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We study theoretically and experimentally pressure-driven flow between a flat wall and a parallel corrugated wall, a design used widely in microfluidics for low-Reynolds-number mixing and particle separation. In contrast to previous work, which focuses on recirculating helicoidal flows along the microfluidic channel that result from its confining lateral walls, we study the three-dimensional pressure and flow fields and trajectories of tracer particles at the scale of each corrugation. Employing a perturbation approach for small surface roughness, we find that anisotropic pressure gradients generated by the surface corrugations, which are tilted with respect to the applied pressure gradient, drive transverse flows. We measure experimentally the flow fields using particle image velocimetry and quantify the effect of the ratio of the surface wavelength to the channel height on the transverse flows. Further, we track tracer particles moving near the surface structures and observe three-dimensional skewed helical trajectories. Projecting the helical motion to two dimensions reveals oscillatory near-surface motion with an overall drift along the surface corrugations, reminiscent of earlier experimental observations and independent of the secondary helical flows that are induced by confining lateral walls. Finally, we quantify the hydrodynamically induced drift transverse to the mean flow direction as a function of distance to the surface and the wavelength of the surface corrugations. 

We study the capillary rise of viscous liquids into sharp corners formed by two surfaces whose geometry is described by power laws, $$h_i(x) = c_i x^n$$, $i = 1,2$, where $$c_2 > c_1$$ for $$n \geq 1$$. Prior investigations of capillary rise in sharp corners have shown that the meniscus altitude increases with time as $$t^{1/3}$$, a result which is universal, i.e., applies to all corner geometries. The universality of the phenomenon of capillary rise in sharp corners is revisited in this work through the analysis of a partial differential equation for the evolution of a liquid column rising into power-law-shaped corners, which is derived using lubrication theory. Despite the lack of geometric similarity of the liquid column cross-section for $n>1$, there exists a scaling and a similarity transformation that are independent of $$c_i$$ and $$n$$, which gives rise to the universal $$t^{1/3}$$ power-law for capillary rise. However, the prefactor, which corresponds to the tip altitude of the self-similar solution, is a function of $$n$$, and it is shown to be bounded and monotonically decreasing as $$n\to \infty$$. Accordingly, the profile of the interface radius as a function of altitude is also independent of $$c_i$$ and exhibits slight variations with $$n$$. Theoretical results are compared against experimental measurements of the time evolution of the tip altitude and of profiles of the interface radius as a function of altitude. 

Bacterial biofilms are communities of cells adhered to surfaces. These communities represent a predominant form of bacterial life on Earth. A defining feature of a biofilm is the three-dimensional extracellular polymer matrix that protects resident cells by acting as a mechanical barrier to the penetration of chemicals, such as antimicrobials. Beyond being recalcitrant to antibiotic treatment, biofilms are notoriously difficult to remove from surfaces. A promising, but relatively under explored approach to biofilm control, is to disrupt the extracellular polymer matrix by enabling penetration of particles to increase the susceptibility of biofilms to antimicrobials. In this work, we investigate externally imposed chemical gradients as a mechanism to transport polystyrene particles into bacterial biofilms. We show that pre-conditioning the biofilm with a pre-wash step using deionized (DI) water is essential for altering the biofilm so it takes up the micro- and nanoparticles by the application of a further chemical gradient created by an electrolyte. Using different particles and chemicals, we document the transport behavior that leads to particle motion into the biofilm and its further reversal out of the biofilm. Our results demonstrate the importance of chemical gradients in disrupting the biofilm matrix, regulating particle transport in crowded macromolecular environments, and suggest potential applications of particle transport and delivery in other physiological systems. 

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. 

At low Reynolds numbers, axisymmetric ellipsoidal particles immersed in a shear flow undergo periodic tumbling motions known as Jeffery orbits, with the orbit determined by the initial orientation. Understanding this motion is important for predicting the overall dynamics of a suspension. While slender fibres may follow Jeffery orbits, many such particles in nature are neither straight nor rigid. Recent work exploring the dynamics of curved or elastic fibres have found Jeffery-like behaviour along with chaotic orbits, decaying orbital constants and cross-streamline drift. Most work focuses on particles with reflectional symmetry; we instead consider the behaviour of a composite asymmetric slender body made of two straight rods, suspended in a two-dimensional shear flow, to understand the effects of the shape on the dynamics. We find that for certain geometries the particle does not rotate and undergoes persistent drift across streamlines, the magnitude of which is consistent with other previously identified forms of cross-streamline drift. For this class of particles, such geometry-driven cross-streamline motion may be important in giving rise to dispersion in channel flows, thereby potentially enhancing mixing.