Ring stains in the presence of electrokinetic interactions

Self-assembly of highly ordered micro- and nanoparticle deposits

The evaporation of particle-laden sessile droplets is associated with capillary-driven outward flow and leaves nonuniform coffee-ring-like particle patterns due to far-from-equilibrium effects. Traditionally, the surface energies of the drop and solid phases are tuned, or external forces are applied to suppress the coffee-ring; however, achieving a uniform and repeatable particle deposition is extremely challenging. Here, we report a simple, scalable, and noninvasive technique that yields uniform and exceptionally ordered particle deposits on a microscale surface area by placing the droplet on a near neutral-wet shadow mold attached to a hydrophilic substrate. The simplicity of the method, no external forces, and no tuning materials' physiochemical properties make the present generic approach an excellent candidate for a wide range of sensitive applications. We demonstrate the utility of this method for fabricating ordered mono- and multilayer patternable coatings, producing nanofilters with controlled pore size, and creating reproducible functionalized nanosensors.

Spatio-temporal modulation of self-assembled central aggregates of buoyant colloids in sessile droplets using vapor mediated interactions

A functional sessile droplet containing buoyant colloids (ubiquitous in applications like chemical sensors, drug delivery systems, and nanoreactors) forms self-assembled aggregates. The particles initially dispersed over the entire drop-flocculates at the center. We attribute the formation of such aggregates to the finite radius of curvature of the drop and the buoyant nature of particles. Initially, larger particles rise to the top of the droplet (due to higher buoyancy force), and later the smaller particles join the league, leading to the graded size distribution of the central aggregate. This can be used to segregate polydisperse hollow spheres based on size. The proposed scaling analysis unveils insights into the distinctive particle transport during evaporation. However, the formation of prominent aggregates can be detrimental in applications like spray painting, sprinkling of pesticides, washing, coating, lubrication, etc. One way to avoid the central aggregate is to spread the droplets completely (contact angle ~ 0⁰), thus theoretically creating an infinite radius of curvature leading to uniform deposition of buoyant particles. Practically, this requires a highly hydrophilic surface, and even a small inhomogeneity on the surface would pin the droplet giving it a finite radius of curvature. Here, we demonstrate using non-intrusive vapor mediated Marangoni convection (Velocity scale ~ O(10³) higher than the evaporation-driven convection) can be vital to an efficient and on-demand manipulation of the suspended micro-objects. The interplay of surface tension and buoyancy force results in the transformation of flow inside the droplet leads to spatiotemporal disbanding of agglomeration at the center of the droplet.

Differences between Colloidal and Crystalline Evaporative Deposits

Evaporative deposits from drops are widely studied due to their numerous applications in low-effort self-assembly, including for inkjet printing, microscale separations, and sensing/diagnostics. This phenomenon has been broadly explored for drops containing suspended colloidal particles but has been less quantified for drops with dissolved solutes. When a drop of solute/solvent mixture is evaporated on a substrate, nonvolatile solutes become supersaturated as the solvent evaporates, which then leads to crystal nucleation at the substrate-drop contact line. Emerging crystals alter the local wettability and fundamentally alter the dynamics of evaporation, which, in turn, influences the resultant evaporative deposit. Here we investigate the role of interactions between the substrate, crystals, and solution by comparing the evaporative deposition of three different salts as solutes against an evaporating colloidal solution. We show that nucleation effects can cause crystalline deposits to have a temperature relationship that is opposite to that of colloidal deposits and demonstrate how a balance between the contact-line pinning force and nucleation controls the deposit size.

Efficient electrochemomechanical energy conversion in nanochannels grafted with end-charged polyelectrolyte brushes at medium and high salt concentration

We develop a theory to study the generation of the streaming potential and the resulting electrochemomechanical energy conversion (ECMEC) in the presence of pressure-driven transport in nanochannels grafted with end-charged polyelectrolyte (PE) brushes. Our theory gives a thermodynamically self-consistent coupled description of the PE-brush and the electrostatics of the electric double layer (EDL) induced by the PE charges. The end-charged brushes localize the maximum EDL charge density away from the wall, thereby enabling a larger magnitude of pressure-driven transport to stream the ions downstream. This effect is retarded by the drag force imparted by the brushes as well as by the enhanced electroosmotic transport in a direction opposite to the pressure-driven transport. An interplay of these three issues leads to highly non-trivial electrohydrodynamic transport that eventually allows us to converge on appropriate properties of the brushes (e.g., grafting density and the number of monomers) that lead to the generation of a significantly larger streaming potential and a much improved efficiency of the ECMEC as compared to the brush-free nanochannels particularly at medium and high salt concentrations.

A review on suppression and utilization of the coffee-ring effect

Evaporation of sessile droplets containing non-volatile solutes dispersed in a volatile solvent leaves behind ring-like solid stains. As the volatile species evaporates, pinning of the contact line gives rise to capillary flows that transport non-volatile solutes to the contact line. This phenomenon, called the coffee-ring effect, compromises the overall performance of industrially relevant manufacturing processes involving evaporation such as printing, biochemical analysis, manufacturing of nano-structured materials through colloidal and macromolecular patterning. Various approaches have been developed to suppress this phenomenon, which is otherwise difficult to avoid. The coffee-ring effect has also been leveraged to prepare new materials through convection induced assembly. This review underlines not only the strategies developed to suppress the coffee-ring effect but also sheds light on approaches to arrive at novel processes and materials. Working principles and applicability of these strategies are discussed together with a critical comparison.

Effect of Salt Concentration on the Motion of Particles near the Substrate in Drying Sessile Colloidal Droplets

The motions of the particles on the substrate of a drying sessile colloidal droplet of water were measured using multiparticle tracking. Droplets with different concentrations (0-250 mM) of sodium chloride (NaCl) were compared. Several statistical quantities were proposed to characterize the heterogeneous behaviors of the particles and distinguish the effects of the flow field and the substrate interaction. For the salt-free droplet, most of the particles were nonadsorbed and mobile without friction. With the presence of salt, the fraction of the adsorbed particles increases with increasing evaporation time and the initial salt concentration, which was explained by Derjaguin-Landau-Verwey-Overbeek interaction. The fraction of mobile particles is mostly frictionless for all samples. At low salt concentrations, the velocity of mobile particles increases with the evaporation time to a peak and then decreases. The velocity is lower for higher salt concentrations. The effect of salt on the nonadsorbed particles was attributed to the electrokinetic effect.

Alternative mechanism for coffee-ring deposition based on active role of free surface

When a colloidal sessile droplet dries on a substrate, the particles suspended in it usually deposit in a ringlike pattern. This phenomenon is commonly referred to as the "coffee-ring" effect. One paradigm for why this occurs is as a consequence of the solutes being transported towards the pinned contact line by the flow inside the drop, which is induced by surface evaporation. From this perspective, the role of the liquid-gas interface in shaping the deposition pattern is somewhat minimized. Here, we propose an alternative mechanism for the coffee-ring deposition. It is based on the bulk flow within the drop transporting particles to the interface where they are captured by the receding free surface and subsequently transported along the interface until they are deposited near the contact line. That the interface captures the solutes as the evaporation proceeds is supported by a Lagrangian tracing of particles advected by the flow field within the droplet. We model the interfacial adsorption and transport of particles as a one-dimensional advection-generation process in toroidal coordinates and show that the theory reproduces ring-shaped depositions. Using this model, deposition patterns on both hydrophilic and hydrophobic surfaces are examined in which the evaporation is modeled as being either diffusive or uniform over the surface.

Impact of the collective diffusion of charged nanoparticles in the convective/capillary deposition directed by receding contact lines

The motion of electrically charged particles under crowding conditions and subjected to evaporation-driven capillary flow might be ruled by collective diffusion. The concentration gradient developed inside an evaporating drop of colloidal suspension may reduce by diffusion the number of particles transported toward the contact line by convection. Unlike self-diffusion coefficient, the cooperative diffusion coefficient of interacting particles becomes more pronounced in crowded environments. In this work, we examined experimentally the role of the collective diffusion of charge-stabilized nanoparticles in colloidal patterning. To decouple the sustained evaporation from the contact line motion, we conducted evaporating menisci experiments with driven receding contact lines at low capillary number. This allowed us to explore convective assembly at fixed and low bulk concentration, which enabled to develop high concentration gradients. At fixed velocity of receding contact line, we explored a variety of substrate-particle systems where the particle-particle electrostatic interaction was changed (via p H) as well as the substrate receding contact angle and the relative humidity. We found that the particle deposition directed by receding contact lines may be controlled by the interplay between evaporative convection and collective diffusion, particularly at low particle concentration.

Effect of particle geometry on triple line motion of nano-fluid drops and deposit nano-structuring

We illustrate the importance of particle geometry on droplet contact line pinning, 'coffee-stain' formation and nano-structuring within the resulting rings. We present the fundamentals of pure liquid droplet evaporation and then discuss the effect of particles on the evaporation process. The resulting coffee-stain patterns and particle structuring within them are presented and discussed. In the second part, we turn our attention to the effect of particle geometry on the evaporation process. A wide range of particle shapes, categorised according to aspect ratio, from the simple shape of a sphere to the highly irregular shapes of platelets and tubes is discussed. Particle geometry effect on evaporation behaviour was quantified in terms of change in contact angle and contact radius for the stick-slip cases. Consequently the hysteretic energy barrier pinning the droplets was estimated, showing an increasing trend with particle aspect ratio. The three-phase contact line (TL) motion kinetics are complemented with analysis of the nano-structuring behaviour of each shape, leading to the identification of the two main parameters affecting nanoparticle self-assembly behaviour at the wedge. Flow velocity and wedge constraints were found to have antagonist effects on particle deposition, although these varied with particle shape. This description should help in understanding the drying behaviour of more complex fluids. Furthermore, knowing the fundamentals of this simple and inexpensive surface patterning technique should permit its tailoring to the needs of many potential applications.

Filling of charged cylindrical capillaries

We provide an analytical model to describe the filling dynamics of horizontal cylindrical capillaries having charged walls. The presence of surface charge leads to two distinct effects: It leads to a retarding electrical force on the liquid column and also causes a reduced viscous drag force because of decreased velocity gradients at the wall. Both these effects essentially stem from the spontaneous formation of an electric double layer (EDL) and the resulting streaming potential caused by the net capillary-flow-driven advection of ionic species within the EDL. Our results demonstrate that filling of charged capillaries also exhibits the well-known linear and Washburn regimes witnessed for uncharged capillaries, although the filling rate is always lower than that of the uncharged capillary. We attribute this to a competitive success of the lowering of the driving forces (because of electroviscous effects), in comparison to the effect of weaker drag forces. We further reveal that the time at which the transition between the linear and the Washburn regime occurs may become significantly altered with the introduction of surface charges, thereby altering the resultant capillary dynamics in a rather intricate manner.

Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping electric double layers

In this paper, we unravel new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with thick overlapping Electric Double Layers (EDLs). We observe that the streaming potential, for a given value of the capillary zeta (ζ) potential, varies with the EDL thickness and a dimensionless parameter R, quantifying the conduction current. Depending on the value of R, variation of the streaming potential with the EDL thickness demonstrates distinct scaling regimes: one can witness a Quadratic Regime where the streaming potential varies as the square of the EDL thickness, a Weak Regime where the streaming potential shows a weaker variation with the EDL thickness, and a Saturation Regime where the streaming potential ceases to vary with the EDL thickness. Effective viscosity, characterizing the electroviscous effect, obeys the variation of the streaming potential for smaller EDL thickness values; however, for larger EDL thickness the electroosmotic flow profile dictates the electroviscous effect, with insignificant contribution of the streaming potential.

Electric double-layer interactions in a wedge geometry: change in contact angle for drops and bubbles

In this paper, we provide a theory to pinpoint the role of electric double layer (EDL) interactions in governing the contact angle of an electrolyte drop on a charged solid in air or a bubble on a charged surface within an electrolyte solution. The EDL interactions are analytically solved by representing the three phase contact line as a wedge edge, with the wedge being formed by the solid-liquid and the air-liquid interfaces, and calculating the corresponding Maxwell stresses. We demonstrate that the EDL effects induce an "electrowetting-like" behavior, resulting in a lowering of the contact angle. As a specific example, we use this model to analyze the effect of added salt on preformed surface nanobubbles, and find, in contrast to what has been reported earlier, that even for most moderate conditions, added salt may have remarkable effect in altering the contact angle in preformed surface nanobubbles.

Effects of non-Newtonian power law rheology on mass transport of a neutral solute for electro-osmotic flow in a porous microtube

Mass transport of a neutral solute for a power law fluid in a porous microtube under electro-osmotic flow regime is characterized in this study. Combined electro-osmotic and pressure driven flow is conducted herein. An analytical solution of concentration profile within mass transfer boundary layer is derived from the first principle. The solute transport through the porous wall is also coupled with the electro-osmotic flow to predict the solute concentration in the permeate stream. The effects of non-Newtonian rheology and the operating conditions on the permeation rate and permeate solute concentration are analyzed in detail. Both cases of assisting (electro-osmotic and poiseulle flow are in same direction) and opposing flow (the individual flows are in opposite direction) cases are taken care of. Enhancement of Sherwood due to electro-osmotic flow for a non-porous conduit is also quantified. Effects if non-Newtonian rheology on Sherwood number enhancement are observed.

Reaction spreading on percolating clusters

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t)~t(d(l)), where d(l) is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed. While the front speed is a low-fluctuating quantity and its behavior can be understood using a simple theoretical argument, the front width is a high-fluctuating quantity showing a power-law behavior as a function of the size of the channel.

Structural transitions in a ring stain created at the contact line of evaporating nanosuspension sessile drops

Monodisperse nanosuspension droplets, placed on a flat surface, evaporated following the stick-slip motion of the three-phase contact line. Unexpectedly, a disordered region formed at the exterior edge of a closely packed nanocolloidal crystalline structure during the "stick" period. In order to assess the role of particle velocity on particle structuring, we did experiments in a reduced pressure environment which allowed the enhancement of particle velocity. These experiments revealed the promotion of hexagonal packing at the very edge of the crystallite with increasing velocity. Quantification of particle velocity and comparison with measured deposit shape for each case allowed us to provide a tentative description of the underlying mechanisms that govern particle deposition of nanoparticles at the triple line of an evaporating droplet. Behavior is governed by an interplay between the fluid, and hence particle, flow velocity (main ordering parameter) and wedge constraints, and consequently disjoining pressure (main disordering parameter). Furthermore, the formation of a second disordered particle region at the interior edge of the deposit (towards bulk fluid) was found and attributed to the rapid motion of the triple line during the "slip" regime. Additionally, the magnitude of the pinning forces acting on the triple line of the same drops was calculated. These findings provide further insight into the mechanisms of the phenomenon and could facilitate its exploitation in various nanotechnological applications.

Ring stains in the presence of electromagnetohydrodynamic interactions

In a recent paper [Das et al., Phys. Rev. E 85, 046311 (2012)], we delineated the role of electrokinetic transport in modifying the classical "coffee stain" effect. In this study, we extend this calculation to incorporate the consequences of a generalized electromagnetohydrodynamic transport in the coffee stain phenomenon. The magnetohydrodynamic (MHD) effect enhances the velocities at the beginning of the drop life, whereas the electrokinetic effect increases the "disordering" effect in particle deposition at the end of the drop, triggered by a velocity divergence. For a suitable combination of the strength of the MHD and electrokinetic transport, however, this disordering effect is substantially enhanced, and, most nonintuitively, such velocity divergence and the disordering effect may occur at a time that is much earlier than the end of the drop life, or may occur even instantaneously after the start of the drop evaporation. This work will provide useful insight in the understanding of the dynamics of mesoscopic patterns formed as the magnetic nanocrystals deposit in the presence of a combined transport driven by evaporation and magnetic field effects.