Direct and noninvasive measurement of the pressure distribution in test sections of a micro-channel is a challenging, if not an impossible, task. Here, we present an analytical method for extracting the pressure distribution in a deformable micro-channel under flow. Our method is based on a measurement of the channel deflection profile as a function of applied \emph{hydrostatic} pressure; this initial measurement generates "constitutive curves" for the deformable channel. The deflection profile under flow is then matched to the constitutive curves, providing the \emph{hydrodynamic} pressure distribution. The method is validated by measurements on planar micro-fluidic channels against analytic and numerical models. The accuracy here is independent of the nature of the wall deformations and is not degraded even in the limit of large deflections, $ζ_{\rm{max}}/2h_{0}= {\cal{O}}(1)$, with $ζ_{\rm{max}}$ and $2h_0$ being the maximum deflection and the unperturbed height of the channel, respectively. We discuss possible applications of the method in characterizing micro-flows, including those in biological systems.
The emerging field of deformable microfluidics widely employed in the Lab-on-a-Chip and MEMS communities offers an opportunity to study a relatively under-examined physics. The main objective of this work is to provide a deeper insight into the underlying coupled fluid-solid interactions of a low-Reynolds-number fluid flow through a shallow deformable microchannel with ultra-low height-to-width ratios. The fabricated deformable microchannels of several microns in height and few millimeters in width, whose aspect ratio is about two orders of magnitude smaller than that of the previous reports, …
Inertial migration of deformable particles has become appealing in recent years due to its numerous applications in microfluidics and biomedicine. The physics underlying the motion of such particles is contingent upon the presence of lift forces in microchannels. This importance initiated several works to analyze and quantify such forces acting on particles. However, since most of such attempts have focused on solid and non-deformable particles, we extend the lift force analysis for the case of deformable droplets and study the effects of Capillary numbers on their dynamics in this paper. Furt…
The migration characteristics of a suspended deformable droplet in a parallel plate microchannel is studied, both analytically and numerically, under the combined influence of a constant temperature gradient in the transverse direction and an imposed pressure driven flow. Any predefined transverse position in the micro channel can be attained by the droplet depending on the applied temperature gradient in the cross-stream direction or how small the droplet is with respect to the channel width. For the analytical solution, an asymptotic approach is used, where we neglect any effect of inertia o…
The electroosmotic flow of non-Newtonian fluids in deformable microchannels is fundamentally important in the understanding of the hydrodynamics in physiological flows. The performance of these microchannels is governed by the load bearing capacity indicating the maximum amount of load that the device can withstand. While significant research efforts are aimed towards the coupling of electrokinetics with substrate deformability, the corresponding enhancement in the performances still remains elusive. Towards this, employing an intricate coupling between substrate compliance, hydrodynamic, and …
A Modified Suspension-Balance Model for Deformable Particle Suspensions: Application to Blood Flows with Cell-Free Layer
FAMU–FSU College of Engineering（FAMU-FSU工程学院）；University of New Mexico（新墨西哥大学）；Sandia National Laboratories（桑迪亚国家实验室）；Institute for Successful Longevity, Florida State University（佛罗里达州立大学成功长寿研究所）
Dynamics of a deformable capsule in an oscillatory flow of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, capsule deformability, and channel flow rate have been explored by simulating the capsule within a microchannel. In addition, the simulation captures the effect of the type of imposed pressure oscillations on the migration pattern of the capsule. An oscillatory channel flow enables the focusing of extremely small biological particles by eliminating the need to design impractically long channels. The presented results show that the eq…
Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a nonlinear function of the pressure drop due to the deformation of the upper soft wall. Here, we extend the steady theory of Christov et al. (2018) by considering the start-up flow from rest, both in pressure-controlled and in flow-rate-controlled configurations. The characteristic scales and relevant parameters governing the transient flow are first identified,…
We present a comparative modelling study of fluid-structure interactions in microchannels. Through a mathematical analysis based on plate theory and the lubrication approximation for low-Reynolds-number flow, we derive models for the flow rate-pressure drop relation for long shallow microchannels with both thin and thick deformable top walls. These relations are tested against full three-dimensional two-way-coupled fluid-structure interaction simulations. Three types of microchannels, representing different elasticity regimes and having been experimentally characterized previously, are chosen …
Laminar flow in devices fabricated from soft materials causes deformation of the passage geometry, which affects the flow rate--pressure drop relation. For a given pressure drop, in channels with narrow rectangular cross-section, the flow rate varies as the cube of the channel height, so deformation can produce significant quantitative effects, including nonlinear dependence on the pressure drop [{Gervais, T., El-Ali, J., Günther, A. \& Jensen, K.\ F.}\ 2006 Flow-induced deformation of shallow microfluidic channels.\ \textit{Lab Chip} \textbf{6}, 500--507]. Gervais et. al. proposed a successfu…
CNN-powered micro- to macro-scale flow modeling in deformable porous media
Institute of Mechanics and Computational Mechanics (IBNM), Leibniz University Hannover（莱布尼茨汉诺威大学力学与计算力学研究所（IBNM））；Institute of Applied Mechanics, University of Stuttgart（斯图加特大学应用力学研究所）；Institute of General Mechanics, RWTH Aachen University（亚琛工业大学普通力学研究所）
Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes. Well established models based on poroelasticity theory exist for describing coupled fluid-solid mechanics. However, these models are not adapted to describe systems with multiple fluid phases or 'hybrid-scale' systems containing both solid-free regions and porous matrices. To address this problem, we present a novel computational fluid dynamics approach bas…
In this paper, the dynamic of inertial capsules into microfluidic bifurcations is studied. The fluid evolution is based on the solution of the BGK -- lattice Boltzmann scheme including a forcing term accounting for immersed geometries. The dynamic-Immersed Boundary forcing strategy is adopted for imposing no-slip boundary conditions on moving deformable or rigid structures, while, on fixed immersed geometries the Bouzidi-Firdaouss-Lallemand second-order bounce back technique is implemented. The proposed computational framework is employed to detail dynamics and deformation of rigid and deforma…
Viscous flows through configurations manufactured from soft materials apply both pressure and shear stress at the solid-liquid interface, leading to deformation of the cross-section, which affects the flow rate-pressure drop relation. Conventionally, calculating this flow rate-pressure drop relation requires solving the complete elastohydrodynamic problem, which couples the fluid flow and elastic deformation. In this work, we use the reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate-pressure drop relation in deformable channels, bypa…
In this study we attempt to explore the consequences of surfactant coating on the electrohydrodynamic manipulation of a drop motion in a plane Poiseuielle flow. In addition we consider bulk insoluble surfactants and a linear dependency of the surface tension on the surfactant concentration. Subsequently a double asymptotic perturbation method is used in terms of small electric Reynolds number and capillary number in the limit of a diffusion-dominated surfactant transport mechanism. Also going beyond the widely employed axisymmetric framework, the coupled system of governing differential equati…
The mechanical deformability of single cells is an important indicator for various diseases such as cancer, blood diseases and inflammation. Lab-on-a-chip devices allow to separate such cells from healthy cells using hydrodynamic forces. We perform hydrodynamic simulations based on the lattice-Boltzmann method and study the behavior of an elastic capsule in a microfluidic channel flow in the inertial regime. While inertial lift forces drive the capsule away from the channel center, its deformability favors migration in the opposite direction. Balancing both migration mechanisms, a deformable c…
