Effect of Viscosity on Bouncing Dynamics of Elliptical Footprint Drops on Non-Wettable Ridged Surfaces

An initial drop shape can alter the bouncing dynamics and significantly decrease the residence time on superhydrophobic surfaces. Elliptical footprint drops show asymmetric dynamics owing to a pronounced flow driven by the initial drop shape. However, the fundamental understanding of the effect of viscosity on the asymmetric dynamics has yet to be investigated, although viscous liquid drop impact on textured surfaces is of scientific and industrial importance. Here, the current study focuses on the impact of elliptical footprint drops with various liquid properties (density, surface tension, and viscosity), drop sizes, and impact velocities to study the bouncing dynamics and residence time on non-wettable ridged surfaces numerically by using a volume-of-fluid method. The underlying mechanism behind the variation in residence time is interpreted by analyzing the shape evolution, and the results are discussed in terms of the spreading, retraction, and bouncing. This study provides an insight on possible outcomes of viscous drops impinging on non-wettable surfaces and will help to design the desired spraying devices and macro-textured surfaces under different impact conditions, such as icephobic surfaces for freezing rain or viscous liquids.

Molecular Dynamics: A Study on Slip, Drops, and Graphene

<p>Molecular dynamics (MD) is a computational tool used to study physical systems by modeling the atomic-scale interactions between atoms. MD can accurately predict the properties of materials where models are well developed. For new materials, models may be in their early stages and may lack the ability to produce accurate results; however, MD can still provide insight into the physical properties of these new materials. This thesis will use MD to study two different systems. First, the Lennard-Jones (L-J) liquid is used to study how the intrinsic slip lengths of atomic sized surfaces add to produce an effective slip of a larger surface made up of these atomic constituents. The results show that the effective slip of a surface is dominated by its smallest slip, and these results show good agreement with a theory that predicts effective slip given the intrinsic slip and roughness of a surface. The L-J model is also used to investigate the rolling and sliding motion of viscous drops on super-hydrophobic surfaces. The effects of drop size, slip length, and gravity on drop velocities are investigated, and a model that predicts drop speed given the characteristics of a drop and a surface is proposed. The model shows good agreement with simulation results, especially for certain regimes. Second, graphene is studied with MD using various atomistic models. The energies of layers of graphene are reproduced using an Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential, and the energies required to exfoliate graphene from crystal graphite and nickel nano-particles are calculated. The calculations from MD show good agreement with literature and experiment, and these results demonstrate how simple models in MD can produce useful results to aid research and experiment. Finally, the formation of nano-bubbles in graphene grown on platinum is studied using the AIREBO and L-J potentials. The basic formation of graphene nano-bubbles is demonstrated by compressing the edges of graphene flakes. The simulations highlight the importance of proper boundary conditions, such as atom pinning, in order to produce tall, smooth nano-bubbles. The results also suggest that accurate models will be required to effectively demonstrate bubble formation.</p>

Molecular Dynamics: A Study on Slip, Drops, and Graphene

<p>Molecular dynamics (MD) is a computational tool used to study physical systems by modeling the atomic-scale interactions between atoms. MD can accurately predict the properties of materials where models are well developed. For new materials, models may be in their early stages and may lack the ability to produce accurate results; however, MD can still provide insight into the physical properties of these new materials. This thesis will use MD to study two different systems. First, the Lennard-Jones (L-J) liquid is used to study how the intrinsic slip lengths of atomic sized surfaces add to produce an effective slip of a larger surface made up of these atomic constituents. The results show that the effective slip of a surface is dominated by its smallest slip, and these results show good agreement with a theory that predicts effective slip given the intrinsic slip and roughness of a surface. The L-J model is also used to investigate the rolling and sliding motion of viscous drops on super-hydrophobic surfaces. The effects of drop size, slip length, and gravity on drop velocities are investigated, and a model that predicts drop speed given the characteristics of a drop and a surface is proposed. The model shows good agreement with simulation results, especially for certain regimes. Second, graphene is studied with MD using various atomistic models. The energies of layers of graphene are reproduced using an Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential, and the energies required to exfoliate graphene from crystal graphite and nickel nano-particles are calculated. The calculations from MD show good agreement with literature and experiment, and these results demonstrate how simple models in MD can produce useful results to aid research and experiment. Finally, the formation of nano-bubbles in graphene grown on platinum is studied using the AIREBO and L-J potentials. The basic formation of graphene nano-bubbles is demonstrated by compressing the edges of graphene flakes. The simulations highlight the importance of proper boundary conditions, such as atom pinning, in order to produce tall, smooth nano-bubbles. The results also suggest that accurate models will be required to effectively demonstrate bubble formation.</p>

Theory for the coalescence of viscous lenses

Drop coalescence occurs through the rapid growth of a liquid bridge that connects the two drops. At early times after contact, the bridge dynamics is typically self-similar, with details depending on the geometry and viscosity of the liquid. In this paper we analyse the coalescence of two-dimensional viscous drops that float on a quiescent deep pool; such drops are called liquid lenses. The analysis is based on the thin-sheet equations, which were recently shown to accurately capture experiments of liquid lens coalescence. It is found that the bridge dynamics follows a self-similar solution at leading order, but, depending on the large-scale boundary conditions on the drop, significant corrections may arise to this solution. This dynamics is studied in detail using numerical simulations and through matched asymptotics. We show that the liquid lens coalescence can involve a global translation of the drops, a feature that is confirmed experimentally.

Spreading or contraction of viscous drops between plates: single, multiple or annular drops

The behaviour of a viscous drop squeezed between two horizontal planes (a squeezed Hele-Shaw cell) is treated by both theory and experiment. When the squeezing force $F$ is constant and surface tension is neglected, the theory predicts ultimate growth of the radius $a\sim t^{1/8}$ with time $t$. This theory is first reviewed and found to be in excellent agreement with experiment. Surface tension at the drop boundary reduces the interior pressure, and this effect is included in the analysis, although it is negligibly small in the squeezing experiments. An initially elliptic drop tends to become circular as $t$ increases. More generally, the circular evolution is found to be stable under small perturbations. If, on the other hand, the force is reversed ($F<0$), so that the plates are drawn apart (the ‘contraction’, or ‘lifting plate’, problem), the boundary of the drop is subject to a fingering instability on a scale determined by surface tension. The effect of a trapped air bubble at the centre of the drop is then considered. The annular evolution of the drop under constant squeezing is still found to follow a ‘one-eighth’ power law, but this is unstable, the instability originating at the boundary of the air bubble, i.e. the inner boundary of the annulus. The air bubble is realised experimentally in two ways: first by simply starting with the drop in the form of an annulus, as nearly circular as possible; and second by forcing four initially separate drops to expand and merge, a process that involves the resolution of ‘contact singularities’ by surface tension. If the plates are drawn apart, the evolution is still subject to the fingering instability driven from the outer boundary of the annulus. This instability is realised experimentally by levering the plates apart at one corner: fingering develops at the outer boundary and spreads rapidly to the interior as the levering is slowly increased. At a later stage, before ultimate rupture of the film and complete separation of the plates, fingering spreads also from the boundary of any interior trapped air bubble, and small cavitation bubbles appear in the very low-pressure region, far from the point of leverage. This exotic behaviour is discussed in the light of the foregoing theoretical analysis.

Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels

The steady propagation of air bubbles through a Hele-Shaw channel with either a rectangular or partially occluded cross section is known to exhibit solution multiplicity for steadily propagating bubbles, along with complicated transient behaviour where the bubble may visit several edge states or even change topology several times, before typically reaching its final propagation mode. Many of these phenomena can be observed both in experimental realisations and in numerical simulations based on simple Darcy models of flow and bubble propagation in a Hele-Shaw cell. In this paper, we investigate the corresponding problem for the propagation of a viscous drop (with viscosity $$\nu $$ ν relative to the surrounding fluid) using a Darcy model. We explore the effect of drop viscosity on the steady solution structure for drops in rectangular channels or with imposed height variations. Under the Darcy model in a uniform channel, steady solutions for bubbles map directly on to those for drops with any internal viscosity $$\nu \ne 1$$ ν ≠ 1 . Hence, the solution multiplicity predicted for bubbles also occurs for drops, although for $$\nu >1$$ ν > 1 , the interface shape is reversed with inflection points appearing at the rear rather than the front of the drop. The equivalence between bubbles and drops breaks down for transient behaviour, at the introduction of any height variation, for multiple bodies of different viscosity ratios and for more detailed models which produce a more complicated flow in the interior of the drop. We show that the introduction of topography variations affects bubbles and drops differently, with very viscous drops preferentially moving towards more constricted regions of the channel. Both bubbles and drops can undergo transient behaviour which involves breakup into two almost equal bodies, which then symmetry break before either recombining or separating indefinitely.

Motion of Newtonian drops deposited on liquid-impregnated surfaces induced by vertical vibrations

We have studied the motion of drops on inclined liquid-impregnated surfaces (LISs) subject to vertical vibrations. The liquid drops comprise distilled water and different aqueous solutions of glycerol of increasing viscosity. The use of weak pinning LISs strongly affects the dynamical phase diagram. First of all, there is no trace of the dominant static region at low oscillating amplitudes reported for oscillating solid surfaces characterized by contact angle hysteresis. On the contrary, at sufficiently low oscillating amplitudes, the drops always move downwards with a velocity that depends only on the drop viscosity. Further increasing the oscillating amplitude may drive the drop upwards against gravity, as reported for dry surfaces. The use of more viscous drops widens this climbing region. Arguably, the main novelty of this work concerns the observation of two distinct descending regimes where the downhill speed differs by a factor of five or more. Fast-rate videos show that the evolution of the drop profile is diverse in the two regimes, likely because the vertical oscillations reduce the effect of the oil meniscus surrounding the drop at high accelerations.