Solute Concentration Gradients Research Articles

Harnessing elastic instabilities for enhanced mixing and reaction kinetics in porous media

Turbulent flows have been used for millennia to mix solutes; a familiar example is stirring cream into coffee. However, many energy, environmental, and industrial processes rely on the mixing of solutes in porous media where confinement suppresses inertial turbulence. As a result, mixing is drastically hindered, requiring fluid to permeate long distances for appreciable mixing and introducing additional steps to drive mixing that can be expensive and environmentally harmful. Here, we demonstrate that this limitation can be overcome just by adding dilute amounts of flexible polymers to the fluid. Flow-driven stretching of the polymers generates an elastic instability, driving turbulent-like chaotic flow fluctuations, despite the pore-scale confinement that prohibits typical inertial turbulence. Using in situ imaging, we show that these fluctuations stretch and fold the fluid within the pores along thin layers ("lamellae") characterized by sharp solute concentration gradients, driving mixing by diffusion in the pores. This process results in a [Formula: see text] reduction in the required mixing length, a [Formula: see text] increase in solute transverse dispersivity, and can be harnessed to increase the rate at which chemical compounds react by [Formula: see text]-enhancements that we rationalize using turbulence-inspired modeling of the underlying transport processes. Our work thereby establishes a simple, robust, versatile, and predictive way to mix solutes in porous media, with potential applications ranging from large-scale chemical production to environmental remediation.

The impact of membrane orientation on ion flux in bipolar membranes

Bipolar membranes (BPMs) are asymmetric, layered ion exchange membranes that are increasingly being explored for use in electrochemical devices. This study aims to investigate the effect that the direction of a diffusive driving force across a salt solution concentration gradient has on the flux through a BPM due to its asymmetric nature. BPMs were fabricated using PiperION poly(aryl piperidinium) A40 as the anion exchange layer (AEL) and Nafion 212 as the cation exchange layer (CEL) with no interfacial junction catalyst. The permeability of sodium chloride through the BPM membranes was measured across a 0.5molL-1 concentration differential for both orientations of the membrane, e.g. AEL facing the 0.5molL-1 NaCl solution versus the CEL facing the 0.5molL-1 NaCl solution. A flux differential of (76.3 ± 4.8)% was measured for the BPM depending on the direction of the driving force. A model based on Fick’s law and the Donnan equilibrium was developed and used to show that the flux differential results from changes in the ionic environment at the AEL–CEL junction due to differences in the ion diffusion coefficients and fixed charge concentrations of the two layers.

Diffusiophoretic Behavior of Polyelectrolyte-Coated Particles.

Diffusiophoresis, the movement of particles under a solute concentration gradient, has practical implications in a number of applications, such as particle sorting, focusing, and sensing. For diffusiophoresis in an electrolyte solution, the particle velocity is described by the electrolyte relative concentration gradient and the diffusiophoretic mobility of the particle. The electrolyte concentration, which typically varies throughout the system in space and time, can also influence the zeta potential of particles in space and time. This variation affects the diffusiophoretic behavior, especially when the zeta potential is highly dependent on the electrolyte concentration. In this work, we show that adsorbing a single bilayer (or 4 bilayers) of a polyelectrolyte pair (PDADMAC/PSS) on the surface of microparticles resulted in effectively constant zeta potential values with respect to salt concentration throughout the experimental range of salt concentrations. This allowed a constant potential model for diffusiophoretic transport to describe the experimental observations, which was not the case for uncoated particles in the same electrolyte system. This work highlights the use of simple polyelectrolyte pairs to tune the zeta potential and maintain constant values for precise control of diffusiophoretic transport.

Generation of shear flows in composite-structured nanochannels driven by solute concentration gradients

Generation of shear flows in composite-structured nanochannels driven by solute concentration gradients

Microfluidic-based human prostate-cancer-on-chip.

Lack of adequate models significantly hinders advances in prostate cancer treatment, where resistance to androgen-deprivation therapies and bone metastasis remain as major challenges. Current in vitro models fail to faithfully mimic the complex prostate physiology. In vivo animal models can shed light on the oncogenes involved in prostate cancer development and progression; however, the animal prostate gland is fundamentally different from that of human, and the underlying genetic mechanisms are different. To address this problem, we developed the first in vitro microfluidic human Prostate-Cancer-on-Chip (PCoC) model, where human prostate cancer and stromal fibroblast cells were co-cultivated in two channels separated by a porous membrane under culture medium flow. The established microenvironment enables soluble signaling factors secreted by each culture to locally diffuse through the membrane pores affecting the neighboring culture. We particularly explored the conversion of the stromal fibroblasts into cancer-associated fibroblasts (CAFs) due to the interaction between the 2cell types. Immunofluorescence microscopy revealed that tumor cells induced CAF biomarkers, αSMA and COL1A1, in stromal fibroblasts. The stromal CAF conversion level was observed to increase along the flow direction in response to diffusion agents, consistent with simulations of solute concentration gradients. The tumor cells also downregulated androgen receptor (AR) expression in stromal fibroblasts, while an adequate level of stromal AR expression is maintained in normal prostate homeostasis. We further investigated tumor invasion into the stroma, an early step in the metastatic cascade, in devices featuring a serpentine channel with orthogonal channel segments overlaying a straight channel and separated by an 8µm-pore membrane. Both tumor cells and stromal CAFs were observed to cross over into their neighboring channel, and the stroma's role seemed to be proactive in promoting cell invasion. As control, normal epithelial cells neither induced CAF conversion nor promoted cell invasion. In summary, the developed PCoC model allows spatiotemporal analysis of the tumor-stroma dynamic interactions, due to bi-directional signaling and physical contact, recapitulating tissue-level multicellular responses associated with prostate cancer in vivo. Hence, it can serve as an in vitro model to dissect mechanisms in human prostate cancer development and seek advanced therapeutic strategies.

A Novel Cellular Automata Framework for Modeling Depth-Averaged Solute Transport during Pluvial and Fluvial Floods

Currently, for modeling two-dimensional (2D) solute transport during pluvial and fluvial floods, the finite volume (FV) models are widely used because of their strong ability to handle steep concentration and velocity gradients from the flow advection term. However, heavy computational requirements are subsequently introduced which limit the numerical efficiency. To further increase numerical efficiency but keep the required accuracy, this study proposes a novel Solute Transport Modeling based on Cellular Automata framework (STMCA) to simulate solute transport due to the flow advection, turbulent diffusion, and material decay mechanisms in several sets of explicit algebraic equations. Four studied cases involving steep gradients of solute concentration and velocities in steady/unsteady violent flow conditions are used to compare the accuracy of the STMCA approach with a Godunov-type FV solute transport approach with a total variation diminishing (TVD) scheme. Then, the performances of the two approaches on water quality modeling are assessed through the E. Coli transport modeling during pluvial/fluvial floods on a real-scale terrain. The proposed STMCA approach is found to achieve almost the same accuracy as the FV approach. As to the numerical efficiency, the STMCA approach is faster than the FV approach by 289.6–328.6%. Hence, the proposed STMCA approach is proven to be an effective tool for simulating solute transport.

Concentration gradients probed in microfluidics by gate-array electrolyte organic transistor

We propose a device architecture termed gate-array electrolyte gated organic transistor (GA-EGOFET) that quantitatively measures the solute concentration gradient created in a spatially inhomogeneous solution, for instance a (biological) fluid. The integrated H-cell microfluidics yields a diffusive concentration profile along the microfluidics channel according to the flow rate of the input streams. We demonstrate this concept by monitoring the formation of self-assembly monolayers (SAMs) on top of an array of parallel Au gate electrodes exposed to a different local concentration of alkanethiols. The deposition rate and the coverage both increase from the entrance towards the H-cell end. The voltage change at each gate is transduced in the transfer curve acquired with the specific gate electrode. For short chain length SAMs (n = 3), the trend of the current hints to a diffusion-limited surface reaction. For longer thiols (n = 6, 9), instead, the slower surface diffusion or incorporation in the more stable and compact SAM yields a current that is independent of the longitudinal gradient. The microfluidics/GA-EGOFET platform is viable for constructing dose curves in reproducible manner and for validating different electrode functionalization strategies where the deposition rates are different at each substrate site.

Shocker─A Molecular Dynamics Protocol and Tool for Accelerating and Analyzing the Effects of Osmotic Shocks.

The process of osmosis, a fundamental phenomenon in life, drives water through a semipermeable membrane in response to a solute concentration gradient across this membrane. In vitro, osmotic shocks are often used to drive shape changes in lipid vesicles, for instance, to study fission events in the context of artificial cells. While experimental techniques provide a macroscopic picture of large-scale membrane remodeling processes, molecular dynamics (MD) simulations are a powerful tool to study membrane deformations at the molecular level. However, simulating an osmotic shock is a time-consuming process due to slow water diffusion across the membrane, making it practically impossible to examine its effects in classic MD simulations. In this article, we present Shocker, a Python-based MD tool for simulating the effects of an osmotic shock by selecting and relocating water particles across a membrane over the course of several pumping cycles. Although this method is primarily aimed at efficiently simulating volume changes in vesicles, it can also handle membrane tubes and double bilayer systems. Additionally, Shocker is force field-independent and compatible with both coarse-grained and all-atom systems. We demonstrate that our tool is applicable to simulate both hypertonic and hypotonic osmotic shocks for a range of vesicular and bilamellar setups, including complex multicomponent systems containing membrane proteins or crowded internal solutions.

Diffusioosmotic dispersion of solute in a long narrow channel

Solute–surface interactions have garnered considerable interest in recent years as a novel control mechanism for driving unique fluid dynamics and particle transport with potential applications in fields such as biomedicine, the development of microfluidic devices and enhanced oil recovery. In this study, we will discuss dispersion induced by the diffusioosmotic motion near a charged wall in the presence of a solute concentration gradient. Here, we introduce a plug of salt with a Gaussian distribution at the centre of a channel with no background flow. As the solute diffuses, the concentration gradient drives a diffusioosmotic slip flow at the walls, which results in a recirculating flow in the channel; this, in turn, drives an advective flux of the solute concentration. This effect leads to cross-stream diffusion of the solute, altering the effective diffusivity of the solute as it diffuses along the channel. We derive theoretical predictions for the solute dynamics using a multiple-time-scale analysis to quantify the dispersion driven by the solute–surface interactions. Furthermore, we derive a cross-sectionally averaged concentration equation with an effective diffusivity analogous to that from Taylor dispersion. In addition, we use numerical simulations to validate our theoretical predictions.

Programmable and Pixelated Solute Concentration Fields Controlled by Three-Dimensionally Networked Microfluidic Source/Sink Arrays.

Membrane-integrated microfluidic platforms have played a pivotal role in understanding natural phenomena coupled with solute concentration gradients at the micro- and nanoscale, enabling on-chip microscopy in well-defined planar concentration fields. However, the standardized two-dimensional fabrication schemes in microfluidics have impeded the realization of more complex and diverse chemical environmental conditions due to the limited possible arrangements of source/sink conditions in a fluidic domain. In this study, we present a microfluidic platform with a three-dimensional microchannel network design, where discretized membranes can be integrated and individually controlled in a two-dimensional array format at any location within the entire quasi-two-dimensional solute concentration field. We elucidate the principles of the device to implement operations of the pixel-like sources/sinks and dynamically programmable control of various long-lasting solute concentration fields. Furthermore, we demonstrate the application of the generated solute concentration fields in manipulating the transport of micrometer or submicrometer particles with a high degree of freedom, surpassing conventionally available solute concentration fields. This work provides an experimental tool for investigating complex systems under high-order chemical environmental conditions, thereby facilitating the extensive development of higher-performance micro- and nanotechnologies.

Diffusiophoresis-enhanced particle deposition for additive manufacturing.

The ability to govern particle assembly in an evaporative-driven additive manufacturing (AM) can realize multi-scale features fundamental to creating printed electronics. However, existing techniques remain challenging and often require templates or contaminating solutes. We explore the control of particle deposition in 3D-printed colloids by diffusiophoresis, a previously unexplored mechanism in multi-scale AM. Diffusiophoresis can introduce spontaneous phoretic particle motion by establishing local solute concentration gradients. We show that diffusiophoresis can play a dominant role in complex evaporative-driven particle assembly, enabling a fundamentally new and versatile control of particle deposition in a multi-scale AM process.

Exploring the Synergistic Effects of Dual‐Layer Electrodes for High Power Li‐Ion Batteries

AbstractThe electrification of the transport sector has created an increasing demand for lithium‐ion batteries that can provide high power intermittently while maintaining a high energy density. Given the difficulty in designing a single redox material with both high power and energy density, electrodes based on composites of several electroactive materials optimized for power or capacity are being studied extensively. Among others, fast‐charging LiFePO4 and high energy Li(NixMnyCoz)O2 are commonly employed in industrial cell manufacturing. This study focuses on comparing different approaches to combining these two active materials into a single electrode. These arrangements were compared using standard electrochemical (dis)charge procedures and using synchrotron X‐ray fluorescence to identify variations in solution concentration gradient formation. The electrochemical performance of the layered electrodes with the high‐power material on top is found to be enhanced relative to its blended electrode counterpart when (dis)charged at the same specific currents. These findings highlight dual‐layer lithium‐ion batteries as an inexpensive way of increasing energy and power density of lithium‐ion batteries as well as a model system to study and exploit the synergistic effects of blended electrodes.

Dynamics of Drop Formation in the Presence of Interfacial Mass Transfer.

The dynamics of drop formation have been investigated in the presence of interfacial mass transfer through controlled flow visualization experiments. The mixtures of n-hexane (solvent) and acetone (solute) were used as a dispersed phase, having different initial compositions varying over a broad range. Drops were formed at the submerged position in the continuous phase (water) at the same operating flow conditions. The unsteady force balance model is developed to analyze the implications of the simultaneously occurring interfacial transfer of the solute on the formation dynamics in real time, and predictions are validated with experimental results. Based on initial compositions, the analysis of the transient drop shape shows a sharp transition in the drop formation regime. At lower initial solute concentrations, i.e., ϕ0 < 0.2, axisymmetric drop formation occurs and the interfacial solute transfer has negligible effects on the formation dynamics. Over an intermediate range of solute concentrations, i.e., 0.2 < ϕ0 < 0.5, Marangoni instability is triggered along the evolving interface, and therefore, the interface deformations and contractions occur during the drop formation. At ϕ0 = 0.5, the drop takes highly nonaxisymmetric shapes and remains away from equilibrium until its detachment from an orifice. For ϕ0 > 0.5, the spontaneous ejection of plumes of the solute results in the rapid generation of multiple droplets of smaller size. This work shows that higher solute concentration gradients not only lead to faster solute transport but also induce strong interfacial instability simultaneously. Thus, the coupled effects of transient change in composition and fluid properties govern the drop size and its formation time in such systems under non-equilibrium.

Exploration of rheological behavior of an Ellis fluid on the onset of thermosolutal porous convection

The initiation of thermosolutal convective instability is investigated in a horizontal porous layer saturated by a shear-thinning fluid following Ellis’ rheology. The porous layer is heated as well as salted from below and a basic horizontal throughflow prompted by the prescribed pressure gradient is considered. The linear stability analysis is performed using normal mode analysis and the threshold conditions for the onset of convection are obtained in a closed form. The imposed horizontal pressure gradient and the solute concentration gradient reinforce together in resulting the onset of convection through oscillatory motions. The transverse rolls are the most unstable which are found to be both travelling and non-travelling in the reference frame comoving with the basic throughflow. The effect of increasing the Ellis power-law index and the solute Darcy-Rayleigh number is to stabilise, while an increase in the Darcy-Ellis number is to destabilise the base flow. The pressure and temperature/solute concentration lines are presented at the critical state. The results delineated under the limiting cases are shown to be in agreement with those published previously.

Numerical model supplemented by thin-layer analysis for diffusiophoresis of a particle incorporating finite ion size effects

The impact of finite-sized ions on the diffusiophoresis of a charged colloid subjected to a concentration gradient of electrolyte solution consisting monovalent or multivalent ionic species, is studied. In diffusiophoresis, the ion concentration is of O(1M). In this non-dilute electrolyte solutions, the ion–ion steric interaction is important. We have adopted the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model to account for the ion steric interactions and the Batchelor–Green expression for the relative viscosity of suspension. We have solved the standard model numerically considering ions as point charge (PNP-model), the modified Nernst–Planck equations incorporating the ion steric interaction with constant viscosity (MNP-model), and modification of the MNP-model by incorporating the viscosity variation with the ionic volume fraction (MNPV-model). Semi-analytical expressions for mobility based on a linear perturbation technique under a thinner Debye length is presented for PNP- and MNP-models. In the MNP-model, counterion saturation in the Debye layer due to the ion steric interaction enhances the surface potential by attenuating the shielding effect, diminishes the surface conduction, and magnifies the induced electric field. These in combination create a larger mobility at a thinner Debye length compared with the PNP-model. This increment in mobility attenuates when the MNPV-model is considered. The MNPV-model is more appropriate to analyze the finite ion size effects, and it is found to yield the mobility values more close to the experimental data compared with the MNP- and PNP-model. The semi-analytical expressions for mobility based on the PNP- and MNP-models agree with the corresponding exact numerical solutions when the surface potential is in the order of thermal potential. However, a large discrepancy between the simplified expression and the exact numerical results is found for a concentrated electrolyte in which the induced electric field is large.

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

HypothesisA 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. ExperimentsA 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. FindingsPolymer/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.

Diffusiophoresis of hydrophobic spherical particles in a solution of general electrolyte

The present article deals with the diffusiophoresis of hydrophobic rigid colloids bearing arbitrary ζ-potential. We derived the generic expression for the diffusiophoretic velocity of such a colloid exposed in an externally applied concentration gradient of the general electrolyte solution. The derived expression takes into account the relaxation effect and is applicable for all values of surface ζ-potential and hydrodynamic slip length at large κa (κa≥ca.50), where κ−1 is the thickness of the electric double layer and a is the particle radius. We further derived several closed-form expressions for particle velocity derived under various electrostatic and hydrodynamic conditions when the particle is exposed in an applied concentration gradient of binary symmetric (e.g., z:z), asymmetric (1:2, 2:1, 3:1, 1:3), and a mixed electrolyte (mixture of 1:1 and 2:1 electrolytes). The results for diffusiophoretic velocity are further illustrated graphically to indicate the mutual interaction of chemiphoresis, induced electrophoresis due to unequal mobilities of cations and anions of the electrolyte, and the mechanism by which the sufficiently charged particle migrates opposite to the direction of the applied concentration gradient. The impact of hydrophobicity is further discussed.

Characterisation of fully developed and equilibrium states of non-electrolyte diffusiophoretic systems via numerical simulations

Diffusiophoresis takes place when a particle in solution moves due to the presence of a solute concentration gradient. This phenomenon is often studied under some simplifying assumptions, such as negligible diffusive layer thickness or infinite diffusion coefficient. In this work we simulate diffusiophoresis without these simplifications. The goal of this numerical study is to investigate equilibrium and fully developed states of non-electrolyte phoretic systems. Simulation results show that equilibrium states depend on solute diffusivity and on a reference solute concentration far from the particle. An expression is regressed that gives the (equilibrium) diffusiophoretic velocity as a function of solute concentration gradient, solute diffusion coefficient and the reference solute concentration far from the particle. A different set of results reveals that the state of phoretic systems does not depend on the initial conditions when time goes to infinity. This motivates the definition of fully developed states, designating those systems whose properties no longer depend on initial conditions. Apart from these findings, this work also depicts the effect of solute–interface interactions on diffusiophoresis. Simulation results for two solid particles with different interaction potentials are used to illustrate particle separation via diffusiophoresis. Finally, values of particle mobility are calculated for different solute–interface attraction strengths. These results are compared with another work in the literature, which studies polymer diffusiophoresis via molecular simulations (Ramírez-Hinestrosa et al., J. Chem. Phys., vol. 152, 2020, p. 164901).

Diffusiophoresis and Diffusio-osmosis into a Dead-End Channel: Role of the Concentration-Dependence of Zeta Potential.

Chemically induced transport methods open up new opportunities for colloidal transport in dead-end channel geometries. Diffusiophoresis, which describes particle movement under an electrolyte concentration gradient, has previously been demonstrated in dead-end channels. The presence of solute concentration gradients in such channels induces particle motion (phoresis) and fluid flow along solid walls (osmosis). The particle velocity inside a dead-end channel is thus influenced by particle diffusiophoresis and wall diffusio-osmosis. The magnitude of phoresis and osmosis depends on the solute's relative concentration gradient, the electrokinetic parameters of the particle and the wall, and the diffusivity contrast of cations and anions. Although it is known that some of those parameters are affected by electrolyte concentration, e.g., zeta potential, research to date often interprets results using averaged and constant zeta potential values. In this work, we demonstrate that concentration-dependent zeta potentials are essential when the zeta potential strongly depends on electrolyte concentration for correctly describing the particle transport inside dead-end channels. Simulations including concentration-dependent zeta potentials for the particle and wall matched with experimental observations, whereas simulations using constant, averaged zeta potentials failed to capture particle dynamics. These results contribute to the fundamental understanding of diffusiophoresis and the diffusio-osmosis process.

The role of variable zeta potential on diffusiophoretic and diffusioosmotic transport

Diffusiophoresis is the spontaneous motion of colloidal particles induced by the presence of a local solute concentration gradient, and diffusioosmosis is the analogous motion of fluid near a surface. The zeta potential, a measure of the electrokinetic potential at the slipping plane in the Debye layer, plays an important role in these processes, as it is a measure of the strength of interactions between solute and surface molecules. Many previous studies on diffusiophoresis/diffusioosmosis have relied on the assumption of constant zeta potential, in part due to the significant theoretical simplification introduced by this assumption. However, in general the zeta potential varies as a function of solute concentration, which often varies by orders of magnitude in typical setups. We seek to characterize the role of variable zeta potential on diffusiophoresis/diffusioosmosis by revisiting recent studies that treated zeta potential as constant. For each case, we characterize and quantify the change in the particle/solute/fluid dynamics when a variable zeta potential model is considered. The four test problems that are considered are: (1) diffusiophoresis-induced particle banding in a stopped-flow diffusion cell, (2) one-dimensional particle injection in a dead-end pore, (3) arrested particle spreading in a solute/particle co-diffusion system, and (4) diffusioosmotic pumping in a micropore connecting solute streams. The results provide examples of the qualitative and quantitative differences that can result when using materials that satisfy constant potential, constant charge, or even charge-regulating surface properties, and stress the importance of selecting the appropriate surface model. This work provides guidance to experimentalists and modelers in selecting efficient and accurate models for their diffusiophoretic/diffusioosmotic systems, and these results indicate that finite Debye layer effects typically affect transport much more than variable zeta potential effects, but detailed problem-specific simulations are needed to quantify these effects.