Rouslan Krechetnikov

Crown-forming instability phenomena in the drop splash problem

The objective of this work is to study the fundamental instability behind the crown formation in the problem of drop splashing on a pre-existing liquid film. Based on experimental and theoretical insights, we demonstrate that the most plausible instability mechanism is of the Richtmyer-Meshkov type associated with a nearly impulsive acceleration of the interface. We also discover frustration phenomena in the wave number selection of the crown spike structure and study the corresponding bifurcation picture.

Surfactant effects in the Landau–Levich problem

In this work we study the classical Landau–Levich problem of dip-coating. While in the clean interface case and in the limit of low capillary numbers it admits an asymptotic solution, its full study has not been conducted. With the help of an efficient numerical algorithm, based on a boundary-integral formulation and the appropriate set of interfacial and inflow boundary conditions, we first study the film thickness behaviour for a clean interface problem. Next, the same algorithm allows us to investigate the response of this system to the presence of soluble surface active matter, which leads to clarification of its role in the flow dynamics. The main conclusion is that pure hydrodynamical modelling of surfactant effects predicts film thinning and therefore is not sufficient to explain the film thickening observed in many experiments.

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

In this work we present an experimental study of deviations from the classical Landau-Levich law in the problem of dip coating. Among the examined causes leading to deviations are the nature of the liquid-gas and liquid-solid interfaces. The thickness of the coating film created by withdrawal of a plate from a bath was measured gravimetrically over a wide range of capillary numbers for both smooth and well-characterized rough substrates, and for clean and surfactant interface cases. In view of the dependence of the lifetime of a film on the type of liquid and substrate, and liquid-gas and liquid-solid interfaces, we characterized the range of measurability of the film thickness in the parameter space defined by the withdrawal capillary number, the surfactant concentration, and substrate roughness size. We then study experimentally the effect of a film thickening due to the presence of surfactants. Our recent theory based on a purely hydrodynamic role of the surface active substance suggests that there is a sorption-controlled coating regime in which Marangoni effects should lead to film thinning. However, our experiments conducted in this regime demonstrate film thickening, calling into question the conventional wisdom, which is that Marangoni stresses (as accounted by the conventional interfacial boundary conditions) lead to film thickening. Next we examine the effect of well-characterized substrate roughness on the coated film thickness, which also reveals its influence on wetting-related processes and an effective boundary condition at the wall. In particular, it is found that roughness results in a significant thickening of the film relative to that on a smooth substrate and a different power of capillary number than the classical Landau-Levich law.

Landau-Levich flow visualization: Revealing the flow topology responsible for the film thickening phenomena

An extensive body of experimental work has proven the validity of the analysis of Landau and Levich, who were the first to determine theoretically the thickness of the film deposited by the withdrawal of a flat substrate from a bath of liquid with a clean interface. However, there are a number of experimental investigations that have shown that surfactants in the liquid may result in a thickening of the deposited film. Marangoni phenomena have usually been considered responsible for this effect. However, some careful experiments and numerical simulations reported in the literature seemed to rule out this view as the cause of the observed behavior. Despite all these studies and the number of reports of film thickening, an experimental study of the flow field close to the coated substrate in the presence of surfactants has never been undertaken. In this paper we will present a set of flow visualization experiments on coating of a planar substrate in the range of capillary numbers 10−4 ≲ Ca ≲ 10−3 for sodium dodecyl sulfate solutions with bulk concentrations of 0.25 CMC ⩽ C ⩽ 5.0 CMC (critical micelle concentration). It was evident during experiments that the flow field near the meniscus region exhibits patterns that can only be explained with a stagnation point residing in the bulk and not at the interface. As opposed to patterns with an interfacial stagnation point, the observed flow fields allow for the increase in film thickness due to the presence of surfactants compared to the clean interface case.

Rayleigh–Taylor and Richtmyer–Meshkov instabilities of flat and curved interfaces

In this work we discuss a non-trivial effect of the interfacial curvature on the stability of uniformly and suddenly accelerated interfaces, such as liquid rims. The new stability analysis is based on operator and boundary perturbation theories and allows us to treat the Rayleigh–Taylor and Richtmyer–Meshkov instabilities as a single phenomenon and thus to understand the interrelation between these two fundamental instabilities. This leads, in particular, to clarification of the validity of the original Richtmyer growth rate equation and its crucial dependence on the frame of reference. The main finding of this study is the revealed and quantified influence of the interfacial curvature on the growth rates and the wavenumber selection of both types of instabilities. Finally, the systematic approach taken here also provides a generalization of the widely accepted ad hoc idea, due to Layzer ( Astrophys. J ., vol. 122, 1955, pp. 1–12), of approximating the potential velocity field near the interface.

Stability of liquid sheet edges

Accelerating edges of thin liquid sheets are ubiquitous and are known to experience a longitudinal (along-the-edge) instability, which often leads to their break-up and atomization. The fundamental physical mechanisms of this instability are studied analytically in the quasisteady regime, which admits a concise modeling. It is discovered that the classical Rayleigh–Taylor mechanism is substantially modified which leads to a stability picture different from that for flat interfaces, in part due to an interplay with Rayleigh–Plateau mechanisms. In particular, as the Bond number increases, first, only one critical wavenumber is excited, but for higher values of the Bond number several critical wavenumbers can coexist with the same growth rates. This allows for the transition from the regular picture, in which one wavelength sets the pattern, to the frustrated picture, in which a few wavenumbers compete with each other.

On physical mechanisms in chemical reaction-driven tip-streaming

In this work we provide a basic physical modeling of the spatiotemporal pattern of emulsification produced by chemical reaction-driven tip-streaming and observed by Fernandez and Homsy [Phys. Fluids 16, 2548 (2004)]. Features of this phenomenon—nonlinear autooscillations, a conical drop shape, tip-streaming, and droplet trajectory splitting—are addressed in this paper. In particular, the experimentally found regimes of self-sustained periodic motion and the transitions between them are explained with the help of a nonlinear relaxation oscillator model. An exact self-similar solution for the steady tip-streaming mode supports the suggested mechanism of a Marangoni-driven phenomenon. Finally, the ionic nature of the surfactant produced at the interface offers a reasonable explanation for the formation of a spray cone, which is due to repulsive electrostatic interactions between droplets. These features distinguish this phenomenon from standard tip-streaming.

On application of lubrication approximations to nonunidirectional coating flows with clean and surfactant interfaces

In this work, the characteristic properties of the lubrication approximation are studied and its weak ellipticity is established, in contradistinction to the commonly accepted parabolic character of the lubrication equations resulting from the underlying unidirectional flow assumption. The weak ellipticity property allows the lubrication analysis to capture flow topologies around stagnation points, contact lines, and flows over edges, all of which normally require elliptic operators to be accounted for. This is used to explain the empirically observed overperformance of the lubrication approximation from the perspective of characteristic analysis. While the analysis is developed in the context of the classical Landau–Levich problem of dip-coating, which is known to possess an interfacial stagnation point both in the clean and surfactant interface cases, the analysis is general since the Landau–Levich equation is common to many other lubrication problems. The analytical approach presented here when applied...

Dip coating in the presence of a substrate-liquid interaction potential

In this work we investigate theoretically the Landau-Levich problem of dip coating in the presence of a strong interaction potential normal to the substrate. This study is motivated by dip coating at very low capillary numbers when the deposited film thickness is less than 1 µm and such interaction forces become important. The objective of this work is to demonstrate that in the presence of an extra body force the solution procedure differs significantly from the classical one and leads to substantial deviations from the Landau-Levich law for the entrained film thickness. In particular, attractive potentials produce film thickening and the resulting film thickness is independent of speed to lowest order. Repulsive potentials bring about more complicated behavior and lead either to films whose thickness is also independent of speed, or to a modification of the leading order constant in the classical Ca^(2/3) law. Demonstration of these effects is given for a model potential. The analysis is generally applicable to many physical situations when there is an interaction between a coating liquid and a substrate, e.g., dip coating of ferromagnetic liquids on magnetic substrates, or dip coating of liquids carrying charges.

On a new surfactant-driven fingering phenomenon in a Hele-Shaw cell

According to the Saffman–Taylor criterion there is no instability when a more viscous fluid is displacing a less viscous one in a Hele-Shaw cell. Yet an instability was observed experimentally (Chan et al. 1997) in the same classical set-up but with the inner walls of the cell coated with surfactant solution. Linear stability analysis is applied to reveal the basic mechanism of this new instability. Asymptotic theory for low capillary numbers allows us to predict the long-wave instability, along with the dependence of the critical parameters on the material properties of the surfactant.