Diffusioosmotic flow reversals due to ion-ion electrostatic correlations.

Existing theories of diffusioosmosis have neglected ion-ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion-ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion-ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis. Such a reversal is not captured by existing theories, occurs at ≈ 0.4 M for a monovalent electrolyte, and at a much lower concentration of ≈ 0.003 M for a divalent electrolyte in a channel with the same surface charge. This highlights that diffusioosmosis of a concentrated electrolyte can be qualitatively different from that of a dilute electrolyte, not just in its magnitude but also its direction. Second, we predict a separate diffusioosmotic flow reversal, which is not due to electrostatic correlations but the competition between the underlying chemiosmosis and electroosmosis. This reversal can be achieved by varying the magnitude of the channel surface charge without changing its sign. However, electrostatic correlations can radically change how this flow reversal depends on the channel surface charge and ion diffusivity between a concentrated and a dilute electrolyte. The mathematical model developed here can be used to design diffusioosmosis of dilute and concentrated electrolytes, which is central to applications such as species mixing and separation, enhanced oil recovery, and reverse electrodialysis.

Unidirectional drying of a suspension of diffusiophoretic colloids under gravity.

Recent experiments (K. Inoue and S. Inasawa, RSC Adv., 2020, 10, 15763-15768) and simulations (J.-B. Salmon and F. Doumenc, Phys. Rev. Fluids, 2020, 5, 024201) demonstrated the significant impact of gravity on unidirectional drying of a colloidal suspension. However, under gravity, the role of colloid transport induced by an electrolyte concentration gradient, a mechanism known as diffusiophoresis, is unexplored to date. In this work, we employ direct numerical simulations and develop a macrotransport theory to analyze the advective-diffusive transport of an electrolyte-colloid suspension in a unidirectional drying cell under the influence of gravity and diffusiophoresis. We report three key findings. First, drying a suspension of solute-attracted diffusiophoretic colloids causes the strongest phase separation and generates the thinnest colloidal layer compared to non-diffusiophoretic or solute-repelled colloids. Second, when colloids are strongly solute-repelled, diffusiophoresis prevents the formation of colloid concentration gradient and hence gravity has a negligible effect on colloidal layer formation. Third, our macrotransport theory predicts new scalings for the growth of the colloidal layer. The scalings match with direct numerical simulations and indicate that the colloidal layer produced by solute-repelled diffusiophoretic colloids could be an order of magnitude thicker compared to non-diffusiophoretic or solute-attracted colloids. Our results enable tailoring the separation of colloid-electrolyte suspensions by tuning the interactions between the solvent, electrolyte, and colloids under Earth's or microgravity, which is central to ground-based and in-space applications.

Diffusiophoresis of a spherical particle in porous media.

Recent experiments by Doan et al. (Nano Lett., 2021, 21, 7625-7630) demonstrated and measured colloid diffusiophoresis in porous media but existing theories cannot predict the observed colloid motion. Here, using regular perturbation method, we develop a mathematical model that can predict the diffusiophoretic motion of a charged colloidal particle driven by a binary monovalent electrolyte concentration gradient in a porous medium. The porous medium is modeled as a Brinkman medium with a constant Darcy permeability. The linearized Poisson-Boltzmann equation is employed to model the equilibrium electric potential distribution that is driven out-of-equilibrium under diffusiophoresis. We report three key findings. First, we demonstrate that colloid diffusiophoresis could be drastically hindered in a porous medium due to the additional hydrodynamic drag compared to diffusiophoresis in a free electrolyte solution. Second, we show that the variation of the diffusiophoretic motion with respect to a change in the electrolyte concentration in a porous medium could be qualitatively different from that in a free electrolyte solution. Third, our results match quantitatively with experimental measurements, highlighting the predictive power of the present model. The mathematical model developed here could be employed to design diffusiophoretic colloid transport in porous media, which are central to applications such as nanoparticle drug delivery and enhanced oil recovery.

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.

Surfactant Driven Marangoni Spreading in the Presence of Predeposited Insoluble Surfactant Monolayers.

When an insoluble surfactant is deposited on the surface of a thin fluid film, stresses induced by surface tension gradients drive Marangoni spreading across the subphase surface. The presence of a predeposited layer of an insoluble surfactant alters that spreading. In this study, the fluid film was aqueous, the predeposited insoluble surfactant was dipalmitoylphosphatidylcholine (DPPC), and the deposited insoluble surfactant was oleic acid. An optical density-based method was used to measure subphase surface distortion, called the Marangoni ridge, associated with propagation of the spreading front. The movement of the Marangoni ridge was correlated with movement of surface tracer particles that indicated both the boundary between the two surfactant layers and the surface fluid velocities. As the deposited oleic acid monolayer spread, it compressed the predeposited DPPC monolayer. During spreading, the surface tension gradient extended into the predeposited monolayer, which was compressed nonuniformly, from the deposited monolayer. The spreading was so rapid that the compressed predeposited surfactant could not have been in quasi-equilibrium states during the spreading. As the initial concentrations of the predeposited surfactant were increased, the shape of the Marangoni ridge deformed. When the initial concentration of the predeposited surfactant reached about 70 A2/molecule, there was no longer a Marangoni ridge but rather a broadly distributed excess of fluid above the initial fluid height. The nonuniform compression of the annulus of the predeposited monolayer also caused tangential motion ahead of both the Marangoni ridge and the boundary between the two monolayers. Spreading ceased when the two monolayers reached the same final surface tension. The final area per molecule of the DPPC monolayer matched that expected from the equilibrium DPPC isotherm at the same final surface tension. Thus, at the end of spreading, there was a simple surface tension balance between the two distinct monolayers.

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.

Toward a nonequilibrium Stokes-Einstein relation via active microrheology of hydrodynamically interacting colloidal dispersions.

We derive a theoretical model for the nonequilibrium stress in a flowing colloidal suspension by tracking the motion of a single embedded probe. While Stokes-Einstein relations connect passive, observable diffusion of a colloidal particle to properties of the suspending medium, they are limited to linear response. Actively forcing a probe through a suspension produces nonequilibrium stress that at steady state can be related directly to observable probe motion utilizing an equation of motion rather than an equation of state, giving a nonequilibrium Stokes-Einstein relation [J. Rheol., 2012, 56, 1175-1208]. Here that freely-draining theory is expanded to account for hydrodynamic interactions. To do so, we construct an effective hydrodynamic resistance tensor, through which the particle flux is projected to give the advective and diffusive components of a Cauchy momentum balance. The resultant phenomenological relation between suspension stress, viscosity and diffusivity is a generalized nonequilibrium Stokes-Einstein relation. The phenomenological model is compared with the statistical mechanics theory for dilute suspensions as well as dynamic simulation at finite concentration which show good agreement, indicating that the suspension stress, viscosity, and force-induced diffusion in a flowing colloidal dispersion can be obtained simply by tracking the motion of a single Brownian probe.

TNF primes endothelial cells for angiogenic sprouting by inducing a tip cell phenotype.

Pathological angiogenesis associated with wound healing often occurs subsequent to an inflammatory response that includes the secretion of cytokines such as tumor necrosis factor (TNF). Controversy exists on the angiogenic actions of TNF, with it being generally proangiogenic in vivo, but antiangiogenic in vitro. We find that whereas continuous administration of TNF in vitro or in vivo inhibits angiogenic sprouting, a 2- to 3-day pulse stimulates angiogenesis by inducing an endothelial "tip cell" phenotype. TNF induces the known tip cell genes platelet-derived growth factor B (PDGFB) and vascular endothelial cell growth factor receptor-2 (VEGFR2), while at the same time blocking signaling through VEGFR2, thus delaying the VEGF-driven angiogenic response. Notch signaling regulates tip cell function, and we find that TNF also induces the notch ligand jagged-1, through an NFkappaB-dependent mechanism. Enrichment of jagged-1 in tip cells was confirmed by immunofluorescent staining as well as by laser capture microdissection/quantitative reverse-transcription-polymerase chain reaction (qRT-PCR) of tip cells sprouting in vitro. Thus, in angiogenesis, the temporal expression of TNF is critical: it delays angiogenesis initially by blocking signaling through VEGFR2, but in addition by inducing a tip cell phenotype through an NFkappaB-dependent pathway, it concomitantly primes endothelial cells (ECs) for sprouting once the initial inflammatory wave has passed.