Electrostatic suppression of the "coffee stain effect"

Redox Control of Particle Deposition from Drying Drops

The coffee-ring effect (CRE), which denotes the accumulation of nonvolatile compounds at the periphery of a pinned sessile drying drop, is a universal and ubiquitous yet complex phenomenon. It is crucial to better understand and control it, either to avoid its various deleterious consequences in many processes requiring homogeneous deposition or to exploit it for applications ranging from controlled particle patterning to low cost diagnostics. Here, we report for the first time the use of a reduction-oxidation (redox) stimulus to cancel the CRE or harness it, leading to a robust and tunable control of particle deposition in drying sessile drops. This is achieved by implementing redox-sensitive ferrocenyl cationic surfactants of different chain lengths in drying drops containing anionic colloids. Varying surfactant hydrophobicity, concentration, and redox state allows us not only to control the overall distribution of deposited particles, including the possibility to fully cancel the CRE, but also to modify the microscopic organization of particles inside the deposit. Notably, with all other parameters being fixed, this method allows the adjustment of the deposited particle patterns, from polycrystalline rings to uniform disks, as a function of the oxidation rate. We show that the redox control can be achieved either chemically by the addition of oxidants or electrochemically by applying a potential for additive-free and reversible actuation in a closed system. This correlation between the redox state and the particle pattern opens a perspective for both redox-programmable particle patterning and original diagnostic applications based on the visual determination of a redox state. It also contributes to clarify the role of surfactant charge and its amphiphilic character in directing particle deposition from drying suspensions.

Equivalence of sessile droplet dynamics under periodic and steady electric fields

The electrohydrodynamics of a sessile droplet under the influence of periodic and steady electric fields in microgravity conditions is theoretically investigated using an inertial lubrication model. Previous studies have revealed that a freely suspended spherical droplet with unequal conductivity and permittivity ratios exhibits distinct dynamics under periodic and equivalent steady forcing in the root mean-square sense. However, it is unclear when (if at all) such distinct dynamics occur for periodic and equivalent steady forcing in the case of sessile droplets. The equivalence between periodic and steady forcing is shown to be governed by the interfacial charge buildup, which further depends on the competition between the charge relaxation and forcing timescales. A circulation-deformation map is introduced for the sessile droplet that acts as a guideline to achieve electric field-induced wetting or dewetting as the case may be. We also demonstrate that a droplet may be rendered either more or less wetting solely by tuning the forcing frequency.

Droplet evaporation on soft solid substrates

Droplet evaporation on soft solid substrates is relevant to applications such as fabrication of microlenses and controlled particle deposition. Here, we develop a lubrication-theory-based model to advance fundamental understanding of the important limiting case of a planar droplet evaporating on a linear viscoelastic solid. A set of partial differential equations describing the time evolution of the liquid-air and liquid-solid interfaces is derived and solved with a finite-difference method. A disjoining-pressure/precursor-film approach is used to describe contact-line motion, and the one sided model is used to describe solvent evaporation. Parametric studies are conducted to investigate the effect of solid properties (thickness, viscosity, shear modulus, wettability) and evaporation rate on droplet dynamics. Our results indicate that softer substrates speed up droplet evaporation due to prolonged pinning of the contact line. Results from our model are able to qualitatively reproduce some key trends observed in experiments. Due to its systematic formulation, our model can readily be extended to more complex situations of interest such as evaporation of particle-laden droplets on soft solid substrates.

A thin-film model for droplet spreading on soft solid substrates

The spreading of droplets on soft solid substrates is relevant to applications such as tumor biophysics and controlled droplet condensation and evaporation. In this paper, we apply lubrication theory to advance fundamental understanding of the important limiting case of spreading of a planar droplet on a linear viscoelastic solid. The contact-line region is described by a disjoining-pressure/precursor-film approach, and nonlinear evolution equations describing how the liquid-air and liquid-solid interfaces evolve in space and time are derived and solved numerically. Parametric studies are conducted to investigate the effects of solid thickness, viscosity, shear modulus, and wettability on droplet spreading. Softer substrates are found to speed up spreading for perfectly wetting droplets but slow down spreading for partially wetting droplets. For perfectly wetting droplets, faster spreading is a result of more liquid being pumped toward the contact line due to a larger liquid-film thickness there arising from the repulsive component of the disjoining pressure. In contrast, slower spreading of partially wetting droplets is a result of less liquid being pumped toward the contact line due to a smaller liquid-film thickness there arising from the attractive component of the disjoining pressure. The model predictions for partially wetting droplets are qualitatively consistent with experimental observations, and allow us to disentangle the effects of substrate deformability and wettability on droplet spreading. Due to its systematic formulation, our model can readily be extended to more complex situations involving multiple droplets, substrate inclination, and droplet phase changes.

Self-Assembly of Ordered Microparticle Monolayers from Drying a Droplet on a Liquid Substrate

Drying droplets on solid substrates has always formed a nonuniform and disordered "coffee ring" stain, which has a great negative effect on the application of inject printing and colloidal assembly. We obtain a macrouniform and micro-ordered pattern through evaporation of a colloidal droplet resting on a liquid substrate. The evaporative convection and the capillary forces were responsible for the formation of the ordered structures, which assembled into a monolayer pattern at the liquid-air interface under the action of the weak capillary flow and shrinkage of the triple line. The central bump deposits with disordered particle stacking on the liquid-liquid interface could be attributed to the fast meeting of the descending particles (gravitational sedimentation) and ascending liquid-liquid interface; they would scatter on the ordered monolayer structure and form the final uniform pattern.

Size-based analysis of extracellular vesicles using sequential transfer of an evaporating droplet

We report spatial separation of extracellular vesicle (EVs) populations based on particle size by using an approach that exploits Marangoni flow and the coffee-ring effect in microdroplets. Sequential transfer of a drying droplet progressively increases the mean size of EVs in the sample by repeated subsampling of a droplet during coffee-ring formation. This method allows size-based sorting, separation, and eventual retrieval of EVs for RNA and protein analysis. To demonstrate the biomedical relevance of this method, EVs from prostate cancer patients were analyzed; results revealed that the expression of cancer-associated genes and proteins was higher in small EVs than in large EVs. This ability to sort EVs using a combination of coffee ring with Marangoni flow and sequential droplet-transfer allows analysis of subpopulations of EVs, and will facilitate further studies of EVs.

Biofluid spectroscopic disease diagnostics: A review on the processes and spectral impact of drying

The complex patterns observed from evaporated liquid drops have been examined extensively over the last 20 years. Complete understanding of drop deposition is vital in many medical processes, and one which is essential to the translation of biofluid spectroscopic disease diagnostics. The promising use of spectroscopy in disease diagnosis has been hindered by the complicated patterns left by dried biological fluids which may inhibit the clinical translation of this technology. Coffee-ring formation, cracking and gelation patterns have all been observed in biofluid drops, and with surface homogeneity being a key element to many spectroscopic techniques, experimental issues have been found to arise. A better understanding of the fundamental processes involved in a drying droplet could allow efficient progression in this research field, and ultimately benefit the population with the development of a reliable cancer diagnostic.

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.

Modulation of Spatiotemporal Particle Patterning in Evaporating Droplets: Applications to Diagnostics and Materials Science

Spatiotemporal particle patterning in evaporating droplets lacks a common design framework. Here, we demonstrate autonomous control of particle distribution in evaporating droplets through the imposition of a salt-induced self-generated electric field as a generalized patterning strategy. Through modeling, a new dimensionless number, termed "capillary-phoresis" (CP) number, arises, which determines the relative contributions of electrokinetic and convective transport to pattern formation, enabling one to accurately predict the mode of particle assembly by controlling the spontaneous electric field and surface potentials. Modulation of the CP number allows the particles to be focused in a specific region in space or distributed evenly. Moreover, starting with a mixture of two different particle types, their relative placement in the ensuing pattern can be controlled, allowing coassemblies of multiple, distinct particle populations. By this approach, hypermethylated DNA, prevalent in cancerous cells, can be qualitatively distinguished from normal DNA of comparable molecular weights. In other examples, we show uniform dispersion of several particle types (polymeric colloids, multiwalled carbon nanotubes, and molecular dyes) on different substrates (metallic Cu, metal oxide, and flexible polymer), as dictated by the CP number. Depending on the particle, the highly uniform distribution leads to surfaces with a lower sheet resistance, as well as superior dye-printed displays.

Drying of Droplets of Colloidal Suspensions on Rough Substrates

In many technological applications, excess solvent must be removed from liquid droplets to deposit solutes onto substrates. Often, the substrates on which the droplets rest may possess some roughness, either intended or unintended. Motivated by these observations, we present a lubrication-theory-based model to study the drying of droplets of colloidal suspensions on a substrate containing a topographical defect. The model consists of a system of one-dimensional partial differential equations accounting for the shape of the droplet and depth-averaged concentration of colloidal particles. A precursor film and disjoining pressure are used to describe the contact-line region, and evaporation is included using the well-known one-sided model. Finite-difference solutions reveal that when colloidal particles are absent, the droplet contact line can pin to a defect for a significant portion of the drying time due to a balance between capillary-pressure gradients and disjoining-pressure gradients. The time-evolution of the droplet radius and contact angle exhibits the constant-radius and constant-contact-angle stages that have been observed in prior experiments. When colloidal particles are present and the defect is absent, the model predicts that particles will be deposited near the center of the droplet in a cone-like pattern. However, when a defect is present, pinning of the contact-line accelerates droplet solidification, leading to particle deposition near the droplet edge in a coffee-ring pattern. These predictions are consistent with prior experimental observations, and illustrate the critical role contact-line pinning plays in controlling the dynamics of drying droplets.

Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation

The evaporation of a liquid drop on a solid substrate is a remarkably common phenomenon. Yet, the complexity of the underlying mechanisms has constrained previous studies to spherically symmetric configurations. Here we investigate well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a universal scaling law for the evaporation rate valid for any shape and demonstrate that more curved regions lead to preferential localized depositions in particle-laden drops. Furthermore, geometry induces well-defined flow structures within the drop that change according to the driving mechanism. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. Our results suggest that the drop geometry can be exploited to prescribe the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops, which may be of interest to a wide range of industrial and scientific applications.

Drop evaporation can be used as a fabrication technology for targeted particle deposition or microflow control, yet previous research is limited to spherical drops. Here, Sáenz et al. generalize the evaporation dynamics for arbitrary drop geometry and show its potential for more sophisticated control.

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.

Evaporation of Sessile Droplets Laden with Particles and Insoluble Surfactants

We consider the flow dynamics of a thin evaporating droplet in the presence of an insoluble surfactant and noninteracting particles in the bulk. On the basis of lubrication theory, we derive a set of evolution equations for the film height, the interfacial surfactant, and bulk particle concentrations, taking into account the dependence of liquid viscosity on the local particle concentration. An important ingredient of our model is that it takes into account the fact that the surfactant adsorbed at the interface hinders evaporation. We perform a parametric study to investigate how the presence of surfactants affects the evaporation process as well as the flow dynamics with and without the presence of particles in the bulk. Our numerical calculations show that the droplet lifetime is affected significantly by the balance between the ability of the surfactant to enhance spreading, suppressing the effect of thermal Marangoni stresses-induced motion, and to hinder the evaporation flux through the reduction of the effective interfacial area of evaporation, which tend to accelerate and decelerate the evaporation process, respectively. For particle-laden droplets and in the case of dilute solutions, the droplet lifetime is found to be weakly dependent on the initial particle concentration. We also show that the particle deposition patterns are influenced strongly by the direct effect of the surfactant on the evaporative flux; in certain cases, the "coffee-stain" effect is enhanced significantly. A discussion of the delicate interplay between the effects of capillary pressure and solutal and thermal Marangoni stresses, which drive the liquid flow inside of the evaporating droplet giving rise to the observed results, is provided herein.

Spreading of Thin Droplets of Perfect and Leaky Dielectric Liquids on Inclined Surfaces

The spreading of droplets may be influenced by electric fields, a situation that is relevant to applications such as coating, printing, and microfluidics. In this work we study the effects of an electric field on the gravity-driven spreading of two-dimensional droplets down an inclined plane. We consider both perfect and leaky dielectric liquids, as well as perfectly and partially wetting systems. In addition to the effects of electric fields, we examine the use of thermocapillary forces to suppress the growth of the capillary ridge near the droplet front. Lubrication theory is applied to generate a set of coupled partial differential equations for interfacial height and charge, which are then solved numerically with a finite-difference method. Electric fields increase the height of the capillary ridge in both perfect and leaky dielectric droplets due to electrostatic pressure gradients that drive liquid into the ridge. In leaky dielectrics, large interfacial charge gradients in the contact-line region create shear stresses that also enhance ridge growth and the formation of trailing minor ridges. The coalescence of these ridges can significantly affect the long-time thinning rate of leaky dielectric droplets. In partially wetting liquids, electric fields promote the splitting of smaller droplets from the primary droplet near the receding contact line due to the interplay between electrostatic forces and disjoining pressure. Cooling from below and heating from above generates thermocapillary forces that counteract the effects of electric fields and suppress the growth of the capillary ridge. The results of this work have important implications for manipulating the spreading of droplets down inclined surfaces.

Electrowetting Controls the Deposit Patterns of Evaporated Salt Water Nanodroplets

So-called "coffee-ring" stains are the deposits remaining after complete evaporation of droplets containing nonvolatile solutes. In this paper we use molecular dynamics to simulate the evaporation of salt water nanodroplets in the presence of an applied electric field. We demonstrate, for the first time, that electrowetted nanodroplets can produce various deposit patterns, which vary substantially from the original ringlike deposit that occurs when there is no electric field. If a direct current (dc) electric field with strength greater than 0.03 V/Å is imposed parallel to the surface, after the water evaporates the salt crystals form a deposit on the substrate in a ribbon pattern along the field direction. However, when an alternating current (ac) electric field is applied the salt deposit patterns can be either ringlike or clump, depending on the strength and frequency of the applied ac field. We find that an ac field of high strength and low frequency facilitates the regulation of the deposit patterns: the threshold electric field strength for the transition from ringlike to clump is approximately 0.006 V/Å. These findings have potential application in fabricating nanostructures and surface coatings with desired patterns.

Elimination of Coffee-Ring Formation by Humidity Cycling: A Numerical Study

Periodically switching between evaporation and condensation, or "humidity cycling", has potential for controlling the film shape that results from volatile droplets containing a nonvolatile material. It does not require adaptation of material properties nor the introduction of an external field to achieve a change in film shape. It was shown experimentally by Doi and coworkers [Kajiya et al. Langmuir 2010, 26, pp 10429-10432] that ring-shaped deposits can be removed through careful selection of the atmospheric conditions. We present a model, based on lubrication theory, that can predict the final film shape resulting from the humidity cycling process. We confirm that the refluidization of gelled regions during condensation and the subsequent inward flow is the mechanism responsible for the improved profiles. Furthermore, we find that an increase in the time spent condensing to that spent evaporating results in flatter films and that an optimal humidity cycling frequency exists.

Acoustic suppression of the coffee-ring effect

We study the influence of acoustic fields on the evaporative self-assembly of solute particles suspended inside sessile droplets of complex fluids. The self-assembly process often results in an undesirable ring-like heterogeneous residue, a phenomenon known as the coffee-ring effect. Here we show that this ring-like self-assembly can be controlled acoustically to form homogeneous disc-like or concentrated spot-like residues. The principle of our method lies in the formation of dynamic patterns of particles in acoustically excited droplets, which inhibits the evaporation-driven convective transport of particles towards the contact line. We elucidate the mechanisms of this pattern formation and also obtain conditions for the suppression of the coffee-ring effect. Our results provide a more general solution to suppress the coffee-ring effect without any physiochemical modification of the fluids, the particles or the surface, thus potentially useful in a broad range of industrial and analytical applications that require homogenous solute depositions.

The impact of trough geometry on film shape. A theoretical study of droplets containing polymer, for P-OLED display applications

For P-OLED display fabrication, it is important to control the final film shape, arising from drying of volatile droplets containing polymer. Due to peripheral pinning and subsequent outward capillary flow, a coffee-ring typically develops. This is inconvenient since a spatially uniform height, above the substrate, is required to ensure uniform current across the device. Typically the droplets are deposited inside a trough-like structure on the substrate. We present a thin-film lubrication model that tracks the drying dynamics through to the final film shape. The governing equations are derived and solved numerically. We investigate the effect of the trough's depth and the slope of the walls. Increasing the depth or the wall's gradient increases coffee-ring formation. This is due to an increase in horizontal velocity, caused by the substrate's shape as well as delayed gelation of the polymer. The latter allows the outward capillary flow to act for a longer time, before the height becomes fixed.

Sagging of evaporating droplets of colloidal suspensions on inclined substrates

A droplet of a colloidal suspension placed on an inclined substrate may sag under the action of gravity. Solvent evaporation raises the concentration of the colloidal particles, and the resulting viscosity changes may influence the sag of the droplet. To investigate this phenomenon, we have developed a mathematical model for perfectly wetting droplets based on lubrication theory and the rapid-vertical-diffusion approximation. Precursor films are assumed to be present, the colloidal particles are taken to be hard spheres, and particle and liquid dynamics are coupled through a concentration-dependent viscosity and diffusivity. Evaporation is assumed to be limited by how rapidly solvent molecules can transfer from the liquid to the vapor phase. The resulting one-dimensional system of nonlinear partial differential equations describing the evolution of the droplet height and particle concentration is solved numerically for a range of initial particle concentrations and substrate temperatures. The solutions reveal that the interaction between evaporation and non-Newtonian suspension rheology gives rise to several distinct regimes of droplet shapes and particle concentration distributions. The results provide insight into how evaporation and suspension rheology can be tuned to minimize sagging as well as the well-known coffee-ring effect, an outcome which is important for industrial coating processes.