In this chapter drop impacts onto a liquid layer of the same liquid as in the drop are considered. The chapter begins with consideration of such weak drop impacts on a liquid layer that they result only in capillary waves propagating over the surface. An interesting feature of these waves is that they are self-similar (Section 6.1). In the following Section 6.2 crown formation in strong (high-velocity) impacts onto thin liquid films is considered. Normal and oblique impacts of a single drop onto a wet wall are studied, as well as crown–crown interaction in sprays impacting the wall. Also, the evolution of the free rim on top of the crown is described. Then, in Section 6.3 drop impacts onto a thick liquid layer are considered and the dynamics of the crater formation is explained. Drop impacts onto a wet wall leave a residual liquid film on the wall which is addressed in Section 6.4. Drop impacts onto deep liquid pools produce a plethora of interesting morphological structures considered in Section 6.5. In the following Section 6.6 bending instability of a free rim is considered and the splashing mechanism is discussed. Splashing resulting from impacts of drop trains one-by-one is discussed in Section 6.7, where its physical mechanism and the link to splashing of a single drop impacting onto a liquid layer are elucidated. Several other regimes of drop impact are also mentioned.

Drop Impact onto Thin Liquid Layer on a Wall: Weak Impacts and Self-similar Capillary Waves

Consider patterns of capillary waves propagating over the free surface of a thin liquid film from the point where it was impacted normally by a tiny droplet or a stick (Fig. 6.1), as an example of a relatively weak (low-velocity) impact. For scales of the order of several millimeters the gravity effect on these waves is negligibly small, and for time scales of the order of several milliseconds viscosity effects can also be neglected.

Surface texture, e.g. roughness, porosity, wettability and chemical composition can significantly affect the outcome of drop impact. Section 5.1 deals with the splashing threshold on rough, textured and also porous solid surfaces. In Section 5.2 an impact of a single Newtonian drop near a hole in a flat substrate is considered as a simplified model of drop spreading on a porous substrate. The experiments described in Section 5.3 deal with drop impacts of such different liquids as water and oily Fluorinerts onto suspended thin membranes with microscopic pores of different wettability. They reveal that liquid penetration is possible even through a non-wettable porous medium if the impact velocity is high enough. A similar conclusion stems from the experiments with water drop impacts onto membranes coated with much less permeable nanofiber layers discussed in Section 5.4. In the case of nanofiber mats deposited onto impermeable surfaces, drop splashing and bouncing after impact can be fully suppressed, as the experiments of Section 5.5 show. The reason for the phenomena observed in Sections 5.3–5.5 is the hydrodynamic focusing of liquid brought by a millimeter-sized drop into micron-sized pores. The theory of the hydrodynamic focusing phenomenon is given in Section 5.6, and the results are illustrated experimentally by the amazing fact that liquid velocity in the jets which penetrated through the entire porous medium thickness is higher than that in the impacting drop, even though the viscous dissipation in flow through porous medium is extremely high. Liquid penetration following drop impact onto a nonwettable porous medium is also visualized in the experiments with the entrained seeding particles in Section 5.7, which also contains the evaluation of the critical filter thickness which can be fully penetrated in spite of the viscous dissipation in the pores. Drop impacts onto hot surfaces covered with nanofiber mats also reveal significant enhancement of surface cooling due to the hydrodynamic focusing. The latter sustains the contact of liquid coolant with the hot surface underneath and thus facilitates complete liquid vaporization and significant heat removal in the form of latent heat of evaporation (Section 5.8).

This introductory chapter overviews the fundamentals of collision phenomena in liquids and solids. It begins with the physical estimates in Section 1.1, which ascertain the conditions of the commonality of phenomena characteristic of liquid and solid collisions and the historical and modern reasons for deep interest in them. Before embarking on a discussion of the governing equations some basic dimensionless groups are introduced in Section 1.2. Then, the reader encounters the basic laws of mechanics of liquids and solids formulated as the mass and momentum balance equations in Section 1.3. The distinction between liquids and solids can stem from rheological constitutive equations, which are to be added to the basic laws. Two rheological models, of an inviscid and Newtonian viscous liquid, are introduced in Section 1.4, which transforms the basic laws to the Laplace equation for the kinematics of potential flows of inviscid fluids accompanied by the Bernoulli integral of the momentum balance, as well as to the Navier–Stokes equations describing general flows of viscous fluids, or in the limiting case, to the Stokes equations for the creeping flows dominated by viscosity. A special case of a strong short impact of solid onto any type of liquid reveals the potential impulsive motions introduced in Section 1.5. On the other hand, high-speed flows of low-viscosity liquids near a solid surface reveal traditional boundary layers, while near free liquid surfaces the other, less frequently discussed, boundary layers arise. Both types of the boundary layers and the corresponding equations are considered in Section 1.6. Geometric peculiarities of flows in thin liquid layers on solid surfaces allow for such simplifications as the quasi-one-dimensional and lubrication approximations discussed in Section 1.7. Special physical conditions exist at the moving contact line where liquid surface is in contact with both the underlying solid surface and the surrounding gas, which involves such issues as the Navier slip also covered in Section 1.7. The static configurations of sessile and pendant liquid drops, in particular their contact angles with solid surfaces, can be significantly affected by the surface texture and chemical composition – the group of questions elucidated in Section 1.8 and associated with wettability.

Collision phenomena can be ordinary like a rain drop impacting onto a window, a leaf or a puddle, or extraordinary such as a meteorite or a bolide collision with Earth. Some are frequently encountered in science and everyday life, others are extremely rare. Being very different at first sight, collision phenomena in liquids and solids share many underlying common features.

The subject of the present book is highly cross-disciplinary with a very wide scope of applications in mind, and such a collection of topics in one book does not yet exist, as to our knowledge. One of the main motivations for providing such a collection of topics is to underline the commonality among the various occurrences of collision phenomena, which lead to similar physical and technological ideas and modeling approaches. An improved in-depth understanding of the phenomena can be expected after recognizing the common underlying physics involved. A second motivation is that the knowledge presently available on the subject is extremely widely scattered, mainly according to applications, and in a large number of different journals. For example, collisions in the solid mechanics context are considered as a totally different subject than impacts in the fluid mechanical context, whereas in reality inevitable geometric similarities dictate inevitable kinematic similarities, and in some cases similar rheological behavior, which greatly unifies these two fields to the extent still unrecognized by the majority of practitioners. This obscures the true state of the art, with the associated danger that research may be unintentionally and unnecessarily duplicated or some novel developments delayed.

A further motivation can be found in the rapid progress made over the last decade in this field, partly attributed to the much improved means for visualization of collision phenomena with high-speed cameras. In this respect the proposed book is timely. There is sufficient material to justify a concise and coherent collection of recent advances, which may also help initiate further research in a complementary manner.

Our personal research experience covers and spans practically all the topics covered in the book, which is a monograph significantly based on our own results published in peer-reviewed journals over the last 20 years.

The impact of sprays onto walls is of great industrial importance and for this reason has attracted the attention of researchers in an effort to predict the outcome. While some applications expressly avoid splashing, e.g. coating or spray painting, many result in a secondary spray. In fact, spray impact may even be used to intentionally change the size distribution of droplets in a spray, such as with inhalation nebulizers or in direct injection fuel systems. While Chapters 4, 5 and 6 dealt with the impact of single drops onto surfaces or liquid layers, the present chapter addresses the impact of sprays onto such surfaces. Fundamentally, similar questions are asked: how many secondary droplets of what size and velocity are generated and what part of the impacting liquid remains on the surface? If heat transfer is involved then interest lies with the heat flux density at the surface or the effective Nusselt number, which, as with single drops, will depend strongly on the temperature of the surface; hence on which regime of the Nukiyama curve describing heat transfer at the surface is applicable (Nukiyama 1934, Kutateladze 1963, Carey 1992). This chapter encompasses spray impact onto liquid films (Section 9.1), discusses the secondary spray formation in Section 9.2 and outlines useful empirical correlations in Section 9.3

Two main approaches are commonly used to predict the outcome of a spray impact with a rigid wall or with a wall covered by a liquid film. The first approach is formulated in the framework of an Euler/Lagrange numerical simulation and describes the spray as the superposition of a large number of isolated, non-interacting drops (Cossali et al. 2005). Numerous models for single drop impact have been proposed (Bai and Gosman 1995, Stanton and Rutland 1996, Mundo et al. 1998, Lee and Bergman 2002), all having empirical origins. Roisman et al. (1999), Moreira et al. (2010) and Park and Watkins (1996) have provided overviews of many existing models and presented also direct comparisons of their predictive capabilities. It is a characteristic of all models that they provide reliable predictions at most over the narrow range of impact parameters from which they were derived. Indeed, several models in use for spray impact are even based on the impact of single drops onto a dry surface, which may be completely inappropriate.

Drop spreading after an impact onto a dry rigid wall is covered in Sections 4.1 to 4.4 taking into account the inertial and viscous effects, and liquid compressibility as well as geometric and thermal effects, for example associated with phase transition. In addition, the rim dynamics is considered in Section 4.5. The effect of the target curvature on drop spreading as well as surface encapsulation are dealt with in Section 4.6. Different scenarios accompanying drop impacts onto rigid walls are described in Section 4.7. The effect of the reduced gas pressure on drop impact is outlined in Section 4.8. Nonisothermal drop impacts are discussed in Section 4.9. This is extended to solidification and icing accompanying drop impact in Section 4.10.

Drop impact onto a dry wall is an important element of various industrial processes; among them are spray cooling, cleaning, coating, wetting and ink-jet printing. Also, naturally occurring impacts can be of interest, for instance raindrop impacts are studied due to their relevance to soil detachment and erosion (Abuku et al. 2009, Imeson et al. 1981) and plant disease spreading. In Guigon et al. (2008) first steps have been made towards harvesting of the energy of raindrop impacts by transforming it to electricity using a piezoelectric system. Other examples include the impact of high-speed drops leading to the erosion of turbine blades (Li et al. 2008, Zhou et al. 2008) or to the deformation and fraction of rocks (Momber 2004). On the latter, also see Section 1.1 in Chapter 1.

The phenomena associated with drop impacts have fascinated many researchers over the years. Recent advances in the theoretical modeling, the appearance of user-friendly, high-speed visualization systems and improvement of numerical methods for simulations of interfacial flows allow the elucidation of the drop impact and spreading on the wall in great detail. Drop impact is also a convenient model process to systematically investigate other physical phenomena, such as the nature of the dynamic contact angle: e.g., in Bayer and Megaridis (2006) contact line dynamics was studied and results explained in terms of hydrodynamic wetting theory and the molecular-kinetic theory of wetting.

The chapter begins with an important case of a relatively weak normal impact of an elastic bar onto a rigid wall leading to propagation of elastic sound waves in the bar (Section 12.1). In such weak impacts significant deformations of the bar are absent. This technique is useful for material characterization, since not only purely elastic but also anelastic viscoelastic (viscoplastic) bars can be used in such impact experiments, which is briefly discussed in Section 12.1. Strong impacts of bars result in formation of plastic waves in such solid materials as metals and significant irreversible plastic deformations of such bars. These phenomena are also mentioned in Section 12.1. Section 12.2 is devoted to the impingement and break up of ice particles.

Relatively Weak and Strong Impacts, the Split Hopkinson Pressure Bar: Propagation of Elastic Waves in Long Rods – Inertial Effects and Anelastic Material Properties. Strong Impacts and Irreversible Plastic Effects

The present section considers impacts of solid rods weak enough not to cause significant irreversible plastic deformations, but rather wave propagation. The similarity with a weak drop impact onto a shallow liquid layer, when only capillary waves rather than crown-like splashing are generated (see Section 6.1 in Chapter 6), is quite transparent. The split Hopkinson pressure bar apparatus sketched in Fig. 12.1 is an important example of such a situation in solid–solid impacts. It is frequently used to measure anelastic dynamic material properties of a sample of interest in a wide range of frequencies, as was first proposed by Kolsky (1949). A short cylindrical specimen in question is located between two coaxial rods made of high-strength steel. A striker bar (on the left in Fig. 12.1) impacts onto the left-hand side steel rod and initiates a rectangular compressive stress pulse propagating through the rod as an elastic wave. It is accompanied by a wave of displacements of very small (in the elastic regime) but measurable amplitude. This wave reaches the specimen and is partially reflected and partially transmitted through it. Similarly, the wave propagating through the specimen is partially reflected and partially transmitted into the right-hand side steel rod. Strain gauges are used to analyze the elastic waves propagating in the rods, and their comparison yields information on the rheological behavior of the specimen, in particular, its anelastic viscoelastic (viscoplastic) properties, which definitely affect the transmitted wave.

A description of collision phenomena involving drops and/or sprays requires a characterization of the drops before and after the collision as well as information about possible liquid films if impact on a solid surface is involved. The present chapter is devoted to the various techniques used to visualize and characterize drops, sprays and films. Independent of the measurement technique employed, collision phenomena are often described in terms of statistical quantities and Section 7.1 provides some fundamental definitions in common use. The remainder of the chapter, dealing with measurement techniques for drops and sprays, is divided into three sections: non-optical measurement techniques (Section 7.2), direct imaging techniques (Section 7.3) and non-imaging optical techniques (Section 7.4). The measurement of liquid films on a surface is treated separately in Section 7.5.

Very general reviews of measurement techniques for drops and sprays can be found in textbooks (Lefebvre 1989, Liu 1999), handbooks (Crowe 2005) and review articles (Bachalo 1994, Chigier 1983, Jones 1977); however, many techniques discussed have been superseded by more recent developments of imaging and non-imaging optical methods. The field of optical diagnostics has developed rapidly in recent years, primarily due to improvements in illumination technology (LEDs, solid-state lasers, etc.) and camera/detector technology, offering higher temporal and spatial resolution visualization of transient phenomena. Perhaps for this reason more recent review articles and handbook entries addressing spray measurement technology concentrate more on developments of optical techniques, e.g. (Bachalo 2000, Fansler and Parrish 2015, Tropea 2011).

Fundamentals

In this section some basic relations expressing the most common quantities necessary to describe impacting drops and sprays onto surfaces – input and outcome – will be presented, with special attention on how these quantities are derived from experimental measurements. The most important fundamental quantities to be acquired are

1. • flux density distributions (e.g. number or diameter flux density)

2. • local concentration (e.g. number or mass concentration)

3. • local probability density function (PDF) of particle properties (e.g. diameter, velocity, and their moments).

The process of atomization involves the generation of drops from bulk fluid, achieved using a wide variety of atomization concepts, depending on the desired local drop number, size and velocity flux densities, as well as on the bulk fluid and its properties, e.g. pure liquids, dispersions, suspensions, emulsions, etc. In the context of collision phenomena, atomization plays a key role in applications such as spray cooling, touchless cleaning and spray coating, whereby the latter can be understood in a very broad sense, encompassing applications such as spray painting, crop spraying, spray based encapsulation, domestic sprays (e.g. hair sprays, polishes) or even inhalators. Indeed, a majority of liquid collision phenomena involve atomization for the generation of individual drops and this fact motivates the present examination of the atomization process in more detail, with the aim of establishing an understanding between the atomization conditions and the resulting properties of the spray.

This chapter divides the atomization process into primary atomization (Section 8.1), i.e. overcoming the consolidating influence of surface tension by the action of internal and external forces (Lefebvre 1989), secondary atomization, and binary drop collisions in a spray, whereby several special modes of secondary atomization are treated in the final four sections. The causes of secondary atomization are manifold and can significantly alter the size distribution in a spray and are therefore important to consider. Typical causes of secondary atomization include aerodynamic forces whenever a drop is exposed to a relative air flow; covered in Section 8.2. Binary drop collisions can also lead to secondary atomization, as they occur in dense sprays, interacting sprays or when spray drops impinging onto a surface interact with drops ejected from the surface. Binary drop collisions are discussed in Section 8.3. Another cause of secondary atomization is when a drop impinges onto or is forced off a filament, for instance in a filter. This atomization scenario is the topic of Section 8.4. Finally, secondary atomization can also be electrically driven. In this case, evaporation in flight of electrified drops issued from electrostatic atomizers diminishes the drop surface area, while the electric charges they carry remain the same. As a result, the shrinking drop size can reach the so-called Rayleigh limit.

Penetration of solid bodies into liquids can be frequently treated in the framework of inviscid or potential flow hydrodynamics. In addition, collisions and penetration of solid bodies into solids in many cases, especially at the ordnance and ultra-ordnance velocities, can be effectively reduced to potential flows of ideal liquids possessing only inertia, since the stresses involved are significantly higher than the elastic and plastic stresses (see Section 1.1 in Chapter 1). Therefore, the present chapter is mostly devoted to several questions traditional to inviscid or potential flow hydrodynamics, which are either directly relevant in the context of collisions and penetration of solid bodies into liquids, or as simplified models useful for solid–solid collisions. Section 2.1 is devoted to the inviscid film flows on planar and curved surfaces. In the inertia-dominated regime characteristic of drop impact onto a thin liquid film on a wall, such flows give rise to kinematic discontinuities considered in Section 2.2 and associated with crown formation, which is considered in Section 6.7 in Chapter 6. The potential flow about an ovoid of Rankine discussed in Section 2.3 will be also employed in Chapter 13 in the case of projectile penetration into armor. The flow about an expanding and translating sphere outlined in Section 2.3 is also important in a purely hydrodynamic or rigid-projectile penetration context. Flows past axisymmetric bodies of revolution discussed in Section 2.4 are also important in the context of the projectile penetration. Transient motions of solid bodies in liquids inevitably involve deceleration associated with the added masses discussed in Section 2.5. A potential flow with separation about a blunt body (a plate moving normally to itself) is covered in Section 2.6 using the hodograph method of complex analysis to predict the shape drag. Friction drag associated with viscous effects is also discussed in Section 2.6. Finally, the dynamics of a rim bounding a free liquid film, for example a crown formed due to drop impact, is discussed in Section 2.7.