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Register a new userGeometric pumping in autophoretic channels
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Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channel, rather channel geometry alone is sufficient. Using numerical simulations, we determine how geometric characteristics of the wall influence channel flow rate, and confirm our results analytically in the asymptotic limit of lubrication theory.
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Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion, and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only the same scaling but also the same form, albeit in opposite directions. In essence, we show that phoretic interactions effectively reverse the sign of the interactions that would be obtained for swimmers interacting purely hydrodynamically. Yet, hydrodynamic interactions can not be neglected as they significantly impact the magnitude of the interactions. This model is then used to analyse the behaviour of a suspension. The suspension exhibits swirling and clustering collective modes dictated by the orientational interactions between particles, similar to hydrodynamic swimmers, but here governed by the surface properties of the phoretic particle; the reversal in the sign of the interaction tends to slow down the swimming motion of the particles.
Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic interactions with walls or between neighboring particles. Through two-dimensional and three-dimensional simulations and a simple model that reveals the contribution of the main characteristics of the flowing suspension, we discuss the existence of an optimal volume fraction for cell transport and its dependence on the cell mechanical properties. The example of blood is explored in detail, by adopting the commonly used modeling of red blood cells dynamics. We highlight the complexity of optimization at the level of a network, due to the antagonist evolution of local volume fraction and optimal volume fraction with the channels diameter. In the case of the blood network, the most recent results on the size evolution of vessels along the circulatory network of healthy organs suggest that the red blood cell volume fraction (hematocrit) of healthy subjects is close to optimality, as far as transport only is concerned. However, the hematocrit value of patients suffering from diverse red blood cel pathologies may strongly deviate from optimality.
Micro and nanodroplets have many important applications such as in drug delivery, liquid-liquid extraction, nanomaterial synthesis and cosmetics. A commonly used method to generate a large number of micro or nanodroplets in one simple step is solvent exchange (also called nanoprecipitation), in which a good solvent of the droplet phase is displaced by a poor one, generating an oversaturation pulse that leads to droplet nucleation. Despite its crucial importance, the droplet growth resulting from the oversaturation pulse in this ternary system is still poorly understood. We experimentally and theoretically study this growth in Hele-Shaw like channels by measuring the total volume of the oil droplets that nucleates out of it. In order to prevent the oversaturated oil from exiting the channel, we decorated some of the channels with a porous region in the middle. Solvent exchange is performed with various solution compositions, flow rates and channel geometries, and the measured droplets volume is found to increase with the Peclet number $Pe$ with an approximate effective power law $Vpropto Pe^{0.50}$. A theoretical model is developed to account for this finding. With this model we can indeed explain the $Vpropto Pe^{1/2}$ scaling, including the prefactor, which can collapse all data of the porous channels onto one universal curve, irrespective of channel geometry and composition of the mixtures. Our work provides a macroscopic approach to this bottom-up method of droplet generation and may guide further studies on oversaturation and nucleation in ternary systems.
Laminar flow over a bubble mattress is expected to experience a significant reduction in friction since the individual surfaces of the bubbles are shear-free. However, if the bubbles are sufficiently curved, their protrusion into the fluid and along the flow direction can lead to an increase in friction as was recently demonstrated experimentally and computationally. We provide in this paper a simple model for this result. We consider a shear flow at low Reynolds number past a two-dimensional array of bubbles, and calculate analytically the effective slip length of the surface as function of the bubble geometry in the dilute limit. Our model is able to reproduce quantitatively the relationship between effective friction and bubble geometry obtained in numerical computations, and in particular: (a) The asymmetry in friction between convex and concave bubbles, and (b) the existence of a geometric transition from reduced to enhanced friction at a critical bubble protrusion angle.
The geometric phase techniques for swimming in viscous flows express the net displacement of a swimmer as a path integral of a field in configuration space. This representation can be transformed into an area integral for simple swimmers using Stokes theorem. Since this transformation applies for any loop, the integrand of this area integral can be used to help design these swimmers. However, the extension of this Stokes theorem technique to more complicated swimmers is hampered by problems with variables that do not commute and by how to visualise and understand the higher dimensional spaces. In this paper, we develop a treatment for each of these problems, thereby allowing the displacement of general swimmers in any environment to be designed and understood similarly to simple swimmers. The net displacement arising from non-commuting variables is tackled by embedding the integral into a higher dimensional space, which can then be visualised through a suitability constructed surface. These methods are developed for general swimmers and demonstrated on {three} benchmark examples: Purcells two-hinged swimmer, an axisymmetric squirmer in free space {and an axisymmetric squirmer approaching a free interface}. We show in particular that for swimmers with more than two modes of deformation, there exists an infinite set of strokes that generate each net displacement. Hence, in the absence of additional restrictions, general microscopic swimmers do not have a single stroke that maximises their displacement.
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