sheet with surface tension. The first one is the standard point vortex method, which has been known to be unstable in the presence of surface tension, due to spurious growth of waves of high modes. We show, for the first time, that the standard point vortex method is able to calculate the vortex sheet motion with surface tension by employing a Fourier filtering. The second method is a modification of the Pullin method using central differences for numerical differentiations. This method is more convenient to implement than other spectral methods and is free from the aliasing instability. We give a linear stability analysis for the numerical methods and show results for the long‐time evolution of the vortex sheet. We also propose a new redistribution procedure to control point clustering, by setting limits of minimum and maximum distances between neighboring points. This procedure is found to be very efficient for long‐time computations of the explicit methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Structure of the interface between magnetic and conventional fluids: Model of immiscible phases

The structure of the flat interface between a two-component magnetic suspension and a conventional nonmagnetizable fluid immiscible with it is investigated with account for the dependence of the free energy of the system on the magnetization gradients, the concentration of magnetic particles, and the bearing phase density. It is shown that at certain values of the problem parameters the volume concentration of magnetic particles strongly increases near the interface, that is, the particles are substantially adsorbed at this surface. The dependence of the surface tension tensor components on the magnetic field stress is determined.     

Experimental investigation on the slip between oil and water in horizontal pipes

This work is devoted to study of the slip phenomenon between phases in water–oil two-phase flow in horizontal pipes. The emphasis is placed on the effects of input fluids flow rates, pipe diameter and viscosities of oil phase on the slip. Experiments were conducted to measure the holdup in two horizontal pipes with 0.05 m diameter and 0.025 m diameter, respectively, using two different viscosities of white oil and tap water as liquid phases. Results showed that the ratios of in situ oil to water velocity at the pipe of small diameter are higher than those at the pipe of big diameter when having same input flow rates. At low input water flow rate, there is a large deviation on the holdup between two flow systems with different oil viscosities and the deviation becomes gradually smaller with further increased input water flow rate.