Hydrodynamics of contact of a falling drop with a liquid free surface

A fine structure of the flows developing during primary contact of freely falling drops with a deep quiescent fluid is studied using the macrophotography and high-speed video filming methods. Water drops falling in water, alcohol, and oil, as well as drops of oil, petroleum, and aqueous solutions of salt or alcohol falling in water are investigated. The work is focused on the visualization of the finespray scattering from the primary contact area. The collisions of small droplets with the surface of the submerging drop are first recorded. The direction of the spray and streamer scattering is determined by the surface tension coefficients of the coalescing liquids. The conditions under which the spray droplets collide with the drop surface are determined.     

Impact of a drop on a solid surface

A numerical solution is obtained to the unsteady-state problem of a direct collision between a liquid drop of cylindrical form and a rigid surface. It is shown that unsteady-state interaction between shock waves inside the drop leads to the development of broad zones of cavitation, promoting the dispersion of the drop.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 151–155, September–October, 1977.The authors thank L. F. Shaikhatarova for making the calculations.     

Dynamics of the impact of a drop on a solid surface

A numerical method is developed for calculating the non-steady-state motions of a compressible liquid, with application to problems of the impact type. A homogeneous, completely conservative difference scheme of the first order of exactness is used. For isolation of the discontinuities and smoothing of the solution, use is made of the introduction of an artificial viscosity, based on an analysis of the provisional properties of the solution. An investigation is made of the scheme stability and the necessary stability criteria are obtained. The article gives the detailed results of a calculation of the impact interaction between a spherical drop and a rigid surface. It is shown that the maximal pressure arising with the impact of a drop of liquid on a solid surface exceeds by several times the pressurecalculated using the one-dimensional theory; under these circumstances, the rate of expansion of the drop along the surface exceeds the initial velocity of the collision by an order of magnitude.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 36–43, January–February, 1978.In conclusion, the authors thank G. G. Chernyi for his continuing interest and his valuable evaluation of the results of the work, and L. F. Shaikhatarov, who participated in making the calculations.     

The optimal drop shape for vortices generated by drop impacts: the effect of surfactants on the drop surface

Subsurface vortices are frequently created when a falling drop strikes a flat water surface. Prior work has demonstrated that the shape of the drop at the point of impact is critical in determining how deep or how fast the resulting vortex will penetrate into the water bulk. In the present study, the details of this phenomena are explored by using surfactants to vary surface tension. Specifically, Triton X-100 monolayers are created on the surface of the drop, and on the flat water surface. The results of these experiments suggest that there is no single optimal drop shape resulting in best vortex penetration. Rather, the data suggest that the optimal shape depends on the surface tension of the falling drop. An attempt is made to reconcile contradictory results in the literature using this result.

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Hydrodynamics of a drop submerged in an unbounded arbitrary velocity field in the presence of surfactants

A solution is presented for the flow fields interior and exterior to a single spherical droplet submerged in an unbounded fluid, for the general case when the unperturbed velocity is Stokesian but otherwise arbitrary. Surface-active-agents are present in the system and are included in the analysis. A general equation for the terminal settling velocity is derived which contains as special cases the familiar solutions of Levich and our previous solution. Also derived is a general expression for the drag force. This expression contains as special cases the Laws of Faxen and our previous results. The function describing the interface and its deviation from sphericity is derived. This may be used for determining more accurate flow fields in an iterative procedure.     

The impact of a single drop on a wetted solid surface

 The impact of single drops on a thin liquid film was studied to understand the mechanism of secondary atomisation of sprays colliding on a wetted, cold, solid surface. To span a wide range of conditions various mixtures of water and glycerol were used. The use of Weber number, Ohnesorge number and non-dimensional film thickness to describe the peculiarities of the phenomenon allowed to carry out the experiments under appropriate similarity conditions. The impact of millimetric drops was analysed in detail by photographic means, using both still photography to study impact morphology, and laser sheet visualisation to investigate secondary droplet formation. Two mechanisms of splash were identified, depending essentially on the liquid viscosity (Ohnesorge number), a parameter which appears to play an important role also in defining the splash morphology. A photographic documentation is annexed. The characteristic times of the crown formation, the non-linear evolution of cusps (jet formation) and the surface roughness influence are further discussed. The experimental results allow to propose an empirical correlation for the splashing/deposition limit, for a wide range of conditions, and a comparison to available previous works is presented. The influence of the film thickness and liquid viscosity on the splash is confirmed and quantified. Received: 1 March 1996/Accepted: 12 November 1996     

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.     

Supercomputer simulation of liquid drop formation on a solid surface

Using a molecular-dynamics-type approach, we show how to simulate the formation of a liquid drop on a solid surface. Application is made to the case in which the liquid is water and the solid is graphite. The dynamical equations are large systems of nonlinear, ordinary differential equations which must be solved numerically. CRAY X-MP/24 simulations and related contact angle calculations are described and discussed.     

Phenomena of a liquid drop falling to a liquid surface

Two kinds of phenomenon have been observed when a liquid drop falls to a surface of the same liquid. The first, which can nearly always be observed, involves splash and some degree of penetration and cleavage and the conditions for this occurrence are identified. The experimental observations are compared with previous computational results. The second kind of colliding phenomena can be observed only by chance in an ordinary falling drop experiment and appears to be random. It includes the two phenomena investigated in this paper: the floating drop and the rolling drop.     

Numerical study of a single drop impact onto a liquid film up to the consequent formation of a crown

In this paper, the whole dynamic process of a single drop impact onto a thin liquid surface up to the consequent formation of a thin crown is numerically studied using the smoothed particle hydrodynamics (SPH) method. Especially, the gravity, artificial viscosity, and surface tension are introduced into the model. The obtained SPH numerical results are compared with experimental results. The numerical model of the SPH method is valid for simulating the dynamic process of a single drop impact onto a liquid surface. Meanwhile, it is found that the whole dynamic process mainly depends on the depth of the liquid pool and the initial velocity of the droplet.     

Effect of viscosity on motion of splashing crown in high speed drop impact

A splashing crown is commonly observed when a high-speed drop impacts a liquid film. The influence of the liquid viscosity on the crown's evolution is not yet clear.We review several existing theories of this problem, and carry out a series of numerical simulations. We find that a three-segment model can describe the crown's motion. In the very early stage when the crown is barely visible, the influence of viscosity is small.Later, a shallow water approach used in most existing models is applicable as long as the initial conditions are formulated properly. They depend on viscous dissipation in the intermediate period. Preliminary estimation based on a dissipation function is proposed to characterize the influence of viscosity in this problem.     

Effects of surface properties on the impact process of a yield stress fluid drop

The impact of a yield stress fluid drop onto a solid surface with diversified interface properties has been experimentally investigated. Two smooth substrates with distinct surface energies and three similar substrates with different roughnesses have been used. The bulk shear rheological behaviour of Carbopol gels, concentrated suspensions of swollen micro-gels, has been measured. Wall friction has also been characterized on each substrate. Slip effects of gels proved to be greater on a more hydrophobic substrate. They decreased with an increase in roughness. The drop hydrodynamics during the impact was correlated with the wall friction of the gels on all substrates and with the ratio of surface roughness to size of the swollen micro-gels. At very low impact velocities, the gravitational subsidence amplitude depends greatly on surface properties. At higher impact velocities, no significant difference is observed during the spreading phase. The drop behaviour differs during the retraction depending on the substrate. Interface effects during the retraction stage proved to diminish when the yield stress value increases.     

Hydrodynamics of flow over a transversely oscillating circular cylinder beneath a free surface

In this paper, hydrodynamic force coefficients and wake vortex structures of uniform flow over a transversely oscillating circular cylinder beneath a free surface were numerically investigated by an adaptive Cartesian cut-cell/level-set method. At a fixed Reynolds number, 100, a series of simulations covering three Froude numbers, two submergence depths, and three oscillation amplitudes were performed over a wide range of oscillation frequency. Results show that, for a deeply submerged cylinder with sufficiently large oscillation amplitudes, both the lift amplitude jump and the lift phase sharp drop exist, not accompanied by significant changes of vortex shedding timing. The near-cylinder vortex structure changes when the lift amplitude jump occurs. For a cylinder oscillating beneath a free surface, larger oscillation amplitude or submergence depth causes higher time-averaged drag for frequency ratio (=oscillation frequency/natural vortex shedding frequency) greater than 1.25. All near-free-surface cases exhibit negative time-averaged lift the magnitude of which increases with decreasing submergence depth. In contrast to a deeply submerged cylinder, occurrences of beating in the temporal variation of lift are fewer for a cylinder oscillating beneath a free surface, especially for small submergence depth. For the highest Froude number investigated, the lift frequency is locked to the cylinder oscillation frequency for frequency ratios higher than one. The vortex shedding mode tends to be double-row for deep and single-row for shallow submergence. Proximity to the free surface would change or destroy the near-cylinder vortex structure characteristic of deep-submergence cases. The lift amplitude jump is smoother for smaller submergence depth. Similar to deep-submergence cases, the vortex shedding frequency is not necessarily the same as the primary-mode frequency of the lift coefficient. The frequency of the induced free surface wave is exactly the cylinder oscillation frequency. The trends of wave length variation with the Froude number and frequency ratio agree with those predicted by the linear theory of small-amplitude free surface waves.     

Gravity-induced spreading of a drop of a viscous fluid over a surface

The unsteady-state nonlinear problem of spreading of a drop of a viscous fluid on the horizontal surface of a solid under the action of gravity and capillary forces is considered for small Reynolds numbers. The method of asymptotic matching is applied to solve the axisymmetrical problem of spreading when the gravity exerts a significant effect on the dynamics of the drop. The flow structure in the drop is determined at large times in the neighborhood of a self-similar solution. The ranges of applicability of the quasiequilibrium model of drop spreading with a dynamic edge angle and a self-similar solution are found. It is shown that the transition from one flow model to another occurs at very large Bond numbers. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen’ 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 59–67, May–June, 1999.     

Experimental investigation of splash and crown formation during single drop impact on wetted surfaces

Experimental results concerning crown formation during liquid drop impact on wetted surfaces are reported. Different liquids and numerous impact conditions are investigated. In particular, crown-splash (C-S) and deposition-crown (D-C) limits are determined on the basis of the experimental observations. These limits converge for dimensionless film thickness thinner than 0.03, leaving the outcome of crown formation unobserved. The sole Weber number and dimensionless film thickness cannot explain the phenomenon. It appears that all these data can be described using a combination of Weber and Ohnesorge numbers versus dimensionless film thickness.     

Effect of surface electric current on the electrohydrodynamic flow inside and outside a spherical drop

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.     

Effect of surface and volume ionization on the electrode potential drop

We consider the change in the potential of the electric field in the free fall layer at the electrodes as a function of the characteristics of the surface and the volume ionization. Systematic calculations are made of the electrode potential drop for a tungsten cathode and anode in a lithium and cesium plasma. The potential of the electric field is obtained as a function of the plasma pressure, the degree of volume ionization, the electron temperature, the electrode temperature, and the current density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 137–139, July–August, 1970.     

Effects of tangential speed on low-normal-speed liquid drop impact on a non-wettable solid surface

A stream of water drops colliding on a rotating cylindrical Teflon surface was observed. The collision resulted in partial rebound, deposition, and split deposition. The collision outcome was found to depend on the normal Weber number and the tangential Weber number, which represent the collision momentum in the normal and the tangential direction, respectively. The extent of influence of the centrifugal acceleration induced by the rotation was kept negligibly under 2% compared with the impact momentum change. Through careful measurements on the elongation of the liquid drop after impact, the impact regime boundaries are seen to be governed by the long and short axes of the elliptical-disk shape at the maximal spread. Partial rebound first changes to deposition when the long axis is 1.1 times the short axis; and then changes to split deposition when the long axis is 1.46 times the short axis. Furthermore, the dimensionless excess spread area was found to be directly proportional to the tangential Weber number.