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.