Contraction-expansion Channel Research Articles

Geometrically parametrised reduced order models for studying the hysteresis of the Coanda effect in finite element-based incompressible fluid dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behaviour of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution.The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behaviour in a phase space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI.While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

Continuous CTC separation through a DEP-based contraction-expansion inertial microfluidic channel.

The efficient isolation of viable and intact circulating tumor cells (CTCs) from blood is critical for the genetic analysis of cancer cells, prediction of cancer progression, development of drugs, and evaluation of therapeutic treatments. While conventional cell separation devices utilize the size difference between CTCs and other blood cells, they fail to separate CTCs from white blood cells (WBCs) due to significant size overlap. To overcome this issue, we present a novel approach that combines curved contraction-expansion (CE) channels with dielectrophoresis (DEP) and inertial microfluidics to isolate CTCs from WBCs regardless of size overlap. This label-free and continuous separation method utilizes dielectric properties and size variation of cells for the separation of CTCs from WBCs. The results demonstrate that the proposed hybrid microfluidic channel can effectively isolate A549 CTCs from WBCs regardless of their size with a throughput of 300 μL/min, achieving a high separation distance of 233.4 μm at an applied voltage of 50 Vp-p . The proposed method allows for the modification of cell migration characteristics by controlling the number of CE sections of the channel, applied voltage, applied frequency, and flow rate. With its unique features of a single-stage separation, simple design, and tunability, the proposed method provides a promising alternative to the existing label-free cell separation techniques and may have a wide range of applications in biomedicine.

Analysis of Blood Flow Bifurcation Phenomena in Mitral Valve: A Numerical Approach to Predict Cardiac Arrest

Employing FVM, we have investigated numerically the rheological behavior of bifurcation phenomena of blood flow at various Reynolds numbers (Re) and at various values of contraction ratio (h), defined as the ratio of the inlet to narrow sections width of a two-dimensional planner contraction-expansion channel. Blood flow bifurcation through a planar contraction-expansion channel is analogous to the case of regurgitation (i.e., abnormal leakage of blood) in the mitral valve. In this work, we have studied the blood flow bifurcation characteristics including the normalized axial velocity profile, velocity gradient, dimensionless pressure, dimensionless longitudinal pressure gradient, pressure and skin friction coefficients on both the channel walls and analyzed the pressure drop, excess pressure drop for different values of Re. Secondly, blockage in the mitral valve is studied for different values of h. Pressure drops for various values of h are also studied to measure blood pressure. Correlation analyses are presented for normalized vortex length in terms of critical values of Re and h. It is revealed that if Re goes on increasing to 14.4 or more, flow breaks the symmetry at h = 15, and for each , recirculation length increases linearly with the increase in Re but decreases valve flaps that reduce blood flow to the heart muscles.

A sheathless high precise particle separation chip integrated contraction–expansion channel and deterministic lateral displacement

Cell sorting plays an important role in medical and biological research. This study aimed to propose a novel approach combining a contraction–expansion array (CEA) channel and a deterministic lateral displacement (DLD) array to achieve high-throughput and high-precision particle separation of different sizes. The CEA channel could realize the focusing and preliminary sorting of particles with different sizes under the joint action of inertia force and Dean resistance. The separation purity and efficiency could be further improved by coupling triangular microcolumn DLD. The finite element simulation analysis was carried out using commercial software COMSOL Multiphysics 5.4. The flow field distribution and the particle movement trajectory under the CEA channel and DLD array were simulated, respectively. The simulation results showed that this structure could achieve high-throughput and high-precision particle separation of different sizes. Finally, the separation experiments showed that the separation efficiency of 5 µm polystyrene microspheres as the target particles was more than 99%, and the separation purity was 96.1% under a high flow velocity. The microfluidic chip had the advantages of low cost, simple preparation process, and label-free, sheathless characteristics, thus realizing high-efficiency, high-throughput particle separation of different sizes. In general, the proposed approach provided a new pathway for sheathless particle separation with high precision and high throughput.

Numerical visualization of extensional flows in injection molding of polymer melts

Abstract Extensional flows generally take place in a channel with varied cross-sectional areas. During polymer processing with a variety of complex geometric features, it is difficult to separate extensional rates from shear rates in state-of-the-art predictive engineering tools of computational fluid dynamics. The recently proposed method of Tseng [Tseng, H.-C., “A Revisitation of Generalized Newtonian Fluids,” J Rheol 64 493–504 (2020)] decomposed the generalized strain rate as the characteristic shear and extensional rates via the rate-of-deformation tensor rotated along streamline coordinates. As validation for an isothermal center-gated disk flow, the predicted flow field profiles fairly matched the analytical solution for Newtonian fluid. Under injection molding simulations, an objective indicator is defined to visualize the colorful contours of extensional flows encountered in the gate-vicinity and the mid-plane of the cavity’s thickness direction, as well as contraction-expansion channels.

Bifurcation Analysis of Two-Dimensional Laminar Flow Through Sudden Expansion Channel

In this work, bifurcation characteristics of unsteady, viscous, Newtonian laminar flow in two-dimensional sudden expansion and sudden contraction-expansion channels have been studied for different values of expansion ratio. The governing equations have been solved using finite volume method and FLUENT software has been employed to visualize the simulation results. Three different mesh studies have been performed to calculate critical Reynolds number (Recr) for different types of bifurcation phenomena. It is found that Recr decreases with the increase in expansion ratio (ER).

Continuous Particle Separation Driven by 3D Ag-PDMS Electrodes with Dielectric Electrophoretic Force Coupled with Inertia Force.

Cell separation has become @important in biological and medical applications. Dielectrophoresis (DEP) is widely used due to the advantages it offers, such as the lack of a requirement for biological markers and the fact that it involves no damage to cells or particles. This study aimed to report a novel approach combining 3D sidewall electrodes and contraction/expansion (CEA) structures to separate three kinds of particles with different sizes or dielectric properties continuously. The separation was achieved through the interaction between electrophoretic forces and inertia forces. The CEA channel was capable of sorting particles with different sizes due to inertial forces, and also enhanced the nonuniformity of the electric field. The 3D electrodes generated a non-uniform electric field at the same height as the channels, which increased the action range of the DEP force. Finite element simulations using the commercial software, COMSOL Multiphysics 5.4, were performed to determine the flow field distributions, electric field distributions, and particle trajectories. The separation experiments were assessed by separating 4 µm polystyrene (PS) particles from 20 µm PS particles at different flow rates by experiencing positive and negative DEP. Subsequently, the sorting performances of the 4 µm PS particles, 20 µm PS particles, and 4 µm silica particles with different solution conductivities were observed. Both the numerical simulations and the practical particle separation displayed high separating efficiency (separation of 4 µm PS particles, 94.2%; separation of 20 µm PS particles, 92.1%; separation of 4 µm Silica particles, 95.3%). The proposed approach is expected to open a new approach to cell sorting and separating.

Inertial microfluidics: Determining the effect of geometric key parameters on capture efficiency along with a feasibility evaluation for bone marrow cells sorting.

Despite great developments in inertial microfluidics, there is still a lack of knowledge to precisely define the particles' behavior in the microchannels. In the present study, as a prerequisite to experimental studies, numerical simulations have been used to study the capture efficiency of target particles in the contraction-expansion microchannel, aiming to provide an estimation of the conditions at which the channel performs best. Fluid analysis based on Navier-Stokes equations is conducted using the finite element method to determine the streamlines and vortices. The highest capture efficiency for 10, 15, and 19-micron particles occurs when the center of the vortex is approximately in the middle of the wide section (at the flow rate of 0.35ml/min). In addition to investigating the effect of particle diameter and input flow rate, the effect of channel geometry parameters (channel height and initial length of the channel) on particle trapping has also been studied. Also, to consider great interest in separating different-sized bioparticles from a sample, a three-stage platform has been designed to separate four types of bone marrow cells and evaluate the possibility of using contraction-expansion channels in this application.

Secondary-flow-aided single-train elastic-inertial focusing in low elasticity viscoelastic fluids.

Elastic-inertial focusing has attracted increasing interest in recent years due to the three-dimensional (3D) single-train focusing ability it offers. However, multi-train focusing, instead of single-train focusing, was observed in viscoelastic fluids with low elasticity as a result of the competition between inertia effect and viscoelasticity effect. To address this issue, we employed the secondary flow to facilitate single-train elastic-inertial focusing in low elasticity viscoelastic fluids. A three-section contraction-expansion channel was designed to induce the secondary flow to pinch the multiplex focusing trains into a single one exactly at the channel centerline. After demonstrating the focusing process and mechanism in our device, we systematically explored and discussed the effects of particle diameter, operational flow rate, polymer concentration, and channel dimension on particle focusing performances. Our device enables single-train focusing of particles in viscoelastic fluids with low elasticity, and offers advantages of planar single-layer structure, and sheathless, external-field free operation.

Cascaded contraction-expansion channels for bacteria separation from RBCs using viscoelastic microfluidics

Implementation of viscoelasticity-based particle migration techniques has attracted significant interest thanks to its simplicity to achieve particle separation and enrichment at high sensitivity and accuracy for the last decade. Many methods have previously been developed for particle focusing and separation, but they all require long fluidic channels to enable the desired elastic force on particles. Here, a cascade contraction-expansion microfluidic system with a much shorter channel length is presented. Experimental results show that this system achieved continuous, sheathless particle separation in a viscoelastic fluid, and Enterococcus faecalis was successfully separated from red blood cells (RBCs). Thanks to its small size, the system provides extra advantage for its integration into small chips.

Dynamics of viscoelastic flow through axisymmetric constricted microcapillary at high elasticity number

The fundamental understanding of pore scale flow mechanisms associated with the mobilization of trapped oil ganglia during the injection of polymer solutions in porous media requires detailed analysis of viscoelastic flow through pore throats, which can be modeled as constricted capillaries. Despite the vast literature on macroscale and, more recently, microscale viscoelastic flow through contraction–expansion channels, the range of flow parameters covered in previous work does not include the flow dynamics that occur in pore throats of a porous medium, at which the Reynolds number Re is very low and the elasticity number El, defined as the ratio of elastic to inertial forces, is very high. We extend previous analyses of viscoelastic flow through constricted planar channels to axisymmetric geometry and flow conditions closer to pore scale flows. The effects of elastic forces are isolated by comparing the flow of a viscoelastic liquid to that of a Newtonian fluid with the similar shear viscosity. The pressure difference is measured as function of imposed flow rate. The different flow regimes are characterized by measuring the instantaneous and average velocity field near the constriction using micro particle image velocimetry (μ−PIV) technique.

Effects of Polymer Entanglement in Sodium Hyaluronate Solution on Elastic Instability in Abrupt Contraction-Expansion Micro Channels

In this study, the effects of polymer flexibility and entanglement on elastic instability were investigated by observing sodium hyaluronate (Hyaluronic Acid Sodium salt, Na-HA) solution in planar abrupt contraction-expansion microchannels. The rigidity of Na-HA in a solution is affected by ion concentration in the solution. Therefore, we prepared Na-HA water solution and Na-HA PBS solution with concentrations from 0.15 wt% to 0.45 wt%. The rheological properties were measured and analyzed to detect the Na-HA overlap and entanglement concentrations. The flow regimes of the Na-HA solutions in several planar abrupt contraction-expansion channels were characterized in terms of rheological properties, polymer flexibility and polymer entanglement.

An immersed boundary-lattice Boltzmann method for fluid-structure interaction problems involving viscoelastic fluids and complex geometries

An immersed boundary-lattice Boltzmann method (IB-LBM) for fluid-structure interaction (FSI) problems involving viscoelastic fluids and complex geometries is presented in this paper. In this method, the fluid dynamics and the constitutive equations of viscoelastic fluids are both solved using the lattice Boltzmann method. In order to enhance numerical stability in solving the constitutive equations, an artificial damping is introduced which does not affect the numerical results if the damping effect is much smaller than the relaxation and the convective effects. The structural dynamics including 2D and 3D capsules, 2D and 3D rigid particles and flags, are solved by the finite difference method (2D capsules, 2D and 3D rigid particles and flags) and the finite element method (3D capsules). The interaction between the solid structure and the fluid is enforced by an immersed boundary method. The overall framework of this method is very simple, enabling modelling FSI problems involving viscoelastic fluids and the inertia of both fluids and structures. It is very efficient for FSI problems involving high Weissenberg numbers flows, large deformations and complicated geometries without any preconditioner. This work uses IB-LBM to solve for the first time, flows involving viscoelastic fluids coupled with non-massless deforming structures. The method is also capable of solving very high Weissenberg number problems, as demonstrated by simulations of flexible particle flows at Wi=100. The present method and models are validated by several cases including a 2D rigid particle migration in a Giesekus Couette flow, a spherical particle rotation in an Oldroyd-B shear flow, a spherical particle settling in a FENE-CR fluid, 2D and 3D capsules deformation in a Newtonian shear flow, and a 3D flag flapping in a Newtonian free stream. In addition, the present method is also applied to simulate the deformation of 2D and 3D capsules in an Oldroyd-B shear flow, a 3D flag flapping in an Oldroyd-B free stream, and elastic capsule movement in a contraction-expansion channel filled with an Oldroyd-B fluid. Deformation of the capsules decreases with the increase of the Weissenberg number and the capsules experience monotonically increasing deformation when the Weissenberg number is above a critical value which is respectively 10 for 2D and 2 for 3D simulations. Viscoelasticity of the Oldroyd-B fluid hinders the flapping motion of the 3D flag. For elastic capsules passing through a periodic contraction-expansion channel, the capsules mix up after a short-term evolution, and then migrate to the bottom of the channel and almost follow two steady trajectories after a long-term evolution. The validations and applications provide extensive data which may be used to expand the currently limited database available for FSI benchmark studies.

Effects of flexibility and entanglement of sodium hyaluronate in solutions on the entry flow in micro abrupt contraction-expansion channels

In this study, the effects of polymer flexibility and entanglement on elastic instability were investigated by observing sodium hyaluronate (hyaluronic acid sodium salt, Na-HA) solution in planar abrupt contraction-expansion microchannels. As the rigidity of Na-HA depends on the ionic strength of a solvent, Na-HA was dissolved in water and phosphate buffered saline with concentrations from 0.15 wt. % to 0.45 wt. %. The rheological properties were measured and analyzed to detect the Na-HA overlap and entanglement concentrations. The flow regimes of the Na-HA solutions in several planar abrupt contraction-expansion channels were characterized in the Reynolds number and Weissenberg number space. The effects of the solvent, solution concentration, and channel geometry on the elastic corner vortex growth curve and flow regimes characterized by the Weissenberg number were analyzed. It was found that the entanglement of Na-HA in the solution is a more dominant factor affecting the flow regimes than the solution relaxation time and polymer rigidity.

Multiscale Simulations of Flows of a Well-Entangled Polymer Melt in a Contraction–Expansion Channel

We have successfully applied a multiscale simulation (MSS) method [Murashima, T.; Taniguchi, T. Europhys. Lett. 2011, 96, 18002] to flows of a monodispersed linear entangled polymer melt in a contraction–expansion channel. In our MSS method, a macroscopic model is coupled with a microscopic model through the velocity gradient tensor and the stress tensor. The smoothed particle hydrodynamics (SPH) method is employed as the macroscopic model, and a slip-link model is employed as the microscopic model. Two-dimensional flows in a 4:1:4 contraction–expansion channel are examined using our MSS method. From our MSSs, we have evaluated detailed microscopic information from the polymer chain dynamics, such as the local orientation of polymer chains, the average number of entanglements, and the number density of entanglements along a polymer chain. To further understand entanglements on a chain in a polymer melt under flows, we have developed a model equation that describes the time evolution of the number density ...

The Mechanism of Size-Based Particle Separation by Dielectrophoresis in the Viscoelastic Flows

Viscoelastic solution is encountered extensively in microfluidics. In this work, the particle movement of the viscoelastic flow in the contraction–expansion channel is demonstrated. The fluid is described by the Oldroyd-B model, and the particle is driven by dielectrophoretic (DEP) forces induced by the applied electric field. A time-dependent multiphysics numerical model with the thin electric double layer (EDL) assumption was developed, in which the Oldroyd-B viscoelastic fluid flow field, the electric field, and the movement of finite-size particles are solved simultaneously by an arbitrary Lagrangian–Eulerian (ALE) numerical method. By the numerically validated ALE method, the trajectories of particle with different sizes were obtained for the fluid with the Weissenberg number (Wi) of 1 and 0, which can be regarded as the Newtonian fluid. The trajectory in the Oldroyd-B flow with Wi = 1 is compared with that in the Newtonian fluid. Also, trajectories for different particles with different particle sizes moving in the flow with Wi = 1 are compared, which proves that the contraction–expansion channel can also be used for particle separation in the viscoelastic flow. The above results for this work provide the physical insight into the particle movement in the flow of viscous and elastic features.

Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology

We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

Effect of porous media properties on the onset of polymer extensional viscosity

Abstract Based on experimental results, it has been observed that, although the applied polymer solutions in EOR generally demonstrate shear thinning properties in rheometer, in porous media above a critical flow rate, apparent viscosity increases. This behavior is interpreted as the consequence of both elastic properties of polymer solution and rock properties. In this study, elastic properties of polymer solution is imported into numerical simulation by using modified form of the Carreau model and only effect of rock properties on the onset of extensional viscosity are studied. Results proved that for a more tortuous rock sample, extensional viscosity happens at a lower Darcy velocity. To define the onset of extensional viscosity, Deborah number explanation (De= eτ r ) is applied. A linear correlation is proposed as the relationship between stretch rate and Darcy velocity, in which the linearity coefficient is related to the tortuosity of rock sample. By calculating the stretch rate using this modification, De at the onset of extensional viscosity is the same for all rock samples. Furthermore some microscopic properties of pore geometries such as aspect ratio and length of pore throat are studied by using simplified 2D contraction–expansion channels. Initially the simulation is well validated by using experimental results reported by Chauveteau (1981) . By increasing the aspect ratio, the onset of extensional viscosity occurs at lower Darcy velocity as polymer molecules are being exposed to larger stretch rate values. On the other hand by increasing the length of contracted part, the onset of extensional viscosity happens at higher Darcy velocity. This is due to the fact that polymer molecules have more time to be relaxed after being deformed due to the contraction channel.

급축소-확대관에서 비뉴턴유체의 유동 특성에 관한 수치적 연구

대부분의 비뉴턴 유체 모델의 경우 격자볼쯔만 법을 이용한 3차원 유동해석에 효율적으로 적용하기 어려운 문제점을 가지고 있다. 이 연구에서는 이를 해결하기 위해 개발된 격자볼쯔만법 전용 비뉴턴 유체 모델인 Hydro-Kinetic 모델을 3차원 격자볼쯔만법 해석에 적용할 수 있도록 수정하고 이를 3차원 급축소 및 급확대 유동에 적용하여 얻은 결과를 통해서 강한 전단유동장에서 HK모델 유체의 거동을 분석하였다. HK모델은 변형률과 완화시간과의 관계를 나타낸 모델로 강한 전단유동장에서 국소적으로 큰 변형률이 발생하는 경우 완화시간이 급격하게 감소하여 해석이 불안정해지는 경향이 있어 격자볼쯔만법 해석안정성을 확보하기 위해서는 HK모델의 인수 와 완화시간을 일정한 구간에서 변화하도록 제한할 필요가 있다.

Effects of Ampholyte Dissociation Constants on Protein Separation in On-Chip Isoelectric Focusing

Numerical simulations are presented for ampholyte-based isoelectric focusing in 2D microgeometries. In this study, model proteins are focused in the presence of 25 biprotic ampholytes under an applied electric field. Each protein is considered as a simple polypeptide having ten charge states, while the biprotic ampholytes are selected to generate a shallow pH range of 6 to 9. Straight and contraction-expansion microchannels are considered here, and a nominal electric field of 300 V/cm is maintained for separation of proteins. Six distinct values of deltapKs between 1 and 3.5 are investigated for ampholytes to form pH profiles in a 1 cm long microchannel. Simulation results show that relatively larger values of deltapK(deltapK > 3) are required to form stepless pH profiles in the system. The peak heights and differential resolutions of focused proteins are much higher for lower values of deltapK for which a stepped pH profile is evident. For each protein, the time it takes for the two edges of a peak to merge increases linearly with deltapK, while the focusing time goes up exponentially with increasing deltapK. Both merging and focusing times of protein are higher for contraction-expansion microchannel than those of straight microchannel. For a particular value of deltapK, the contracted "Zoom" region of contraction-expansion channel is able to form more tightly focused bands than the expanded region.