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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.

 

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. 

In the study of fluid dynamics and transport phenomena, key quantities of interest are often the force and torque on objects and total rate of heat/mass transfer from them. Conventionally, these integrated quantities are determined by first solving the governing equations for the detailed distribution of the field variables (i.e. velocity, pressure, temperature, concentration, etc.) and then integrating the variables or their derivatives on the surface of the objects. On the other hand, the divergence form of the conservation equations opens the door for establishing integral identities that can be used for directly calculating the integrated quantities without requiring the detailed knowledge of the distribution of the primary variables. This shortcut approach constitutes the idea of the reciprocal theorem, whose closest relative is Green’s second identity, which readers may recall from studies of partial differential equations. Despite its importance and practicality, the theorem may not be so familiar to many in the research community. Ironically, some believe that the extreme simplicity and generality of the theorem are responsible for suppressing its application! In this Perspectives piece, we provide a pedagogical introduction to the concept and application of the reciprocal theorem, with the hope of facilitating its use. Specifically, a brief history on the development of the theorem is given as a background, followed by the discussion of the main ideas in the context of elementary boundary-value problems. After that, we demonstrate how the reciprocal theorem can be utilized to solve fundamental problems in low-Reynolds-number hydrodynamics, aerodynamics, acoustics and heat/mass transfer, including convection. Throughout the article, we strive to make the materials accessible to early career researchers while keeping it interesting for more experienced scientists and engineers. 

The accurate measurement of wall zeta potentials and solute–surface interaction length scales for electrolyte and non-electrolyte solutes, respectively, is critical to the design of many biomedical and microfluidic applications. We present a novel microfluidic approach using diffusioosmosis for measuring either the zeta potentials or the characteristic interaction length scales for surfaces exposed to, respectively, electrolyte or non-electrolyte solutes. When flows containing different solute concentrations merge in a junction, local solute concentration gradients can drive diffusioosmotic flow due to electrokinetic, steric, and other interactions between the solute molecules and solid surfaces. We demonstrate a microfluidic system consisting of a long, narrow pore connecting two large side channels in which solute concentration gradients drive diffusioosmosis within the pore, resulting in predictable fluid velocity/pressure and solute profiles. Furthermore, we present analytical results and a methodology to determine the zeta potential or interaction length scale for the pore surfaces based on the solute concentrations in the main side channels, the flow rate in the pore, and the pressure drop across the pore. We apply this method to the experimental data of Lee et al. to predict the zeta potentials of their system, and we use 3D numerical simulations to validate the theory and show that end effects caused by the junctions are negligible for a wide range of parameters. Because the dynamics in the proposed system are driven by diffusioosmosis, this technique does not suffer from certain disadvantages associated with the use of sensitive electronics in traditional zeta potential measurement approaches such as streaming potential, streaming current, or electroosmosis. To the best of our knowledge this is the first flow-based approach to characterize surface/solute interactions with non-electrolyte solutes. 

We explore the consequences of micelle formation for diffusiophoresis of charged colloidal particles in ionic surfactant concentration gradients, using a quasi-chemical association model for surfactant self assembly. The electrophoretic contribution to diffusiophoresis is determined by re-arranging the Nernst–Planck equations, and the chemiphoretic contribution is estimated by making plausible approximations for the density profiles in the electrical double layer surrounding the particle. For sub-micellar solutions we find that a particle will typically be propelled down the concentration gradient, although electrophoresis and chemiphoresis are finely balanced and the effect is sensitive to the detailed parameter choices and simplifying assumptions in the model. Above the critical micelle concentration (CMC), diffusiophoresis becomes much weaker and may even reverse sign, due to the fact that added surfactant goes into building micelles and not augmenting the monomer or counterion concentrations. We present detailed calculations for sodium dodecyl sulfate (SDS), finding that the typical drift speed for a colloidal particle in a ∼100 μm length scale SDS gradient is ∼1 μm s −1 below the CMC, falling to ≲0.2 μm s −1 above the CMC. These predictions are broadly in agreement with recent experimental work.