The capture of individual cells using microfluidic chips represents a widely adopted and efficient approach for investigating the biochemical microenvironment of singular cells. While conventional methods reliant on boundary effects pose challenges in precisely manipulating individual cells, single-cell capture grounded in the principle of stagnation point flow offers a solution to this limitation. Nevertheless, such capture mechanisms encounter inconsistency due to the instability of the flow field and stagnation point. In this study, a microfluidic device for the stable capture of single cells was designed, integrating the principle of fluid mechanics by amalgamating stagnation point flow and boundary effects. This innovative microfluidic chip transcended the limitations associated with single methodologies, leveraging the strengths of both stagnation point flow and boundary effects to achieve reliable single-cell capture. Notably, the incorporation of capture ports at the stagnation point not only harnessed boundary effects but also enhanced capture efficiency significantly, elevating it from 31.9% to 83.3%, thereby augmenting capture stability. Furthermore, computational simulations demonstrated the efficacy of the capture ports in entrapping particles of varying diameters, including 9 μm, 14 μm, and 18 μm. Experiment validation underscored the capability of this microfluidic system to capture single cells within the chip, maintaining stability even under flow rate perturbations spanning from 60 μL/min to 120 μL/min. Consequently, cells with dimensions between 8 μm and 12 μm can be reliably captured. The designed microfluidic system not only furnishes a straightforward and efficient experimental platform but also holds promise for facilitating deeper investigations into the intricate interplay between individual cells and their surrounding microenvironment.

The purpose of this article is to give a complete proof of a [Formula: see text] regularity result for the pressure for weak solutions of the two-dimensional \'incompressible Euler equations\' when the fluid velocity enjoys the same type of regularity in a compact simply connected domain with [Formula: see text] boundary. To accomplish our result, we realize that it is compulsory to introduce a new weak formulation for the boundary condition of the pressure, which is consistent with, and equivalent to, that of classical solutions. This article is part of the theme issue \'Scaling the turbulence edifice (part 1)\'.

Locomotion characteristics are often recorded within bounded spaces, a constraint which introduces geometry-specific biases and potentially complicates the inference of behavioural features from empirical observations. We describe how statistical properties of an uncorrelated random walk, namely the steady-state stopping location probability density and the empirical step probability density, are affected by enclosure in a bounded space. The random walk here is considered as a null model for an organism moving intermittently in such a space, that is, the points represent stopping locations and the step is the displacement between them. Closed-form expressions are derived for motion in one dimension and simple two-dimensional geometries, in addition to an implicit expression for arbitrary (convex) geometries. For the particular choice of no-go boundary conditions, we demonstrate that the empirical step distribution is related to the intrinsic step distribution, i.e. the one we would observe in unbounded space, via a multiplicative transformation dependent solely on the boundary geometry. This conclusion allows in practice for the compensation of boundary effects and the reconstruction of the intrinsic step distribution from empirical observations.

Active particles, including swimming microorganisms, autophoretic colloids, and droplets, are known to self-organize into ordered structures at fluid-solid boundaries. The entrainment of particles in the attractive parts of their spontaneous flows has been postulated as a possible mechanism underlying this phenomenon. Here, combining experiments, theory, and numerical simulations, we demonstrate the validity of this flow-induced ordering mechanism in a suspension of active emulsion droplets. We show that the mechanism can be controlled, with a variety of resultant ordered structures, by simply altering hydrodynamic boundary conditions. Thus, for flow in Hele-Shaw cells, metastable lines or stable traveling bands can be obtained by varying the cell height. Similarly, for flow bounded by a plane, dynamic crystallites are formed. At a no-slip wall, the crystallites are characterized by a continuous out-of-plane flux of particles that circulate and re-enter at the crystallite edges, thereby stabilizing them. At an interface where the tangential stress vanishes, the crystallites are strictly 2D, with no out-of-plane flux. We rationalize these experimental results by calculating, in each case, the slow viscous flow produced by the droplets and the long-ranged, many-body active forces and torques between them. The results of numerical simulations of motion under the action of the active forces and torques are in excellent agreement with experiments. Our work elucidates the mechanism of flow-induced phase separation in active fluids, particularly active colloidal suspensions, and demonstrates its control by boundaries, suggesting routes to geometric and topological phenomena in an active matter.

Biaxial tests are commonly used to investigate the mechanical behaviour of soft biological tissues and polymers. In the current paper we uncover a fundamental problem associated with the calculation of material stress from measured force in standard biaxial tests. In addition to measured forces, localised unmeasured shear forces also occur at the clamps and the inability to quantify such forces has significant implications for the calculation of material stress from simplified force-equilibrium relationships. Unmeasured shear forces are shown to arise due to two distinct competing contributions: (1) negative shear force due to stretching of the orthogonal clamp, and (2) positive shear force as a result of material Poisson-effect. The clamp shear force is highly dependent on the specimen geometry and the clamp displacement ratio, as consequently, is the measured force-stress relationship. Additionally in this study we demonstrate that commonly accepted formulae for the estimation of material stress in the central region of a cruciform specimen are highly inaccurate. A reliable empirical correction factor for the general case of isotropic materials must be a function of specimen geometry and the biaxial clamp displacement ratio. Finally we demonstrate that a correction factor for the general case of non-linear anisotropic materials is not feasible and we suggest the use of inverse finite element analysis as a practical means of interpreting experimental data for such complex materials.

During the last years, several authors have focused on the characterization of the size and charge of the nanoparticles by capillary electrophoresis. However, considering that nanoparticles are generally suspended in a solvent different from those commonly used as background electrolytes (BGE), an appropriate characterization of the behavior of the nanoparticles in the sample-BGE interface is required, as this might affect the overall electrophoretic behavior of the nanoparticles. In the present work, we address the evaluation of the behavior of COOH-coated maghemite nanoparticles in the vicinity of a pH boundary. To do so, different suspensions of nanoparticles prepared in acid media were injected into a borate/NaOH pH 9.5 BGE. The formation and evolution of boundaries in the sample-BGE interface in such systems was modeled by computer simulation. A systematic evaluation of the effect that parameters such as the co-ion, the sample pH or the injection time have on the electrophoretic behavior of the nanoparticles was carried out.