Evaporation and explosion of liquid drops on a heated surface

The literature pertinent to various aspects of drop evaporation on a heated surface is reviewed. Both the laser shadowgraphic and direct photographic methods are employed to study thermal stability and flow structures in evaporating drops in all heating regimes. It is revealed that four flow regions exist in stable and unstable type drops at low liquid-film type vaporization regime. As the surface temperature is raised, the flow regions reduce to two. In the nucleate-boiling type vaporization regime, the interfacial flow structure changes due to a reduction in the Marangoni number as well as the dielectric constant of the liquid. An evidence of bubble growth in the drops is disclosed. The micro explosion of drops is found to occur in the transition-boiling type heating range. No drop explosion takes place in the spheriodal vaporization regime except when the drop rolls on to a microscratch on the heating surface. It is concluded that the mechanisms for triggering drop explosion include the spontaneous nucleation and growth phenomena and the destabilization of film boiling.     

Impact on the surface of a compressible liquid

The evolution of a weak, nearly plane shock wave produced by the impact on the plane boundary of a compressible liquid is considered. At the initial moment the liquid is at rest and occupies the lower half-plane. Then the points of its boundary get instantly velocities directed into the liquid domain. This leads to the formation of a shock wave the intensity of which is non-uniform due to a non-uniform distribution of the impact velocities. Initially the shock wave is plane but then it bends due to the non-linear effects and can later be focused. To analyze the liquid flow, the method of matched asymptotic expansions is used. For finite times the flow and the evolution of the shock wave are described within the framework of the acoustic approximation. For large times the flow becomes non-linear, and the form of the shock front depends essentially on the characteristics of the liquid flow behind it. If the non-uniformity of the impact velocity distribution is slight then the focusing of the shock wave is shown not to occur. The influence of viscosity of the liquid on the structure of its motion is discussed.     

基于表面力模型的液滴冲击弹性基底SPH模拟

采用光滑粒子动力学SPH方法建立液滴冲击弹性基底的流固耦合数值模型,给出描述粘性流体和弹性固体运动的SPH离散方程和数值处理格式,引入人工耗散项来抑制标准SPH方法的数值震荡。为模拟液滴的表面张力效应,通过精确检测边界粒子,采用拉格朗日插值方法计算表面法向量和曲率,结合界面理论中的连续表面力CSF方法,建立了适用于自由表面液滴的表面力模型,方形液滴变形的模拟结果与拉普拉斯理论解吻合较好。随后,采用SPH流固耦合模型模拟1.0 mm直径水滴以不同速度(0.2 m/s～3.0 m/s)冲击两种薄板型基底,分析了基底弹性变形对液滴铺展、收缩以及回弹行为的影响。     

Formation of secondary drops during impact interaction of a drop with a liquid surface

This paper reports results from experimental studies of the formation of secondary drops during impact interaction of a drop with a liquid surface. The experimental data are compared with analytical estimates of the parameters of the cavern formed and the Rayleigh column.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 55–62, January–February, 2005.     

Impact of a solid on a liquid surface: Asymmetric plane case

The vertical impact of a rigid elliptical cylinder on a compressible liquid surface is considered in a plane asymmetric formulation. Solution of the boundary problem reduces to solving an infinite system of linear Volterra integral equations of the second kind. The results are analyzed in terms of the initial asymmetry angle. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 75–84, September, 1999.     

Diffusional interaction of drops in a liquid

The method of combining asymptotic expansions (with respect to a large Peclet number) is used to investigate the three-dimensional problem of steady-state convective diffusion to the surface of drops, around which flows a laminar stream of a viscous incompressible liquid whose velocity field is assumed to be known from the solution of the corresponding hydrodynamic problem. It is shown that for large Peclet numbers the heat and mass transfer between drops is completely determined by the mutual arrangement of special (starting or ending at the surface of a drop) lines of flow; under these circumstances, in the flow there are chains of drops which have no mutual diffusional effect on one another, and the total diffusional flow to a drop is determined by diffusion to particles located upstream in the same chain. For the case where the distance between the drops in the chain is much leas than P^1/2 (P is the Peclet number), formulas for the distribution of the concentration and the total diffusional flow to the surface of each drop are obtained. It is shown that the total diffusional flow to the surface of a drop approaches zero in inverse proportion to its order number in a chain, which generalizes [1], in which the axisymmetric case is considered. A solution of the diffusional case is obtained for the case where there are critical lines at the surface of the drop. The problem is solved to the end if the singular flow lines are not closed and depart to infinity. With the presence of a region of closed circulation behind the drops, the problem is reduced to an integral equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika, Zhidkosti i Gaza, No. 2, pp. 44–56, March–April, 1978.The author thanks Yu. P. Gupalo and Yu. S. Ryazantsev for their interest in the work.     

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.     

Plastic deformation of a rough surface

Journal of Applied Mechanics and Technical Physics -     

Effect of chamber pressure on spreading and splashing of liquid drops upon impact on a dry smooth stationary surface

Liquid drop impacts on a smooth surface were studied at elevated chamber pressures to characterize the effect of gas pressure on drop spreading and splashing. Five common liquids were tested at impact speeds between 1.0 and 3.5 m/s and pressure up to 12 bars. Based on experiments at atmospheric pressure, a modification to the “free spreading” model (Scheller and Bousfield in AIChE Paper 41(6):1357–1367, 1995) has been proposed that improves the prediction accuracy of maximum spread factors from an error of 15–5%. At high chamber pressures, drop spreading and maximum spread factor were found to be independent of pressure. The splash ratio (Xu et al. in Phys Rev Lett 94:184505, 2005) showed a non-constant behavior, and a power-law model was demonstrated to predict the increase in splash ratio with decreasing impact speed in the low impact speed regime. Also, drop shape was found to affect splash promotion or suppression for an asymmetry greater than 7–8% of the equivalent drop diameter. The observations of the current work could be especially useful for the study of formation of deposits and wall combustion in engine cylinders.     

Impact of a convex solid body on a rough wall

Kaliningrad Technical Institute of the Piscicultural Industry and Economy. Translated from Prikladnaya Mekhanika, Vol. 28, No. 4, pp. 38–42, April, 1992.     

On the motion of a rope on a rough surface

Summary The article deals with dynamical problems of stability of mechanical systems with an infinite number of degrees of freedom, which are acted upon by forces of the dry friction type. Dynamics of a rope moving on a rough flat surface is considered as an example. The article shows that nonhomogeneous properties of friction can result in instability.

---

Über die Bewegung eines Seiles auf einer rauhen Fläche

Übersicht Es handelt sich um dynamische Probleme der Stabilität mechanischer Systeme mit unendlich vielen Freiheitsgraden, auf die Kräfte der trockenen Reibung wirken. Die Dynamik eines Seiles, das sich auf einer rauhen Fläche bewegt, wird als Beispiel betrachtet. Es wird gezeigt, daß nichthomogene Eigenschaften der Reibung Instabilität verursachen können.

---

---

This work was supported by the DAAD (der Deutsche Akademische Austauschdienst). I am very grateful to the Director of the Institute B of Mechanics, the University of Stuttgart, Prof. Dr.-Ing. W. Schiehlen for wonderful conditions under which I could work during my stay at his Institute. Without his support, encouragements and useful advice this work could hardly be written.     

Boundary conditions of gas dynamic slip on a rough surface

The phenomenon of gas dynamic slip associated with the flow of a monatomic, slightly rarefied gas over a rough surface is investigated. It is assumed that the characteristic dimensions of the roughness are comparable with the molecular mean free path. It is shown that if there is anisotropy of the surface shape the relation between the slip velocity and the friction stress vector becomes tensorial. In this case for almost any orientation of the gas dynamic flow the so-called cross slip effect is observed. The symmetry of the slip coefficient matrix is proved for fairly general assumptions concerning the type of roughness, the law of reflection of molecules from the surface, and the law of intermolecular interaction. The components of the slip coefficient matrix are calculated by a variational method for a corrugated model of the roughness.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 180–184, January–February, 1987.     

Motion of a sphere colliding with a rough surface

The following problems of inertial motion of a sphere are considered: between two parallel planes, inside another sphere, and inside a circular cylinder. It is assumed that, at the instant of impact, the no-slip condition is fulfilled: the tangential velocity of the contact point of the sphere is equal to zero; in other words, a constraint is imposed and removed instantaneously. It is shown in the above cases that in the limit the motion of the sphere becomes steady in velocity: the angular velocity of the sphere tends to be constant and the velocity of its center becomes periodic in the first case or conditionally periodic in the second and third cases. In certain cases, the coordinates specifying the position and orientation of the sphere also reach the steady-state regime.     

Quasimolecular simulation of large liquid drops

Large liquid drops are simulated by molecular aggregates called quasimolecules. The quasimolecules interact in accordance with classical molecular-type formulae. Supercomputer examples are described and discussed for both stationary and falling water drops.     

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.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

Viscous flow of a suspension of liquid drops in a cylindrical tube

Viscous flow in a circular cylindrical tube containing an infinite line of viscous liquid drops equally spaced along the tube axis is considered under the assumption that a surface tension, sufficiently large, holds the drops in a nearly spherical shape. Three cases are considered: (1) axial translation of the drops, (2) flow of the external fluid past a line of stationary drops, and (3) flow of external fluid and liquid drops under an imposed pressure gradient. Both fluids are taken to be Newtonian and incompressible, and the linearized equations of creeping flow are used.The results show that both drag and pressure drop per sphere increase as the spacing increases at fixed radius and also increase as the radius of the drop increases. The presence of the internal motion reduces the drag and pressure gradients in all cases compared to rigid spheres, particularly for drops approaching the size of the tube.