Diffusiophoretic Transport of Charged Colloids in Ionic Surfactant Gradients Entirely below versus Entirely above the Critical Micelle Concentration.

When placed in an ionic surfactant gradient, charged colloids will undergo diffusiophoresis at a velocity, uDP = MDP∇ ln S, where MDP is the diffusiophoretic mobility and S is the surfactant concentration. The diffusiophoretic mobility depends in part on the charges and diffusivities of the surfactants and their counterions. Since micellization decreases surfactant diffusivity and alters charge distributions in a surfactant solution, MDP of charged colloids in ionic surfactant gradients may differ significantly when surfactant concentrations are above or below the critical micelle concentration (CMC). The role of micelles in driving diffusiophoresis is unclear, and a previously published model that accounts for micellization suggests the possibility of a change in the sign of MDP above the CMC [Warren, P. B.; . Soft Matter 2019, 15, 278-288]. In the current study, microfluidic channels were used to measure the transport of negatively charged polystyrene colloids in sodium dodecyl sulfate (SDS) surfactant gradients established at SDS concentrations that are either fully above or fully below the CMC. Interpretation of diffusiophoresis was aided by measurements of the colloid electrophoretic mobility as a function of SDS concentration. A numerical transport model incorporating the prior diffusiophoretic mobility model for ionic surfactant gradients was implemented to elucidate signatures of positive and negative diffusiophoretic mobilities and compare with experiments. The theoretically predicted sign of the diffusiophoretic mobility below the CMC was determined to be particularly sensitive to uncertainty in colloid and surfactant properties, while above the CMC, the mobility was consistently predicted to be positive in the SDS concentration range considered in the experiments conducted here. In contrast, experiments only showed signatures of a negative diffusiophoretic mobility for these negatively charged colloids with no change of sign. Colloid diffusiophoretic transport measured in micellar solutions was more extensive than that below the CMC with the same ∇ ln S.

A multiple-timing analysis of temporal ratcheting.

We develop a two-timing perturbation analysis to provide quantitative insights on the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies ω and α ω , where α is a rational number. If α is a ratio of odd and even integers (e.g., 2 1 , 3 2 , 4 3 ), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order perturbation solution predicts the existence of temporal ratchets for α = 2 . Furthermore, we demonstrate, for a reduced model, that the temporal ratcheting effect for α = 3 2 and 4 3 appears at the third-order perturbation solution. More importantly, we find closed-form formulas for the magnitude and direction of the induced net velocities for these α values. On a broader scale, our methodology offers a new mathematical approach to study the complicated nature of temporal ratchets in physical systems.

Self-organized Patterns in Non-reciprocal Active Droplet Systems.

Non-equilibrium patterns are widespread in nature and often arise from the self-organization of constituents through nonreciprocal chemotactic interactions. In this study, we demonstrate how active oil-in-water droplet mixtures with predator-prey interactions can result in a variety of self-organized patterns. By manipulating physical parameters, the droplet diameter ratio and number ratio, we identify distinct classes of patterns within a binary droplet system, rationalize the pattern formation, and quantify motilities. Experimental results are recapitulated in numerical simulations using a minimal computational model that solely incorporates chemotactic interactions and steric repulsion among the constituents. The time evolution of the patterns is investigated and chemically explained. We also investigate how patterns vary with differing interaction strength by altering surfactant composition. Leveraging insights from the binary droplet system, the framework is extended to a ternary droplet mixture composed of multiple chasing droplet pairs to create chemically directed hierarchical organization. Our findings demonstrate how rationalizable, self-organized patterns can be programmed in a chemically minimal system and provide the basis for exploration of emergent organization and higher order complexity in active colloids.

Characterization of the Nonlinear Electrophoretic Behavior of Colloidal Particles in a Microfluidic Channel.

Contemporary findings in the field of insulator-based electrokinetics have demonstrated that in systems under the influence of direct current (DC) fields, dielectrophoresis (DEP) is not the main electrokinetic mechanism responsible for particle manipulation but rather the sum of electroosmosis, linear and nonlinear electrophoresis. Recent microfluidic studies have brought forth a methodology capable of experimentally estimating the nonlinear electrophoretic mobility of colloidal particles. This methodology, however, is limited to particles that fit two conditions: (i) the particle charge has the same sign as the channel wall charge and (ii) the magnitude of the particle ζ-potential is lower than that of the channel wall. The present work aims to expand upon this methodology by including particles whose ζ-potential has a magnitude larger than that of the wall, referred to as "type 2" particles, as well as to report findings on particles that appear to still be under the influence of the linear electrophoretic regime even at extremely high electric fields (∼6000 V/cm), referred to as "type 3" particles. Our findings suggest that both particle size and charge are key parameters in the determination of nonlinear electrophoretic properties. Type 2 microparticles were all found to be small (diameter ∼ 1 µm) and highly charged, with ζ-potentials above -60 mV; in contrast, type 3 microparticles were all large with ζ-potentials between -40 and -50 mV. However, it was also hypothesized that other nonconsidered parameters could be influencing the results, especially at higher electric fields (>3000 V/cm). The present work also aims to identify the current limitations in the experimental determination of µEP,NL and propose a framework for future work to address the current gaps in the evolving topic of nonlinear electrophoresis of colloidal particles.

Effect of speed fluctuations on the collective dynamics of active disks.

Numerical simulations are performed on the collective dynamics of active disks, whose self-propulsion speed (U) varies in time, and whose orientation evolves according to rotational Brownian motion. Two protocols for the evolution of speed are considered: (i) a deterministic one involving a periodic change in U at a frequency ω; and (ii) a stochastic one in which the speeds are drawn from a power-law distribution at time-intervals governed by a Poissonian process of rate ß. In the first case, an increase in ω causes the disks to go from a clustered state to a homogeneous one through an apparent phase-transition, provided that the direction of self-propulsion is allowed to reverse. Similarly, in the second case, for a fixed value of ß, the extent of cluster-breakup is larger when reversals in the self-propulsion direction are permitted. Motility-induced phase separation of the disks may therefore be avoided in active matter suspensions in which the constituents are allowed to reverse their self-propulsion direction, immaterial of the precise temporal nature of the reversal (deterministic or stochastic). Equally, our results demonstrate that phase separation could occur even in the absence of a time-averaged motility of an individual active agent, provided that the rate of direction reversals is smaller than the orientational diffusion rate.

Nonequilibrium structure formation in electrohydrodynamic emulsions.

Application of an electric field across the interface of two fluids with low, but non-zero, conductivities gives rise to a sustained electrohydrodynamic (EHD) fluid flow. In the presence of neighboring drops, drops interact via the EHD flows of their neighbors, as well as through a dielectrophoretic (DEP) force, a consequence of drops encountering disturbance electric fields around their neighbors. We explore the collective dynamics of emulsions with drops undergoing EHD and DEP interactions. The interplay between EHD and DEP results in a rich set of emergent behaviors. We simulate the collective behavior of large numbers of drops; in two dimensions, where drops are confined to a plane; and three dimensions. In monodisperse emulsions, drops in two dimensions cluster or crystallize depending on the relative strengths of EHD and DEP, and form spaced clusters when EHD and DEP balance. In three dimensions, chain formation observed under DEP alone is suppressed by EHD, and lost entirely when EHD dominates. When a second population of drops are introduced, such that the electrical conductivity, permittivity, or viscosity are different from the first population of drops, the interaction between the drops becomes non-reciprocal, an apparent violation of Newton's Third Law. The breadth of consequences due to these non-reciprocal interactions are vast: we show selected cases in two dimensions, where drops cluster into active dimers, trimers, and larger clusters that continue to translate and rotate over long timescales; and three dimensions, where drops form stratified chains, or combine into a single dynamic sheet.

Tuning chemotactic and diffusiophoretic spreading via hydrodynamic flows.

The transport of microorganisms by chemotaxis is described by the same "log-sensing" response as colloids undergoing diffusiophoresis, despite their different mechanistic origins. We employ a recently-developed macrotransport theory to analyze the advective-diffusive transport of a chemotactic or diffusiophoretic colloidal species (both referred to as "colloids") in a circular tube under a steady pressure-driven flow (referred to as hydrodynamic flow) and transient solute gradient. First, we derive an exact solution to the log-sensing chemotactic/diffusiophoretic macrotransport equation. We demonstrate that a strong hydrodynamic flow can reduce spreading of solute-repelled colloids, by eliminating super-diffusion which occurs in an otherwise quiescent system. In contrast, hydrodynamic flows always enhance spreading of solute-attracted colloids. Second, we generalize the exact solution to show that the above tunable spreading phenomena by hydrodynamic flows persist quantitatively for decaying colloids, as may occur with cell death, for example. Third, we examine the spreading of chemotactic colloids by employing a more general model that captures a hallmark of chemotaxis, that log-sensing occurs only over a finite range of solute concentration. Apart from demonstrating for the first time the generality of the macrotransport theory to incorporate an arbitrary chemotactic flow model, we reveal via numerical solutions new regimes of anomalous spreading, which match qualitatively with experiments and are tunable by hydrodynamic flows. The results presented here could be employed to tailor chemotactic/diffusiophoretic colloid transport using hydrodynamic flows, which are central to applications such as oil recovery and bioremediation of aquifers.

Diffusiophoresis of charged colloidal particles in the limit of very high salinity.

Diffusiophoresis is the migration of a colloidal particle through a viscous fluid, caused by a gradient in concentration of some molecular solute; a long-range physical interaction between the particle and solute molecules is required. In the case of a charged particle and an ionic solute (e.g., table salt, NaCl), previous studies have predicted and experimentally verified the speed for very low salt concentrations at which the salt solution behaves ideally. The current study presents a study of diffusiophoresis at much higher salt concentrations (approaching the solubility limit). At such large salt concentrations, electrostatic interactions are almost completely screened, thus eliminating the long-range interaction required for diffusiophoresis; moreover, the high volume fraction occupied by ions makes the solution highly nonideal. Diffusiophoretic speeds were found to be measurable, albeit much smaller than for the same gradient at low salt concentrations.

Interfacially-adsorbed particles enhance the self-propulsion of oil droplets in aqueous surfactant.

Understanding the chemo-mechanical mechanisms that direct the motion of self-propulsive colloids is important for the development of active materials and exploration of dynamic, collective phenomena. Here, we demonstrate that the adsorption of solid particles on the surface of solubilizing oil droplets can significantly enhance the droplets' self-propulsion speeds. We investigate the relationship between the self-propulsion of bromodecane oil droplets containing silica particles of varying concentration in Triton X-100 surfactant, noting up to order of magnitude increases in propulsion speeds. Using fluorescently labeled silica, we observe packing of the particles at the oil-water interfaces of the rear pole of the moving droplets. For bromodecane oil droplets in Triton X-100, the highest droplet speeds were achieved at approximately 40% particle surface coverage of the droplet interface. We find particle-assisted propulsion enhancement in ionic surfactants and different oil droplet compositions as well, demonstrating the breadth of this effect. While a precise mechanism for the propulsion enhancement remains unclear, the simple addition of silica particles to droplet oil-water interfaces provides a straightforward route to tune active droplet dynamics.

Advective-diffusive spreading of diffusiophoretic colloids under transient solute gradients.

We analytically calculate the one-dimensional advective-diffusive spreading of a point source of diffusiophoretic (DP) colloids, driven by the simultaneous diffusion of a Gaussian solute patch. The spreading of the DP colloids depends critically on the ratio of the DP mobility, M (which can be positive or negative), to the solute diffusivity, Ds. For instance, we demonstrate, for the first time, that solute-repelling colloids (M < 0) undergo long-time super-diffusive transport for M/Ds < -1. In contrast, the spreading of strongly solute-attracting colloids (M/Ds≫ 1) can be spatially arrested over long periods on the solute diffusion timescale, due to a balance between colloid diffusion and DP under the evolving solute gradient. Further, a patch of the translating solute acts as a "shuttle" that rapidly transports the colloids relative to their diffusive timescale. Finally, we use numerical computations to show that the above behaviors persist for three-dimensional, radially symmetric DP spreading. The results presented here could guide the use of DP colloids for microscale particle sorting, deposition, and delivery.

The lift force on a charged sphere that translates and rotates in an electrolyte.

The distortion of the charge cloud around a uniformly charged, dielectric, rigid sphere that translates and rotates in an unbounded binary, symmetric electrolyte at zero Reynolds number is examined. The zeta potential of the particle ζ is assumed small relative to the thermal voltage scale. It is assumed that the equilibrium structure of the cloud is slightly distorted, which requires that the Péclet numbers characterizing distortion due to particle translation, Pet=Ua/D , and rotation, Per=Ωa2/D , are small compared to unity. Here, a is radius of the particle; D is the ionic diffusion coefficient; U=|U| and Ω=|Ω| , where U and Ω are the rectilinear and angular velocities of the particle, respectively. Perturbation expansions for small Pet and Per are employed to calculate the nonequilibrium structure of the cloud, whence the force and torque on the particle are determined. In particular, we predict that the sphere experiences a force orthogonal to its directions of translation and rotation. This "lift" force arises from the nonlinear distortion of the cloud under the combined actions of particle translation and rotation. The lift force is given by Flift=L(κa)(εa3ζ2/D2)U×Ω[1+O(Pet,Per)] . Here, ε is the permittivity of the electrolyte; κ-1 is the Debye length; and L(κa) is a negative function that decreases in magnitude with increasing κa . The lift force implies that an unconstrained particle would follow a curved path; an electrokinetic analog of the inertial Magnus effect. Finally, the implication of the lift force on cross-streamline migration of an electrophoretic particle in shear flow is discussed.

Strong Deformation of the Thick Electric Double Layer around a Charged Particle during Sedimentation or Electrophoresis.

The deformation of the electric double layer around a charged colloidal particle during sedimentation or electrophoresis in a binary, symmetric electrolyte is studied. The surface potential of the particle is assumed to be small compared to the thermal voltage scale. Additionally, the Debye length is assumed to be large compared to the particle size. These assumptions enable a linearization of the electrokinetic equations. The particle appears as a point charge in this thick-double-layer limit; the distribution of charge in the diffuse cloud surrounding it is determined by a balance of advection due to the particle motion, Brownian diffusion of ions, and electrostatic screening of the particle by the cloud. The ability of advection to deform the charge cloud from its equilibrium state is parametrized by a Péclet number, Pe. For weak advection (Pe ≪ 1), the cloud is only slightly deformed. In contrast, the cloud can be completely stripped from the particle at Pe ≫ 1; consequently, electrokinetic effects on the particle motion vanish in this regime. Therefore, in sedimentation the drag limits to Stokes' law for an uncharged particle as Pe → ∞. Likewise, the particle velocity for electrophoresis approaches Huckel's result. The strongly deformed cloud at large Pe is predicted to generate a concomitant increase in the sedimentation field in a dilute settling suspension.

Role of Stefan-Maxwell fluxes in the dynamics of concentrated electrolytes.

This theoretical analysis quantifies the effect of coupled ionic fluxes on the charging dynamics of an electrochemical cell. We consider a model cell consisting of a concentrated, binary electrolyte between parallel, blocking electrodes, under a suddenly applied DC voltage. It is assumed that the magnitude of the applied voltage is small compared to the thermal voltage scale, RT/F, where R is the universal gas constant, T is the temperature and F is the Faraday's constant. We employ the Stefan-Maxwell equations to describe the hydrodynamic coupling of ionic fluxes that arise in concentrated electrolytes. These equations inherently account for asymmetry in the mobilities of the ions in the electrolyte. A modified set of Poisson-Nernst-Planck equations, obtained by incorporating Stefan-Maxwell fluxes into the species balances, are formulated and solved in the limit of weak applied voltages. A long-time asymptotic analysis reveals that the electrolyte dynamics occur on two distinct time scales. The first is a faster "RC" time, τRC = κ-1L/DE, where κ-1 is the Debye length, L is the length of the half-cell, and DE is an effective diffusivity, which characterizes the evolution of charge density at the electrode. The effective diffusivity, DE, is a function of the ambi-polar diffusivity of the salt, Da, as well as a cross-diffusivity, D+-, of the ions. This time scale also dictates the initial exponential decay of current in the external circuit. At times longer than τRC, the external current again decays exponentially on a slower, diffusive time scale, τD∼L2/Da, where Da is the ambi-polar diffusivity of the salt. This diffusive time scale is due to the unequal ion mobilities that result in a non-uniform bulk concentration of the salt during the charging process. Finally, we propose an approach by which our theory may be used to measure the cross-diffusivity in concentrated electrolytes.

Colloidal stability dictates drop breakup under electric fields.

Electric fields can deform drops of fluid from their equilibrium shape, and induce breakup at sufficiently large field strengths. In this work, the electric field induced breakup of a squalane drop containing a colloidal suspension of carbon black particles with polyisobutylene succinimide (OLOA 11000) surfactant is studied. The drop is suspended in silicone oil. The breakup mode of a drop containing carbon black depends strongly on the suspension stability. It is observed that a drop of a stable suspension of carbon black has the same breakup mode as a drop with surfactant alone, i.e., without added carbon black. At lower electric fields, these drops break by the formation of lobes at the two ends of the drop; and at higher fields the homogeneous lobes break in a non-axisymmetric manner. However, a drop of an unstable suspension shows a drastically different breakup mode, and undergoes breakup much faster compared to a drop with surfactant alone. These drops elongate and form asymmetric lobes that develop into fingers and eventually disintegrate in an inhomogeneous, three-dimensional fashion. As a basis for comparison, the breakup of a pure squalane drop, and a squalane drop with equivalent surfactant concentrations but no carbon black particles is examined. Axisymmetric boundary integral computations are used to elucidate the mechanism of breakup. Our work demonstrates the impact of colloidal stability on the breakup of drops under an electric field. Colloidal stability on the time scale of drop deformation leads to rich and unexplored breakup phenomena.

A mathematical model for electrical impedance spectroscopy of zwitterionic hydrogels.

We report a mathematical model for ion transport and electrical impedance in zwitterionic hydrogels, which possess acidic and basic functional groups that carry a net charge at a pH not equal to the isoelectric point. Such hydrogels can act as an electro-mechanical interface between a relatively hard biosensor and soft tissue in the body. For this application, the electrical impedance of the hydrogel must be characterized to ensure that ion transport to the biosensor is not significantly hindered. The electrical impedance is the ratio of the applied voltage to the measured current. We consider a simple model system, wherein an oscillating voltage is applied across a hydrogel immersed in electrolyte and sandwiched between parallel, blocking electrodes. We employ the Poisson-Nernst-Planck (PNP) equations coupled with acid-base dissociation reactions for the charge on the hydrogel backbone to model the ionic transport across the hydrogel. The electrical impedance is calculated from the numerical solution to the PNP equations and subsequently analyzed via an equivalent circuit model to extract the hydrogel capacitance, resistance, and the capacitance of electrical double layers at the electrode-hydrogel interface. For example, we predict that an increase in pH from the isoelectric point, pH = 6.4 for a model PCBMA hydrogel, to pH = 8 reduces the resistance of the hydrogel by ∼40% and increases the double layer capacitance by ∼250% at an electrolyte concentration of 0.1 mM. The significant impact of charged hydrogel functional groups to the impedance is damped at higher electrolyte concentration.

Non-Brownian diffusion and chaotic rheology of autophoretic disks.

The dynamics of a two-dimensional autophoretic disk is quantified as a minimal model for the chaotic trajectories undertaken by active droplets. Via direct numerical simulations, we show that the mean-square displacement of the disk in a quiescent fluid is linear at long times. Surprisingly, however, this apparently diffusive behavior is non-Brownian, owing to strong cross correlations in the displacement tensor. The effect of a shear flow field on the chaotic motion of an autophoretic disk is examined. Here, the stresslet on the disk is chaotic for weak shear flows; a dilute suspension of such disks would exhibit a chaotic shear rheology. This chaotic rheology is quenched first into a periodic state and ultimately a steady state as the flow strength is increased.

Poisson-Nernst-Planck framework for modelling ionic strain and temperature sensors.

Ionically conductive hydrogels are gaining traction as sensing and structural materials for use bioelectronic devices. Hydrogels that feature large mechanical compliances and tractable ionic conductivities are compelling materials that can sense physiological states and potentially modulate the stimulation of excitable tissue because of the congruence in electro-mechanical properties across the tissue-material interface. However, interfacing ionic hydrogels with conventional DC voltage-based circuits poses several technical challenges including electrode delamination, electrochemical reaction, and drifting contact impedance. Utilizing alternating voltages to probe ion-relaxation dynamics has been shown to be a viable alternative for strain and temperature sensing. In this work, we present a Poisson-Nernst-Planck theoretical framework to model ion transport under alternating fields within conductors subject to varying strains and temperatures. Using simulated impedance spectra, we develop key insights about the relationship between frequency of the applied voltage perturbation and sensitivity. Lastly, we perform preliminary experimental characterization to demonstrate the applicability of the proposed theory. We believe this work provides a useful perspective that is applicable to the design of a variety of ionic hydrogel-based sensors for biomedical and soft robotic applications.

Effect of polymer/surfactant complexation on diffusiophoresis of colloids in surfactant concentration gradients.

HYPOTHESIS: A concentration gradient of surfactants in the presence of polymers that non-covalently associate with surfactants will exhibit a continually varying distribution of complexes with different composition, charge, and size. Since diffusiophoresis of colloids suspended in a solute concentration gradient depends on the relaxation of the gradient and on the interactions between solutes and particles, polymer/surfactant complexation will alter the rate of diffusiophoresis driven by surfactant gradients relative to that observed in the same concentration gradient in the absence of polymers. EXPERIMENTS: A microfluidic device was used to measure diffusiophoresis of colloids suspended in solutions containing a gradient of sodium dodecylsulfate (SDS) in the presence or absence of a uniform concentration of Pluronic P123 poly(ethylene oxide-b-propylene oxide-b-ethylene oxide) nonionic triblock copolymers. To interpret the effect of P123 on the rate of colloid diffusiophoresis, electrophoretic mobility and dynamic light scattering measurements of the colloid/solute systems were performed, and a numerical model was constructed to account for the effects of complexation on diffusiophoresis. FINDINGS: Polymer/surfactant complexation in solute gradients significantly enhanced diffusiophoretic transport of colloids. Large P123/SDS complexes formed at low SDS concentrations yielded low collective solute diffusion coefficients that prolonged the existence of strong concentration gradients relative to those without P123 to drive diffusiophoresis.

Gravitational settling of active droplets.

The gravitational settling of oil droplets solubilizing in an aqueous micellar solution contained in a capillary channel is investigated. The motion of these active droplets reflects a competition between gravitational and Marangoni forces, the latter due to interfacial tension gradients generated by differences in filled-micelle concentrations along the oil-water interface. This competition is studied by varying the surfactant concentration, the density difference between the droplet and the continuous phase, and the viscosity of the continuous phase. The Marangoni force enhances the settling speed of an active droplet when compared to the Hadamard-Rybczynski prediction for a (surfactant free) droplet settling in Stokes flow. The Marangoni force can also induce lateral droplet motion, suggesting that the Marangoni and gravitational forces are not always aligned. The decorrelation rate (α) of the droplet motion, measured as the initial slope of the velocity autocorrelation and indicative of the extent to which the Marangoni and gravitational forces are aligned during settling, is examined as a function of the droplet size: correlated motion (small values of α) is observed at both small and large droplet radii, whereas significant decorrelation can occur between these limits. This behavior of active droplets settling in a capillary channel is in marked contrast to that observed in a dish, where the decorrelation rate increases with the droplet radius before saturating at large values of droplet radius. A simple relation for the crossover radius at which the maximal value of α occurs for an active settling droplet is proposed.

Gelatin-Based Ingestible Impedance Sensor to Evaluate Gastrointestinal Epithelial Barriers.

Low-profile and transient ingestible electronic capsules for diagnostics and therapeutics can replace widely used yet invasive procedures such as endoscopies. Several gastrointestinal diseases such as reflux disease, Crohn's disease, irritable bowel syndrome, and eosinophilic esophagitis result in increased intercellular dilation in epithelial barriers. Currently, the primary method of diagnosing and monitoring epithelial barrier integrity is via endoscopic tissue biopsies followed by histological imaging. Here, a gelatin-based ingestible electronic capsule that can monitor epithelial barriers via electrochemical impedance measurements is proposed. Toward this end, material-specific transfer printing methodologies to manufacture soft-gelatin-based electronics, an in vitro synthetic disease model to validate impedance-based sensing, and tests of capsules using ex vivo using porcine esophageal tissue are described. The technologies described herein can advance next generation of oral diagnostic devices that reduce invasiveness and improve convenience for patients.