Quantifying the Microstructure of Dried Deposits Using Height-Height Correlation Function.

Colloidal self-assembly has garnered significant attention in recent research, owing to applications in medical and engineering domains. Understanding the arrangement of particles in self-assembled systems is crucial for comprehending the underlying physics and synthesizing complex nano- and microscale structures. In this study, we introduce a novel methodology for analyzing the spatial distribution of particles in colloidal assemblies, focusing specifically on quantifying the microstructure of deposits formed by the evaporation of colloidal particle-laden drops. Utilizing a height-height correlation-function-based approach, we quantify variations in the height profile of deposits in radial and azimuthal directions. This approach enables the classification of the patterns into typical examples encountered in an evaporation-driven assembly. The method is demonstrated to be robust for quantifying synthetic and experimentally obtained deposit patterns, exhibiting excellent agreement in the estimated parameters. The mapping developed between pattern morphology and the quantitative measures introduced in this work may be used in a variety of applications including disease diagnosis as well as in developing pattern recognition tools.

Dynamics of spreading of an asymmetrically placed droplet near a fluid-fluid interface.

Two-dimensional numerical simulations are carried out to study the spreading dynamics of a droplet placed in the vicinity of a fluid-fluid interface. Simulations are performed using the hybrid lattice-Boltzmann technique and the diffuse-interface model by considering three immiscible fluids of the same density and viscosity. In contrast to the well-studied spreading of drops placed symmetrically across fluid-fluid interfaces, this work considers the simultaneous migration, spreading and eventual adsorption of an asymmetrically placed drop. These processes, which are solely driven by interfacial forces, are characterised by monitoring the temporal evolution of geometric parameters, such as the centre of mass, radius and height of the drop, the surface energy of the three interfaces and the associated flow fields inside and outside the droplet. The rate of spreading and rate of adsorption are also calculated to determine the dominant processes that drive the dynamics of the system.

Conducting Gold Nanoparticle Films via Sessile Drop Evaporation.

The deposit patterns obtained from the evaporation of drops containing insoluble solute particles are vital for several technologies, including inkjet printing and optical and electronic device manufacturing. In this work, we consider the evaporation of an aqueous reaction mixture typically used for gold nanoparticle (AuNP) synthesis. The patterns obtained from the evaporation-driven assembly of in situ generated AuNPs are studied using optical microscopy and SEM analyses. The evaporation of drops withdrawn at different reaction times is found to significantly influence the distribution of AuNPs in the dried patterns. The evolution of the deposit patterns is also explored by drying multiple drops on the solid substrate, wherein a drop of a fresh reaction mixture is introduced over the deposit pattern left by the evaporation of the drop dispensed at an earlier time. Using quantitative image analysis, we show that the interparticle separation between the AuNPs in the dried patterns left on the solid substrate decreases when the number of drops is increased. We find optimal conditions to achieve solid-supported AuNP films, wherein the particles are in close physical contact, leading to a conducting deposit. The current through the AuNP deposit is found to increase with increase in the number of drops due to evaporation-driven self-assembly of AuNPs into branch-like structures with reduced interparticle separation. In addition, we also show that it is possible to produce conducting AuNP deposits by drying multiple drops withdrawn from the same reaction mixture. The evaporation-driven assembly of the in situ grown nanoparticles from a reaction mixture presented in this work can be further exploited in optical and electronic device fabrication.

Active compound particles in a quadratic flow: hydrodynamics and morphology.

Generating core-shell particles with a well-controlled morphology is of great interest due to the interdependence between the morphology and different properties of these structures. These particles are often generated in microfluidic devices in a background quadratic flow. Therefore, in this study, we investigate the hydrodynamics and morphology of a concentric active compound particle, an active particle encapsulated in a fluid droplet, in an imposed quadratic flow. Governing equations for fluid flow are analytically solved in the inertia-less limit assuming that the surface tension force dominates the viscous forces (capillary number, Ca ≪ 1). Poiseuille flow deforms the compound particle into a three-lobe structure governed by the hexapolar component of the Poiseuille flow. Activity deforms the compound particle into a prolate shape owing to the velocity field of a force dipole. For an active compound particle in a Poiseuille flow, morphology is sensitive to the orientations and relative strengths of the activity and Poiseuille flow. Primarily, the presence of activity breaks the three-lobe symmetry of the drop shape and makes it more asymmetric and elongated. Moreover, the active compound particle becomes more susceptible to breakup in a quadratic flow when (i) the strength of activity is much stronger than the imposed flow strength, (ii) the active particle is oriented along the symmetry axes of the quadratic flow, (iii) the size ratio of the confining droplet to the encapsulated active particle is small and (iv) the viscosity ratio of the outer fluid to the inner fluid is small. Finally, we demonstrate that imposing the pulsatile quadratic flow prevents the breakup of an active compound particle during its generation and transport, and further assists in tuning the morphology.

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.

Directional polymer crystallisation with a fast-moving sink.

It has previously been shown that non-isothermal directional polymer crystallisation driven by local melting (Zone Annealing), has a close analogy with an equivalent isothermal crystallisation protocol. This surprising analogy is due to the low thermal conductivity of polymers-because they are poor thermal conductors, crystallisation occurs over a relatively narrow spatial domain while the thermal gradient spans a much wider scale. This separation of scales, which occurs in the limit of small sink velocity, allows replacing the crystallinity profile with a step and the temperature at the step acts as an effective isothermal crystallisation temperature. In this paper, we study directional polymer crystallisation under faster moving sinks using both numerical simulations and analytical theory. While, only partial crystallisation occurs, regardless, a steady state exists. At large velocity, the sink quickly moves ahead of a region that is still crystallizing; since polymers are poor thermal conductors, the latent heat dissipation to the sink becomes inefficient, eventually resulting in the temperature increasing back to the melting point thereby resulting in incomplete crystallization. This transition occurs when the two length scales measuring the sink-interface distance and the width of the crystallizing interface become comparable. For steady state and in the limit of large sink velocity, regular perturbation solutions of the differential equations governing heat transport and crystallization in the region between the heat sink and the solid-melt interface are in good agreement with numerical results.

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.

Viscoelastic confinement induces periodic flow reversals in active nematics.

We use linear stability analysis and hybrid lattice Boltzmann simulations to study the dynamical behavior of an active nematic confined in a channel made of viscoelastic material. We find that the quiescent, ordered active nematic is unstable above a critical activity. The transition is to a steady flow state for high elasticity of the channel surroundings. However, below a threshold elastic modulus, the system produces spontaneous oscillations with periodic flow reversals. We provide a phase diagram that highlights the region where time-periodic oscillations are observed and explain how they are produced by the interplay of activity and viscoelasticity. Our results suggest experiments to study the role of viscoelastic confinement in the spatiotemporal organization and control of active matter.

Helical flow states in active nematics.

We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams-this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices-this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.

Physics of Directional Polymer Crystallization.

It has been proposed that the nonisothermal directional crystallization of a polymer driven by a moving sink has an exact analogy to an equivalent isothermal crystallization protocol. We show that this is substantially true because polymers are poor thermal conductors; thus, polymer crystallization occurs over a relatively narrow spatial regime, while the thermal gradients created by this freezing occur over a much broader scale. This separation of scales allows us to replace the crystallization process, which is spatially distributed, with an equivalent step. The temperature at this step, which corresponds to the desired equivalent isothermal crystallization temperature, scales linearly with sink velocity. However, a few metrics, such as the Avrami exponent characterizing the kinetics of crystallization are very different in the two cases. These findings provide new insights into the physics of these spatially varying crystallization protocols and should inspire new experiments to probe the underlying equivalences more deeply.

An experimental and theoretical study of the inward particle drift in contact line deposits.

The coffee ring effect, which refers to the formation of a ring-like deposit along the periphery of a dried particle laden sessile drop, is a commonly observed phenomenon. The migration of particles from the interior to the edge of a drying drop as a result of evaporation driven flow directed outwards, is well studied. In this article, we document the inward drift of a coffee stain, which is governed by the descent of the water-air interface of the drying drop due to solvent evaporation. A combination of experimental study and model predictions is undertaken to elucidate the effect of the diameter of particles in the drying drop, the wettability of the substrate on which the drop resides, and the concentration of particles on the inward drift of the coffee stain. This work also suggests a novel method to estimate the coefficient of friction between the particles and the substrate.

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.

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.

Patterns from drops drying on inclined substrates.

The coffee ring effect results from the migration of particles in a drying particle laden drop and their subsequent deposition at the three phase contact line. The evaporative flux during the drying of sessile drops and the spatial distribution of particles in the coffee ring patterns exhibit azimuthal symmetry. It is possible to break this symmetry with the help of gravity by simply manipulating the inclination of the substrate on which the colloidal droplet undergoes drying. However, the effect of particle size, substrate wettability and inclination angle on the extent of asymmetry in the spatial distribution of particles over the deposit patterns has not been explored and is the subject of the current work. Our experiments on the drying of aqueous dispersions of polystyrene particles show that (i) asymmetry in the deposition of particles is observed irrespective of the diameter of the dispersed particles in the drying drop (ii) the degree of asymmetry increases with a decrease in wettability of the drop on the substrate and (iii) it is a non-monotonic function of the inclination angle of the substrate. These results indicate the possibility of additional particle transport mechanisms working in tandem with evaporation driven capillary flows and demand further investigation of the physics of pattern formation in drops drying on oriented substrates.

Further Insights into Patterns from Drying Particle Laden Sessile Drops.

The evaporation of colloidal dispersions is an elegant and straightforward route to controlled self-assembly of particles on a solid surface. In particular, the evaporation of particle laden drops placed on solid substrates has received considerable attention for more than two decades. Such particle filled drops upon complete evaporation of the solvent leave behind a residue, commonly called particulate deposit pattern. In these patterns, typically, more particles accumulate at the edge compared to the interior, a feature observed when coffee drops evaporate. Consequently, such evaporative patterns are called coffee stains. In this article, the focus is on the evaporation of highly dilute suspension drops containing particles of larger diameters ranging from 3 to 10 µm drying on solid substrates. This helps us to investigate the combined role of gravity-driven settling of particles and capillary flow-driven particle transport on pattern formation in drying drops. In the highly dilute concentration limit, the evaporative patterns are found to show a transition, from a monolayer deposit that consists of a single layer of particles, to a multilayer deposit as a function of particle diameter and initial concentration of particles in the drying drop. Moreover, the spatial distribution of particles as well as the ordering of particles in the deposit patterns are found to be particle size dependent. It is also seen that the order-disorder transition, a feature associated with the organization of particles at the edge of the deposit, observed typically at moderate particle concentrations, disappears at the highly dilute concentrations considered here. The evaporation of drops containing particles of 10 µm diameter, where the effect of gravity on the particle becomes significant, leads to uniform deposition of particles, i.e, suppression of the coffee-stain effect and to the formation of two-dimensional percolating networks.

Hydrodynamic collision between a microswimmer and a passive particle in a micro-channel.

Microswimmers interacting with passive particles in confinement are common in many systems, e.g., spermatozoa encountering other cells or debris in the female reproductive tract or active particles interacting with polymers and tracers in microfluidic channels. The behaviour of such systems is driven by simultaneous, three way hydrodynamic interactions between the microswimmer, the passive particle and the microchannel walls. Therefore, in this work we investigate the hydrodynamic collision between a model microswimmer and a passive particle using three different methods: (i) the point particle approach, (ii) analytical calculations based on method of reflections, and (iii) lattice Boltzmann numerical simulations. We show that the hydrodynamic collision is essentially an asymmetric process - the trajectory of the microswimmer is altered only in an intermediate stage while the passive particle undergoes a three stage displacement with a net displacement towards or away from the microchannel walls. The path of the passive particle is a simple consequence of the velocity field generated by the swimmer: an open triangle in bulk fluid and a loop-like trajectory in confinement. We demonstrate the generality of our findings and conclude that the net displacement of the passive particle due to collision may be capitalised in order to develop applications such as size separation of colloidal particles and deposition of particles in the microchannel interiors.

Modeling polymer crystallisation induced by a moving heat sink.

Recent experimental work has shown that polymer crystallisation can be used to "move" and organize nanoparticles (NP). As a first effort at modeling this situation, we consider the classical Stefan problem but with the modification that polymer crystallisation does not occur at a single temperature. Rather, the rate of crystallisation is proportional to its subcooling, and here we employ a form inspired by the classical Avrami model to describe this functional form. Our results for the movement of the polymer crystallisation front, as defined as the point where the crystallinity is 50%, closely track the results of the classical Stefan problem. Thus, at this level of approximation, the crystallisation kinetics of the polymer do not cause qualitative changes to the physics of this situation. Inspired by this fact we study the more interesting situation where the directional recrystallisation of a polymer melt is considered, e.g., through the application of a moving heat sink over an initially molten polymer, reminiscent of a processing technique termed zone annealing. The polymer crystallisation shows that a steady state exists for a range of sink velocities. The solid-melt interface moves slightly ahead of the sink but at the same velocity. The steady-state distance between the sink and the interface decreases with increasing sink velocity - this is a consequence of the excess cooling provided by the sink over what is required to crystallise the melt. The most interesting new result is that the temperature of the crystal-melt interface decreases with increasing sink velocity. This is in line with the ansatz of Lovinger and Gryte who suggested that larger zone annealing velocities correspond to progressively larger effective undercoolings at which polymer crystallisation occurs.

Particle size and substrate wettability dependent patterns in dried pendant drops.

The particle laden sessile drops when dried on solid surfaces under certain conditions leave a deposit pattern wherein all the particles are confined to a narrow region close to the edge of the deposit. Such patterns which often form when coffee drops dry are referred to as the coffee ring patterns or the coffee stains. Recent research points to the formation of intriguing patterns when colloidal particle laden drops are dried in configurations other than sessile mode. In this article, the combined effect of particle size and wettability of the substrate on the patterns formed by drying drops in sessile and pendant configurations is investigated via experiments. Our results demonstrate a transition from coffee ring to central dome-like deposit morphology with decrease in wettability of the substrates when drops containing 3 µm diameter particles are dried in pendent mode. A similar transition in the deposit morphology is observed with increase in the diameter of the particles in pendant drops dried on substrates of near neutral wettability (θ = 86 ± 3°). The influence of particles size, substrate wettability and drop configuration on the kinetics of deposition of particles at the three phase contact line will also be discussed. We compare our experimental observations with particle based simulations wherein the dried patterns are generated by accounting for three particle transport modes, namely, advective particle transport resulting from capillary flow, gravity driven settling of particles and particle capture by descending interface.

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.

Beyond Coffee Rings: Drying Drops of Colloidal Dispersions on Inclined Substrates.

The patterns resulting from drying particle-laden sessile drops (for example, coffee rings, where the particles are concentrated more at the edge, and their complete suppression, where the particles are uniformly distributed throughout the pattern) have been well studied for more than two decades. For the ubiquitous instance of occurrence of drying of drops containing nonvolatile species (either dissolved or dispersed) on substrates oriented at different angles with respect to gravity, the investigation of resulting evaporative patterns has not received much attention. This mini-review addresses the need to investigate the drying of drops residing on inclined surfaces and highlights recent advances in this field.