The internal dynamics during the coalescence of a sessile droplet and a subsequently deposited impacting droplet, with either identical or distinct surface tension, is studied experimentally in the regime where surface tension is dominant. Two color high-speed cameras are used to capture the rapid internal flows and associated mixing from both side and bottom views simultaneously by adding an inert dye to the impacting droplet. Given sufficient lateral separation between droplets of identical surface tension, a robust surface jet is identified on top of the coalesced droplet. Image processing shows this jet is the result of a surface flow caused by the impact inertia and an immobile contact line. By introducing surface tension differences between the coalescing droplets, the surface jet can be either enhanced or suppressed via a Marangoni flow. The influence of the initial droplet configuration and relative surface tension on the long-term dynamics and mixing efficiency, plus the implications for emerging applications such as reactive inkjet printing, are also considered.
Capillarity always favors drop fusion. Nevertheless sessile drops from different but completely miscible liquids often do not fuse instantaneously upon contact. Rather, intermediate non-coalescence is observed. Two separate drop bodies, connected by a thin liquid neck move over the substrate. Supported by new experimental data a thin film hydrodynamic analysis of this state is presented. Presumably advective and diffusive volume fluxes in the neck region establish a localized and temporarily stable surface tension gradient. This induces a local surface (Marangoni) flow that stabilizes a travel…
Colliding drops are widely encountered in everyday technologies and natural processes, from combustion engines and commodity sprays to raindrops and cloud formation. The outcome of a collision depends on many factors, including the impact velocity and the degree of head-on alignment, in addition to intrinsic properties like surface tension. Yet little is known on the binary impact dynamics of low surface tension oil drops on a low-wetting surface. We experimentally and numerically investigate the dynamics of an oil drop impacting an identical sessile drop sitting on a superamphiphobic surface.…
The evolution of the liquid bridge formed between two coalescing sessile yield-stress drops is studied experimentally. We find that the height of the bridge evolves similar to a viscous Newtonian fluid, $h_0\sim t$, before arresting at long time prior to minimizing its liquid/gas interfacial energy. We numerically solve for the final arrested profile shape and find it depends on the fluid's yield stress $τ_y$ and coalescence angle $α$, represented by the Bingham number $τ_y h_{drop} / σ$ modified by the drop's height-width aspect ratio. We present a scaling argument for the bridge's temporal e…
When two sessile drops of the same liquid touch, they merge into one drop, driven by capillarity. However, the coalescence can be delayed, or even completely stalled for a substantial period of time, when the two drops have different surface tensions, despite being perfectly miscible. A temporary state of non-coalescence arises, during which the drops move on their substrate, only connected by a thin neck between them. Existing literature covers pure liquids and mixtures with low surface activities. In this paper, we focus on the case of large surface activities, using aqueous surfactant solut…
During coalescence of liquid drops contacting a solid, the liquid sweeps wetted and solid-projected areas. The extent of sweeping dictates the performance of devices such as self-cleaning surfaces, anti-frost coatings, water harvesters, and dropwise condensers. For these applications, weakly- and non-wetting solid substrates are preferred as they enhance drop dynamical behavior. Accordingly, our coalescence studies here are restricted to drops with contact angle 90° $\le θ_{0} \le$ 180°. Binary sessile drop coalescence is the focus, with volume of fluid simulations employed as the primary tool…
Coalescence of sessile polymeric fluid drops on a partially wettable substrate exhibits a transition from inertial to viscoelastic regime at concentration ratio $c/c^* \sim 1$. Our findings unveil that the temporal evolution of the growing bridge height follows a power-law behaviour $t^b$, such that the coefficient $b$ continuously decreases from 2/3 in the inertial regime ($c/c^*<1$) to an asymptotic value of 1/2 in the visco-elastic regime ($c/c^*>1$). To account for fluid elasticity and characteristic time-scale in the viscoelastic regime, a modified thin film equation under lubrication app…
The impact of a sessile droplet with a moving meniscus, as encountered in processes such as dip-coating, generically leads to the entrapment of small air bubbles. Here we experimentally study this process of bubble formation by looking through the liquid using high-speed imaging. Our central finding is that the size of the entrapped bubble crucially depends on the location where coalescence between the drop and the moving meniscus is initiated: (i) at a finite height above the substrate, or (ii) exactly at the contact line. In the first case, we typically find bubble sizes of the order of a fe…
Unexpectedly, under certain conditions, sessile drops from different but completely miscible liquids do not always coalesce instantaneously upon contact: the drop bodies remain separated in a temporary state of noncoalescence, connected through a thin liquid bridge. Here we investigate the transition between the states of instantaneous coalescence and temporary noncoalescence. Experiments reveal that it is barely influenced by viscosities and absolute surface tensions. The main system control parameters for the transition are the arithmetic means of the three-phase angles, $\overlineΘ_a$ and t…
Coalescence-induced alignment of anisotropic particles in drying sessile droplets
Forschungszentrum Jülich（于利希研究中心）；Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2)（亥姆霍兹埃尔朗根-纽伦堡可再生能源研究所（IET-2））；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
We present an experimental and theoretical description of the kinetics of coalescence of two water drops on a plane solid surface. The case of partial wetting is considered. The drops are in an atmosphere of nitrogen saturated with water where they grow by condensation and eventually touch each other and coalesce. A new convex composite drop is rapidly formed that then exponentially and slowly relaxes to an equilibrium hemispherical cap. The characteristic relaxation time is proportional to the drop radius R * at final equilibrium. This relaxation time appears to be nearly 10 7 times larger th…
We present a theoretical study related to a recent experiment on the coalescence of sessile drops. The study deals with the kinetics of relaxation towards equilibrium, under the action of surface tension, of a spheroidal drop on a flat surface. For such a nonspherical drop under partial wetting conditions, the dynamic contact angle varies along the contact line. We propose a new nonlocal approach to the wetting dynamics, where the contact line velocity depends on the geometry of the whole drop. We compare our results to those of the conventional approach in which the contact line velocity depe…
Coalescence event in pendant and sessile drop is distinguished by the formation and evolution of the liquid bridge created upon singular contact. The bridge radius, $R$, is known to evolve as $R\sim t^b$, with power-law exponent, $b$, signifying the dominant governing forces. In this work, we experimentally explore the phenomenon in sub-classes of complex fluids namely, colloidal and non-colloidal suspensions that have particle hydrodynamic interactions as origin of viscoelasticity. Our observations suggest that such fluids have flow dependent thinning response with finite elasticity in shear …
While a drop of liquid is placed on another liquid surface, two possible coalescence outcomes are observed. The parent drop bounces several times, floats and then disappears within the liquid pool without producing daughter droplets. This is called complete coalescence. Another outcome is the generation of secondary droplets from the primary drop itself. This is called partial coalescence. Repetitions of such phenomenon as a successive self-similar event is also known as coalescence cascade. In a nutshell, complete coalescence is governed strongly by swallowing mechanism whereas partial coales…
Dynamics of the pendant drop coalescing with a sessile drop to form a single daughter droplet is known to form a bridge. The bridge evolution begins with a point contact between the two drops leading to a liquid neck of size comparable to the diameter of the drops. To probe this phenomenon in polymeric fluids, we quantify the neck radius growth during coalescence using high speed imaging. In the current study, we unveil the existence of three regimes on basis of concentration ratio $c/c^*$ namely, inertio-elastic $c/c^*<c_e/c^*$, viscoelastic $c_e/c^*<c/c^*<20$ and elasticity dominated regimes…
We numerically study the coalescence dynamics of two sessile droplets with radii $R_0$. The droplets are placed on top of a rigid substrate with a contact angle of $θ_{eq.} = π/9$. Having a highly wettable substrate ($θ_{eq} \ll π/2$) theory predicts that the bridge height ($h_0$) scales according to $h_0(t) \sim t^{2/3}.$ This behavior can be altered with e.g. surface tension gradients ($\partial_xγ\neq 0$). These gradients appear for example with heat transfer, surfactants or having different but miscible liquids. Instead of coalescence, these gradients can lead to a stable two droplet state…
In liquid spray applications, the sprays are often created by the formation and destabilization of a liquid sheet or jet. The disadvantage of such atomization processes is that the breakup is often highly irregular, causing a broad distribution of droplet sizes. As these sizes are controlled by the ligament corrugation and size, a monodisperse spray should consist of ligaments that are both smooth and of equal size. A straightforward way of creating smooth and equally sized ligaments is by droplet impact on a mesh. In this work we show that this approach does however not produce monodisperse d…
The directional movement and rebound behaviours of two droplets simultaneously impacting a designed flat surface with wettability difference is investigated based on the three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model. The effects of several factors, such as wettability difference, Weber number and droplet spacing on the directional movement and rebound behaviours are investigated in detail. The numerical results show that the unbalanced Young 's force caused by the wetting difference will cause the droplets to rebound or migrate laterally toward to the side wit…
The rich structures arising from the impingement dynamics of water drops onto solid substrates at high velocities are investigated numerically. Current methodologies in the aircraft industry estimating water collection on aircraft surfaces are based on particle trajectory calculations and empirical extensions thereof in order to approximate the complex fluid-structure interactions. We perform direct numerical simulations (DNS) using the volume-of-fluid method in three dimensions, for a collection of drop sizes and impingement angles. The high speed background air flow is coupled with the motio…
