Cells and other soft particles are often forced to flow in confined geometries in both laboratory and natural environments, where the elastic deformation induces an additional drag and pressure drop across the particle. In contrast with other multiphase flows, the physical parameters that determine this additional pressure are still not known. Here we start by measuring the pressure drop across a single spherical hydrogel particle as it flows in a microfluidic comparator. This pressure is found to depend on the amount of confinement, elastic modulus, fluid viscosity and velocity. A model for the force balance on the particle is then proposed, by incorporating the above ingredients and relying on simulations of bead geometry and lubrication flow considerations. The final model collapses the force measurements forces onto a single scaling law spanning several decades, while providing physical insights by recalling elements from classic multiphase flows and contact mechanics.
We consider pressure-driven, steady state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C = P^2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness…
Understand and predict the dynamics of dispersed micro-objects in microfluidics is crucial in numerous natural, industrial and technological situations. In this paper, we experimentally characterized the equilibrium velocity $V$ and lateral position $\varepsilon$ of various dispersed micro-objects such as beads, bubbles and drops, in a cylindrical microchannel over an unprecedent wide range of parameters. By systematically varying the dimensionless object size ($d \in [0.1; 1]$), the viscosity ratio ($λ\in [10^{-2}; \infty[$), the density ratio ($φ\in [10^{-3}; 2]$), the Reynolds number ($\Re …
Until recently, the accepted paradigm was that the Ohmic electrical response of nanochannel-microchannel systems is determined solely by the nanochannel while the effects of the adjacent microchannels are negligible. Two, almost identical, models were suggested to rationalize experimental observations that appeared to confirm the paradigm. However, recent works have challenged this paradigm and shown that the microchannels contribute in a non-negligible manner, and thus these two models are inadequate in describing realistic nanochannel-microchannel systems. Two newer nanochannel-microchannel …
The overall traffic of droplets in a network of microfluidic channels is strongly influenced by the liquid properties of the moving droplets. In particular, the effective hydrodynamic resistance of individual droplets plays a key role in their global behavior. We here propose two simple and low-cost experimental methods for measuring this parameter by analyzing the dynamics of a regular sequence of droplets injected into an "asymmetric loop" network. The choice of a droplet taking either route through the loop is influenced by the presence of previous droplets which modulate the hydrodynamic r…
Long, shallow microchannels embedded in thick soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid--structure interactions between the internal viscous flow and the soft walls has not been completely understood. Previous models either contain a fitting parameter or are specialized to channels with plate-like walls. This work is a theoretical study of the steady-state response of a compliant microchannel with a thick wall. Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotr…
During the transport of colloidal suspensions in microchannels, the deposition of particles can lead to the formation of clogs, typically at constrictions. Once a clog is formed in a microchannel, advected particles form an aggregate upstream from the site of the blockage. This aggregate grows over time, which leads to a dramatic reduction of the flow rate. In this paper, we present a model that predicts the growth of the aggregate formed upon clogging of a microchannel. We develop an analytical description that captures the time evolution of the volume of the aggregate, as confirmed by experi…
Inertial pumping is a promising new method of moving fluids through microchannels but many of its properties remain unexplored. In this work, inertial flow rates are investigated for different channel lengths, operating temperatures, and resistor pulse energies. Flow in closed channels is visualized by adding fluorescent tracer beads to the test fluid (pure water). A robust methodology of extracting flow rates from high-resolution video recordings is developed. Flow rates are found to scale inversely with the channel length. The observed dependence is explained based on a simple phenomenologic…
We report an experimental study of the motion of magnetized beads driven by a travelling wave magnetic field. For sufficiently large wave speed, we report the existence of a backward motion, in which the sphere can move in the direction opposite to the driving wave. We show that the transition to this new state is strongly subcritical and can lead to chaotic motion of the bead. For some parameters, this counter-propagation of the sphere can be one order of magnitude faster than the driving wave speed. These results are understood in the framework of a model based on the interplay among solid f…
We perform experimental investigations of osmotically driven flows in artificial microchannels by studying the dynamics and structure of the front of a sugar solution traveling in 200 um wide and 50-200 um deep microchannels. We find that the sugar front travels with constant speed, and that this speed is proportional to the concentration of the sugar solution and inversely proportional to the depth of the channel. We propose a theoretical model, which, in the limit of low axial flow resistance, predicts that the sugar front indeed should travel with a constant velocity. The model also predict…
We develop a one-dimensional model for the unsteady fluid--structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it. A beam equation, which accounts for both transverse bending rigidity and nonlinear axial tension, is coupled to a one-dimensional fluid model obtained from depth-averaging the two-dimensional incompressible Navier--Stokes equations across the channel height. Specifically, the Navier--Stokes equations are scaled in the viscous lubrication limit relevant to microfluidics. The resulting set of coupled nonlinear partial differential equations i…
In this article, we construct a novel 1D-model of microfluidic laminar flows in tapered circular and rectangular channels assuming the flow in channels fully developed. In the model, we take into account the inertance and dynamic pressure terms. The model can be used for a wide range of flows: from the pure capillary flow regime, where the capillary forces are the main driver of the liquid in the channel, to the external pressure flow regime where the external pressure applied to the liquid at the entrance to the channel is much larger than the capillary pressure in the channel, so that the ca…
The millimeter-long soil-dwelling nematode {\it C. elegans} propels itself by producing undulations that propagate along its body and turns by assuming highly curved shapes. According to our recent study [PLoS ONE \textbf{7}, e40121 (2012)] all these postures can be accurately described by a piecewise-harmonic-curvature (PHC) model. We combine this curvature-based description with highly accurate hydrodynamic bead models to evaluate the normalized velocity and turning angles for a worm swimming in an unconfined fluid and in a parallel-wall cell. We find that the worm moves twice as fast and na…
