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Diffusiophoresis refers to the movement of colloidal particles in the presence of a concentration gradient of a solute and enables directed motion of colloidal particles in geometries that are inaccessible, such as dead-end pores, without imposing an external field. Previous experimental reports on dead-end pore geometries show that, even in the absence of mean flow, colloidal particles moving through diffusiophoresis exhibit significant dispersion. Existing models of diffusiophoresis are not able to predict the dispersion and thus the comparison between the experiments and the models is largely qualitative. To address these quantitative differences between the experiments and models, we derive an effective one-dimensional equation, similar to a Taylor dispersion analysis, that accounts for the dispersion created by diffusioosmotic flow from the channel sidewalls. We derive the effective dispersion coefficient and validate our results by comparing them with direct numerical simulations. We also compare our model with experiments and obtain quantitative agreement for a wide range of colloidal particle sizes. Our analysis reveals two important conclusions. First, in the absence of mean flow, dispersion is driven by the flow created by diffusioosmotic wall slip such that spreading can be reduced by decreasing the channel wall diffusioosmotic mobility. Second, the model can explain the spreading of colloids in a dead-end pore for a wide range of particle sizes. We note that, while the analysis presented here focuses on a dead-end pore geometry with no mean flow, our theoretical framework is general and can be adapted to other geometries and other background flows. 

We study bubble motion in a vertical capillary tube under an external flow. Bretherton ( J. Fluid Mech. , vol. 10, issue 2, 1961, pp. 166–188) has shown that, without external flow, a bubble can spontaneously rise when the Bond number ( $${Bo} \equiv \rho g R^2 / \gamma$$ ) is above the critical value $${Bo}_{cr}=0.842$$ , where $$\rho$$ is the liquid density, $$g$$ the gravitational acceleration, $$R$$ the tube radius and $$\gamma$$ the surface tension. It was then shown by Magnini et al. ( Phys. Rev. Fluids , vol. 4, issue 2, 2019, 023601) that the presence of an imposed liquid flow, in the same (upward) direction as buoyancy, accelerates the bubble and thickens the liquid film around it. In this work we carry out a systematic study of the bubble motion under a wide range of upward and downward external flows, focusing on the inertialess regime with Bond numbers above the critical value. We show that a rich variety of bubble dynamics occurs when an external downward flow is applied, opposing the buoyancy-driven rise of the bubble. We reveal the existence of a critical capillary number of the external downward flow ( $${Ca}_l \equiv \mu U_l/\gamma$$ , where $$\mu$$ is the fluid viscosity and $$U_l$$ is the mean liquid speed) at which the bubble arrests and changes its translational direction. Depending on the relative direction of gravity and the external flow, the thickness of the film separating the bubble surface and the tube inner wall follows two distinct solution branches. The results from theory, experiments and numerical simulations confirm the existence of the two solution branches and reveal that the two branches overlap over a finite range of $${Ca}_l$$ , thus suggesting non-unique, history-dependent solutions for the steady-state film thickness under the same external flow conditions. Furthermore, inertialess symmetry-breaking shape profiles at steady state are found as the bubble transits near the tipping points of the solution branches, which are shown in both experiments and three-dimensional numerical simulations. 

Diffusiophoresis is the spontaneous movement of colloidal particles in a concentration gradient of solutes. As a small-scale phenomenon that harnesses energy from concentration gradients, diffusiophoresis may prove useful for passively manipulating particles in lab-on-a-chip applications as well as configurations involving interfaces. Though naturally occurring ions are often multivalent, experimental studies of diffusiophoresis have been mostly limited to monovalent electrolytes. In this work, we investigate the motion of negatively charged polystyrene particles in one-dimensional salt gradients for a variety of multivalent electrolytes. We develop a one-dimensional model and obtain good agreement between our experimental and modeling results with no fitting parameters. Our results indicate that the ambipolar diffusivity, which is dependent on the valence combination of cations and anions, dictates the speed of the diffusiophoretic motion of the particles by controlling the time scale at which the electrolyte concentration evolves. In addition, the ion valences also modify the electrophoretic and chemiphoretic contributions to the diffusiophoretic mobility of the particles. Our results are applicable to systems where the chemical concentration gradient is comprised of multivalent ions, and motivate future research to manipulate particles by exploiting ion valence. 

We study the diffusion of multiple electrolytes in a one-dimensional pore. We model the scenario where an electrolyte is in contact with a reservoir of another electrolyte, such that the cation of the two electrolytes is common. The model reveals that several factors influence the ion concentration profiles: (i) relative diffusivities of the ions, (ii) ratio of the electrolyte concentrations in the pore and the reservoir, and (iii) the valence of the ions. We demonstrate that it is crucial to consider the interaction between ion fluxes as treating the electrolytes independently, as is sometimes proposed, does not completely capture the dynamics of ion transport. We validate our numerical predictions by conducting experiments with sodium fluorescein salt in the pore and sodium chloride/sodium sulphate/sodium hydroxide in the reservoir. Our visualization and results demonstrate that ion diffusivities and concentrations in the reservoir can influence the diffusion rates of fluorescein, which underscores that ion fluxes are coupled and that multiple electrolytes cannot be treated independently. These results should be useful to the wide range of situations where concentration variations are imposed on systems with an existing background electrolyte. 

When a confined bubble translates steadily in a cylindrical capillary tube, without the consideration of gravity effects, a uniform thin film of liquid separates the bubble surface and the tube wall. In this work, we investigate how this steady state is established by considering the transitional motion of the bubble as it adjusts its film thickness profile between two steady states, characterized by two different bubble speeds. During the transition, two uniform film regions coexist, separated by a step-like transitional region. The transitional motion also requires modification of the film solution near the rear of the bubble, which depends on the ratio of the two capillary numbers. These theoretical results are verified by experiments and numerical simulations. 

Abstract When chemotactic bacteria are exposed to a concentration gradient of chemoattractant while flowing along a channel, the bacteria accumulate at the interface between the chemoattractant source and bacterial suspension. Assuming that the interface is no‐slip, we can apply the shear flow approximation near the no‐slip boundary and solve a steady‐state convection‐diffusion model for both chemoattractant and bacterial concentrations. We suggest similarity solutions for the two‐dimensional problem and identify a critical length scaleη_cfor bacteria chemotaxis in a given concentration gradient. The analysis identifies three dimensionless groups representing, respectively, chemotactic sensitivity, the chemotaxis receptor constant, and the bacteria diffusion coefficient, which typically show coupled effects in experimental systems. We study the effect of the dimensionless groups separately and provide understanding of the system involving shear flow and chemotaxis.