Ilia V. Roisman

Normal impact of a liquid drop on a dry surface: model for spreading and receding

The normal impact of a liquid drop on a dry solid surface is studied experimentally and theoretically. In this paper a strictly theoretical model is introduced, which predicts the evolution of the drop diameter. The spreading and receding phases of the impact are described by the motion of a rim appearing at the edge of the liquid film (lamella) due to the surface–tension forces. The mass and the momentum equations of the rim are considered, taking into account the effects of inertial, viscous and surface forces, and wettability. Also, simplified approximations for the maximum spreading diameter of the drop and for the velocity of the merging of the rim in the receding phase are obtained. The theoretical predictions agree well with available experimental data.

Dynamic contact angle of spreading droplets: Experiments and simulations

This paper presents results of an experimental investigation of a single drop impact onto a dry, partially wettable substrate and its numerical simulation. Particularly, the drop spreading diameter and the dynamic contact angle are measured at different time instants after impact. Two surfaces, wax (low wettability) and glass (high wettability), are used to study the effect of surface wettability (static contact angle) on the impact dynamics. It is shown that existing empirical models for the dynamic contact angle (e.g., Hoffman–Voinov–Tanner law) do not predict well the change of the dynamic contact angle, especially at high capillary numbers. In addition to the experimental investigations, the drop impact was studied numerically, focusing primarily on the contact angle treatment. The singularity in the neighborhood of the moving contact line is removed from the computational domain and replaced by a local force with some dependence on the instantaneous advancing/receding contact-line velocity. The predi...

Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film

This study is devoted to a theoretical description of an unsteady laminar viscous flow in a spreading film of a Newtonian fluid. Such flow is generated by normal drop impact onto a dry substrate with high Weber and Reynolds numbers. An analytical self-similar solution for the viscous flow in the spreading drop is obtained which satisfies the full Navier–Stokes equations. The characteristic thickness of a boundary layer developed near the wall uniformly increases as a square root of time. An expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter. The theoretical predictions agree well with the existing experimental data. A possible explanation of the mechanism of formation of an uprising liquid sheet leading to splash is also proposed.

Impact of a drop onto a wetted wall: description of crown formation and propagation

The impact of a drop onto a liquid film with a relatively high impact velocity, leading to the formation of a crown-like ejection, is studied theoretically. The motion of a kinematic discontinuity in the liquid film on the wall due to the drop impact, the formation of the upward jet at this kinematic discontinuity and its elevation are analysed. Four main regions of the drop and film are considered: the perturbed liquid film on the wall inside the crown, the unperturbed liquid film on the wall outside the crown, the upward jet forming a crown, and the free rim bounding this jet. The theory of Yarin & Weiss (1995) for the propagation of the kinematic discontinuity is generalized here for the case of arbitrary velocity vectors in the inner and outer liquid films on the wall. Next, the mass, momentum balance and Bernoulli equations at the base of the crown are considered in order to obtain the velocity and the thickness of the jet on the wall. Furthermore, the dynamic equations of motion of the crown are developed in the Lagrangian form. An analytical solution for the crown shape is obtained in the asymptotic case of such high impact velocities that the surface tension and the viscosity effects can be neglected in comparison to inertial effects. The edge of the crown is described by the motion of a rim, formed due to the surface tension. Three different cases of impact are considered: normal axisymmetric impact of a single drop, oblique impact of a single drop, and impact and interaction of two drops. The theoretical predictions of the height of the crown in the axisymmetric case are compared with experiments. The agreement is quite good in spite of the fact that no adjustable parameters are used.

Spray impact: Rim transverse instability initiating fingering and splash, and description of a secondary spray

In this paper, normal spray impact onto a rigid wall, leading to the formation of secondary spray, is considered. The mechanism of splash is explained by the bending instability of a rim bounding a free liquid sheet. The linear stability analysis of the rim is performed in the framework of the long-wave, quasi-one-dimensional approach. The rim instability is caused by the moment of forces associated with the inertia of the liquid entering the rim. Next, two components of the drop velocity and their diameter, as well as various flux density vectors (number, volume, mass fluxes) and tensors (momentum flux), are measured using a phase Doppler instrument. It is shown that the viscous length scale of drop impact can be used in describing the splash threshold, diameter of secondary droplets, and their velocity. Consequently, a closed semi-empirical model for the secondary spray has been proposed and validated using a numerical simulation of spray transport based on an Euler-Lagrange approach.

Inertia dominated drop collisions. I. On the universal flow in the lamella

This study is devoted to the analysis of inertia dominated axisymmetric drop collisions with a dry substrate or with another liquid drop. All the previous theoretical and semiempirical models of drop collisions are based on the assumption that the flow in the lamella and its thickness are determined by the impact conditions, mainly by the Reynolds and Weber numbers. In this study the existing experimental data are compared to existing and new numerical simulations for the shape of the lamella generated at the early times of drop impact for various impact conditions. The results show that if the Reynolds and Weber numbers are high enough, the evolution of the lamella thickness almost does not depend on the viscosity and surface tension. Therefore these results completely change our understanding of the flow generated by drop collisions. Moreover, we demonstrate that the theoretical models based on the approximation of the shape of the deforming drop by a disk and the models based on the energy balance appr...

Drop impact, spreading, splashing, and penetration into electrospun nanofiber mats.

Experiments were conducted to study peculiarities of drop impact onto electrospun polymer nanofiber mats. The nanofiber cross-sectional diameters were of the order of several hundred nanometers, the pore sizes in the mats of about several micrometers, and the mat thicknesses of the order of 200 microm. Polyacrylonitrile (PAN), a polymer which is partially wettable by water, was used to electrospin nanofiber mats. The experiments revealed that drop impact onto nanotextured surfaces of nanofiber mats produce spreading similar to that on the impermeable surfaces. However, at the end of the spreading stage, the contact line is pinned and drop receding is prevented. At higher impact velocities, prompt splashing events with formation of tiny drops were observed. It was shown that the splash parameter K(d) = We(1/2) Re(1/4) (with We and Re being the Weber and Reynolds numbers, respectively) previously used to characterize the experiments with drop impact onto smooth impermeable dry substrates can be also used to describe the onset of splash on substrates coated by nanofiber mats. However its threshold value K(ds) (in particular, corresponding to the minimal impact velocity leading to generation of secondary droplets) for the nanotextured surfaces is higher than that for dry flat substrates. In addition, water penetration and spreading inside wettable nanofiber mats after drop impact was elucidated and quantified. The hydrodynamics of drop impact onto nanofiber mats is important for understanding effective spray cooling through nanofiber mats, recently introduced by the same group of authors.

Investigations on the impact of a drop onto a small spherical target

This paper reports on experimental and theoretical investigations of the impact of a droplet onto a spherical target. Spatial and temporal variation of film thickness on the target surface is measured. Three distinct temporal phases of the film dynamics are clearly visible from the experimental results, namely the initial drop deformation phase, the inertia dominated phase, and the viscosity dominated phase. Experiments are also conducted to study the effect of droplet Reynolds number and target-to-drop size ratio on the dynamics of the film flow on the surface of the target. It is observed that for a given target-to-drop size ratio, the nondimensional temporal variation of film thickness collapses onto a single curve in the first and second phases. The transition to the viscosity dominated regime occurs earlier for the low Reynolds number cases and residual thickness is also larger. A simplified quasi-one-dimensional approach has been used to model the flow on the spherical target. The theory accounts fo...

Chaotic rotation of triaxial ellipsoids in simple shear flow

Chaotic behaviour is found for suciently long triaxial ellipsoidal non-Brownian particles immersed in steady simple shear flow of a Newtonian fluid in an inertialess approximation. The result is first determined via numerical simulations. An analytic theory explaining the onset of chaotic rotation is then proposed. The chaotic rotation coexists with periodic and quasi-periodic motions. Quasi-periodic motions are depicted by regular closed loops and islands in the system Poincare! map, whereas chaotic rotations form a stochastic layer. More than 70 years ago Jeery (1922) calculated the moment of force acting on an arbitrary ellipsoidal particle immersed in creeping shear flow. For the particular case of a spheroidal inertialess particle he deduced that the motion of the particle in a simple shear flow is periodic. Based on Jeery’s result for the moment of force, Gierszewski & Chaey (1978) gave several numerical examples of the dynamic behaviour of a triaxial ellipsoidal inertialess particle in a simple shear flow. Hinch & Leal (1979) considered the same problem in much more detail and showed that the motion of a triaxial ellipsoid with comparable axes is doubly periodic. They also showed double periodicity for a nearly spheroidal ellipsoid with an arbitrary axis ratio. Some of their results are revised in the present work. Szeri, Milliken & Leal (1992) and Szeri (1993) studied the rotation of axisymmetric spheroidal particles in two-dimensional recirculating flows (e.g. in a four-roll mill), which are time periodic in a Lagrangian sense from the particles’ point of view. They showed that in some cases non-periodic rotation of an axisymmetric particle sets in due to the time-dependent character of flow. In three-dimensional flows the rotation of axisymmetric particles becomes quasi-periodic (Szeri & Leal 1993; Szeri 1993). The aim of this work is to study the dynamics of a general triaxial ellipsoidal particle with one axis significantly longer than two others. The particle is immersed in a simple shear flow, and inertial eects are neglected for both particle and fluid. The flow is steady in both the Eulerian and Lagrangian (associated with the particle) sense. Nevertheless, it is shown that chaotic rotation of the particle sets in under appropriate conditions due to its non-axisymmetric shape. In c2 the governing equations and some of the relevant periodic motions of triaxial ellipsoidal particles are outlined. In c3 the stability of the periodic motions is considered via Floquet theory. Chaotic numerical solutions are presented in c4. The analytic theory explaining formation of the stochastic layer is presented and discussed in c5. Conclusions are summarized in c6.

Penetration of a rigid projectile into an elastic-plastic target of finite thickness

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.