Drops spreading on fluid surfaces: Transition from Laplace to Marangoni regime
We show the occurrence of two distinguished classical regimes of wetting, namely, Laplace and solutal Marangoni, during the spreading of oil drops on a surfactant-laden aqueous phase in a single surfactant-oil-water system. The spreading kinetics is found to follow a power-law behavior not only in the Laplace and Marangoni regimes, but also in the transition regime. Our experimental findings are corroborated with the scaling laws. The results demonstrate that increasing the surfactant concentration across the critical micelle concentration is instrumental to obtain the Laplace to Marangoni transition. Moreover, this transition does not depend on surfactant chemistry; instead, it depends on the adsorption/desorption kinetics of surfactant molecules to/from the interfaces that are created or annihilated during drop spreading.
Flow transitions and length scales of a channel-confined active nematic
We perform lattice Boltzmann simulations of an active nematic fluid confined in a two-dimensional channel to study the range of flow states that are stabilised by the confinement: unidirectional flow, oscillatory flow, the dancing state, localised active turbulence and fully-developed active turbulence. We analyse the flows in Fourier space, and measure a range of different length scales which describe the flows. We argue that the different states occur as a result of flow instabilities inherent to the system. As a consequence the characteristic length scale for oscillatory flow, the dancing state and localised active turbulence is set by the channel width. Fully-developed active turbulence occurs only when the channel width is larger than the intrinsic, active length scale of the bulk fluid. The results clarify why the activity number is a control parameter for the flow transitions. This journal is
Planar Rotational Equilibria of Two Nonidentical Microswimmers
We derive a closed analytical form of planar rotational equilibria that exist in the three-dimensional motion of two hydrodynamically coupled nonidentical microswimmers, each modeled as a force dipole with intrinsic self-propulsion. Using the method of images for zero Reynolds number flows near interfaces, we demonstrate that our results remain equally applicable at a stress-free liquid-gas interface as in the bulk of a fluid. For a pair of two pullers and a pair of two pushers the linear stability of the equilibria is analyzed with respect to two- and three-dimensional perturbations. A universal stability diagram of the orbits with respect to two-dimensional perturbations is constructed and it is shown that two nonidentical pushers or two nonidentical pullers moving at a stress-free interface may form a stable rotational equilibrium. For two nonidentical pullers we find stable quasi-periodic localized states, associated with the motion on a two-dimensional torus in the phase space. Stable tori are born from the circular periodic orbits as the result of a torus bifurcation. All stable equilibria in two dimensions are shown to be monotonically unstable with respect to three-dimensional perturbations.
Boundary layer description of directional polymer crystallisation
Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger-Gryte ansatz. This journal is
Drying Drops of Colloidal Dispersions
Drying drops of colloidal dispersions have attracted attention from researchers since the nineteenth century. The multiscale nature of the problem involving physics at different scales, namely colloidal and interfacial phenomena as well as heat, mass, and momentum transport processes, combined with the seemingly simple yet nontrivial shape of the drops makes drying drop problems rich and interesting. The scope of such studies widens as the physical and chemical nature of dispersed entities in the drop vary and as evaporation occurs in more complex configurations. This review summarizes past and contemporary developments in the field, emphasizing the physicochemical and hydrodynamical principles that govern the processes occurring within a drying drop and the resulting variety of patterns generated on the substrate.
Robust Method to Determine Critical Micelle Concentration via Spreading Oil Drops on Surfactant Solutions
The spreading of a liquid on another is often encountered in oil spills and coatings and is also of industrial relevance in pharmaceuticals and petrochemicals. In this study, the spreading of oil drops on aqueous solutions containing cationic, anionic, and nonionic surfactants over a wide range of surfactant concentrations is investigated. The spreading behavior quantified by measuring the time evolution of the projected area of the oil lens reveals the occurrence of a maximum, which is strongly dependent on the concentration of the surfactant in the aqueous solution. Our experiments show that this dependence is different at concentrations above and below the critical micelle concentration (CMC) of the surfactant and can be captured by two straight lines of different slopes. Interestingly, these two straight lines intersect at a concentration that coincides with the CMC of the surfactants in solution. We find that this behavior is universal as shown by performing experiments with different types of surfactants, their purity, and other system variables. Thus, we propose a method to unambiguously determine the CMC of surfactant solutions compared to the conventional techniques. The proposed method is simple, versatile, and applicable for the determination of CMC of both ionic and nonionic surfactants.
Kinetics of evaporation of colloidal dispersion drops on inclined surfaces
Evaporation of colloidal dispersion drops leaves a deposit pattern where more particles are accumulated at the edge, popularly known as the coffee-ring effect. Such patterns formed from dried sessile drops are azimuthally symmetric. When the substrate is inclined, the symmetry of the patterns is altered due to the influence of gravity. This is reflected in the changes in (i) pinning/depinning dynamics of the drop, (ii) the strength of the evaporation-driven flows, and (iii) ultimately, the lifetime of the drop. We present a systematic investigation of the kinetics of evaporation of particle-laden drops on hydrophilic inclined solid substrates. The angle of inclination of the substrate (ϕ) is varied from 0° to 90°. The temporal analysis of the drop shape profile is carried out to unearth the contribution of different processes to kinetics of evaporation of drops on inclined surfaces. The influence of particle concentration, drop volume, and angle of inclination on the kinetics of evaporation and the resulting deposit patterns are discussed.
Rotating-Particle Micropump Inspired by Taylor's Swimming Sheet
The development of size-efficient and cost-effective micropumps is an important problem given their wide applications. However, efficient designs are difficult to realise practically due to the complex machining required at small length scales. Here, we use Taylor's swimming sheet as an exemplar to show that the collective behavior of simple constructs like rotating particles can capture much of the rich behavior exhibited by microorganisms, and propose a compact and easy-to-make micropump based on the swimming sheet. We use analytical techniques and dissipative particle dynamics simulations to show that a staggered arrangement of rotating particles can emulate the flow characteristics of the swimming sheet and work as a micropump. Our analytical calculations, based on two approximate approaches, predict the dependence of the flow rate on control parameters.
Flow States and Transitions of an Active Nematic in a Three-Dimensional Channel
We use active nematohydrodynamics to study the flow of an active fluid in a 3D microchannel, finding a transition between active turbulence and regimes where there is a net flow along the channel. We show that the net flow is only possible if the active nematic is flow aligning and that, in agreement with experiments, the appearance of the net flow depends on the aspect ratio of the channel cross section. We explain our results in terms of when the hydrodynamic screening due to the channel walls allows the emergence of vortex rolls across the channel.
Wall-curvature driven dynamics of a microswimmer
Microorganisms navigate through fluid, often confined by complex environments, to survive and sustain life. Inspired by this fact, we consider a model system and seek to understand the wall curvature driven dynamics of a squirmer, a mathematical model for a microswimmer, using (i) lattice Boltzmann simulations and (ii) analytical theory by D. Papavassiliou and G. P. Alexander [Eur. Phys. Lett. 110, 44001 (2015)10.1209/0295-5075/110/44001]. The instantaneous dynamics of the system is presented in terms of fluid velocity fields, and the translational and angular velocities of the microswimmer, whereas the long time dynamics is presented by plotting the squirmer trajectories near curved boundaries in physical and dynamical space, as well as characterizing them in terms of fixed points and experimentally relevant measures, namely, (i) proximity parameter, (ii) retention time, (iii) swimmer orientation and (iv) tangential velocity near the boundary, and (v) scattering angle during the collision. Our detailed analysis shows that irrespective of the type and strength, microswimmers exhibit a greater affinity towards a concave boundary due to hydrodynamic interactions compared to a convex boundary. In the presence of additional repulsive interactions with the boundary, we find that pullers (propel by forward thrust) have a slightly greater affinity towards the convex-curved walls compared to pushers (propel by backward thrust). Our study provides a comprehensive understanding of the consequence of hydrodynamic interactions in a unified framework that encompasses the dynamics of pullers, pushers, and neutral swimmers in the neighborhood of flat, concave, and convex walls. In addition, the combined effect of oppositely curved surfaces is studied by confining the squirmer in an annulus. The results presented in a unified framework and insights obtained are expected to be useful to design geometrical confinements to control and guide the motion of microswimmers in microfluidic applications.