Deformable Microchannel Research Articles

Droplet migration through deformable stenosed microchannel: Dynamics and blockage

Understanding droplet migration in stenosed microchannels is crucial for various applications. This study explores how droplet properties (viscosity, surface tension, density, and diameter) and channel characteristics (stenosis degree and wall elasticity) affect droplet movement and blockage in deformable stenosed microchannels. Higher viscosities lead to lubrication film formation between droplet and wall, reducing viscous resistance, while increased surface tension enhances wall adherence, amplifying Laplace pressure. Droplet entry is primarily influenced by viscosity, while passage is governed by surface tension and curvature effects at the droplet–wall interface. Surface tension dominates pressure generation in the channel and within the droplet, influencing wall deformation and hydrodynamic resistance. The study examines the relationship among droplet viscosity, density, surface tension, channel wall elasticity, and the maximum capillary number (Camax) on the lubrication film thickness between the droplet and the channel wall. A lubrication film exists for Camax≥0.095, reducing blockage chances. A critical range of the modified Ohnesorge number Oh*×1000≤132 and the capillary number (Camax<0.095) indicates higher chances of droplet blockage. The blockage prediction method based on the modified Ohnesorge exhibits a sensitivity of 100%, specificity of 92.6%, and accuracy of 95.9%. Additionally, the study explores the impact of channel wall elasticity on droplet entry, transit, and hydrodynamic resistance. Higher wall elasticity facilitates faster entry but introduces curvature during passage, increasing frictional resistance and blockage likelihood as the wall softens.

Fluid structure-interaction in a deformable microchannel conveying a viscoelastic fluid

We theoretically analyze the interaction between a viscoelastic fluid flow, whose constitutive equation is the simplified Phan–Thien–Tanner model, and a deformable slender shallow microchannel. The microchannel top wall displacement is analyzed considering two cases: a) as a thin plate, using the Kirchhoff–Love theory, and b) as a thick plate, based on the Reissner–Mindlin theory. The mathematical model is nondimensionalized, and dimensionless parameters related to problem physics arise that control the fluid–structure interaction. The governing equations that describe the hydrodynamic field are simplified using the lubrication theory, and the displacement of the top wall is analyzed for each plate theory, relating the hydrodynamic pressure and the volumetric flow rate. These equations are implicit in the pressure and are solved numerically. The effect of dimensionless parameters on the pressure drop-volumetric flow rate relationship is analyzed, showing that for a viscoelastic fluid flowing through deformable channels, the volumetric flow rate is higher than the case of a Newtonian fluid under the same pressure. Our results are compared against those published in the specialized literature, showing an excellent agreement.

Electro-osmotic nanofluid flow in a curved microchannel

Biological mechanisms offer significant improvement in the efficiency of next generation energy systems. Motivated by new developments in distensible pumping systems, ionic electro-kinetic manipulation and nanoscale liquids (”nanofluids”), in the present study a mathematical model is developed to simulate the entropy generation and electro-osmotic transport of nanofluids in a curved deformable microchannel driven by peristaltic transport. Both thermal and species (nano-particle) buoyancy effects are included and Soret and Dufour cross-diffusion effects. The appropriate conservation equations are normalized with scaled variables and the resulting dimensionless nonlinear boundary value problem is solved in a transformed coordinate system. Simplification of the mathematics is achieved via lubrication approximations and low zeta potential (Debye Hückel linearization). The effects of various parameters, i.e. electro-osmotic velocity, EDL (electrical double layer) thickness and zeta potential ratio on velocity profile and temperature profiles are computed. The effects of Brinkman number (viscous heating parameter) and Joule (electrical field heating) parameter on nano-particle concentration profiles are also simulated. The micro-channel curvature effects on the nanofluid flow characteristics and thermal characteristics are also computed. Furthermore, streamline patterns, temperature contours, nano-particles concentration contours and entropy generation rate contours are plotted for various curvature parameters. Results indicate that the curvature of the channel and electro-osmotic body force influence strongly the sources of entropy generation rate. The study finds applications in bio-inspired electro-osmotic nanofluid pumping in microscale energy applications.

Pressure-Driven Thermal Slip Flow in the Elliptical Channel with Radial Oscillatory Wall

This paper is aimed at presenting thermal slip flow driven by oscillatory pressure gradient in a deformable microchannel of elliptic cross-section. The fully developed flow of Newtonian fluid is considered, and Navier slip is applied on the boundary. The boundary value problem is formulated and applied to the coronary blood flow-heat transfer phenomenon during thermotherapy treatment. Its semianalytical solutions of velocity and temperature fields are carried out by the Ritz method. The effects of oscillatory wall and slip length on velocity and temperature fields of blood are investigated.

Experimental and theoretical investigation of a low-Reynolds-number flow through deformable shallow microchannels with ultra-low height-to-width aspect ratios

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, i.e. $$Re \sim O(10^{-2}$$ – $$10^{+1})$$ , fluid flow through a shallow deformable microchannel with ultra-low height-to-width-ratios, i.e. $$O(10^{-3})$$ . 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, allow us to investigate the fluid flow characteristics spanning a variety of distinct regimes from small wall deflections, where the deformable microchannel resembles its corresponding rigid one, to wall deflections much larger than the original height, where the height-independent characteristic behavior emerges. The effects of the microchannel geometry, membrane properties, and pressure difference across the channel are represented by a lumped variable called flexibility parameter. Under the same pressure drop across different channels, any difference in their geometries is reflected into the flexibility parameter of the channels, which can potentially cause the devices to operate under distinct regimes of the fluid–solid characteristics. For a fabricated microchannel with given membrane properties and channel geometry, on the other hand, a sufficiently large change in the applied pressure difference can alter the flow-structure behavior from one characteristic regime to another. By appropriately introducing the flexibility parameter and the dimensionless volumetric flow rate, a master curve is found for the fluid flow through any long and shallow deformable microchannel. A criterion is also suggested for determining whether the coupled or decoupled fluid–solid mechanics should be considered.

Flow rate–pressure drop relation for deformable shallow microfluidic channels

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 (Gervaiset al.,Lab on a Chip, vol. 6, 2006, pp. 500–507). Gervaiset al. proposed a successful model of the deformation-induced change in the flow rate by heuristically coupling a Hookean elastic response with the lubrication approximation for Stokes flow. However, their model contains a fitting parameter that must be found for each channel shape by performing an experiment. We present a perturbation approach for the flow rate–pressure drop relation in a shallow deformable microchannel using the theory of isotropic quasi-static plate bending and the Stokes equations under a lubrication approximation (specifically, the ratio of the channel’s height to its width and of the channel’s height to its length are both assumed small). Our result contains no free parameters and confirms Gervaiset al.’s observation that the flow rate is a quartic polynomial of the pressure drop. The derived flow rate–pressure drop relation compares favourably with experimental measurements.

Electro-osmotic flow of couple stress fluids in a micro-channel propagated by peristalsis

A mathematical model is developed for electro-osmotic peristaltic pumping of a non-Newtonian liquid in a deformable micro-channel. Stokes' couple stress fluid model is employed to represent realistic working liquids. The Poisson-Boltzmann equation for electric potential distribution is implemented owing to the presence of an electrical double layer (EDL) in the micro-channel. Using long wavelength, lubrication theory and Debye-Huckel approximations, the linearized transformed dimensionless boundary value problem is solved analytically. The influence of electro-osmotic parameter (inversely proportional to Debye length), maximum electro-osmotic velocity (a function of external applied electrical field) and couple stress parameter on axial velocity, volumetric flow rate, pressure gradient, local wall shear stress and stream function distributions is evaluated in detail with the aid of graphs. The Newtonian fluid case is retrieved as a special case with vanishing couple stress effects. With increasing the couple stress parameter there is a significant increase in the axial pressure gradient whereas the core axial velocity is reduced. An increase in the electro-osmotic parameter both induces flow acceleration in the core region (around the channel centreline) and it also enhances the axial pressure gradient substantially. The study is relevant in the simulation of novel smart bio-inspired space pumps, chromatography and medical micro-scale devices.

Droplet generation in a microchannel with a controllable deformable wall

We report the droplet generation behavior of a microfluidic droplet generator with a controllable deformable membrane wall using experiments and analytical model. The confinement at the droplet generation junction is controlled by using external pressure, which acts on the membrane, to generate droplets smaller than junction size (with other parameters fixed) and stable and monodispersed droplets even at higher capillary numbers. A non-dimensional parameter, i.e., controlling parameter K p, is used to represent the membrane deformation characteristics due to the external pressure. We investigate the effect of the controlled membrane deformation (in terms of K p), viscosity ratio λ and flow rate ratio r on the droplet size and mobility. A correlation is developed to predict droplet size in the controllable deformable microchannel in terms of the controlling parameter K p, viscosity ratio λ and flow rate ratio r. Due to the deflection of the membrane wall, we demonstrate that the transition from the stable dripping regime to the unstable jetting regime is delayed to a higher capillary number Ca (as compared to rigid droplet generators), thus pushing the high throughput limit. The droplet generator also enables generation of droplets of sizes smaller than the junction size by adjusting the controlling parameter.

Remote sensing of pressure inside deformable microchannels using light scattering in Scotch tape.

We present a simple but effective method to measure the pressure inside a deformable microchannel using laser scattering in a translucent Scotch tape. Our idea exploits the fact that the speckle pattern generated by a turbid layer is sensitive to the changes in the optical wavefront of an impinging beam. A change in the internal pressure of a channel deforms the elastic channel, which can be detected by measuring the speckle patterns of a coherent laser beam that has passed through the channel and the Scotch tape. We demonstrate that with a proper calibration, internal pressure can be remotely sensed with the resolution of 0.1 kPa within a pressure range of 0-3 kPa after calibration.

Non-invasive measurement of the pressure distribution in a deformable micro-channel

AbstractDirect and non-invasive 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 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 hydrodynamic pressure distribution. The method is validated by measurements on planar microfluidic 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,${\zeta }_{max} / 2{h}_{0} = O(1)$, with${\zeta }_{max} $and$2{h}_{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.

A Latchable Phase-Change Microvalve With Integrated Heaters

This paper presents a latchable phase-change microvalve with integrated microheaters, which is suitable for lab-on-a-chip systems where minimal energy consumption is desired. The microvalve exploits low-melting-point paraffin wax, whose solid-liquid phase changes allow switching of fluid flow through deformable microchannel ceiling. Switching is initiated by melting of paraffin through an integrated microheater, with an additional pneumatic pressure used for the open-to-close switching. The valve consumes energy only during initiation of valve switching. When paraffin solidifies, the switched state is maintained passively. The microvalve was fabricated from polydimethylsiloxane through multilayer soft lithography techniques. Experiments show that the valve can switch flow within 4-8 s due to the small thermal mass and localized melting of paraffin wax; when closed, the valve can passively withstand an inlet pressure over 50 kPa without leakage. Time response of the valve can be further improved with improved heater and wax chamber designs, while the latching ability can be improved by optimizing the wax chamber/membrane design. Compared to existing latchable phase-change valves, the microvalve has no risk of cross-contamination. In addition, the improved sealing offered by the compliant membrane makes the valve robust and flexible in operation, allowing large ranges of initiation pressure from various actuation schemes.

A latchable microvalve using phase change of paraffin wax

This paper presents a novel latchable phase-change microvalve that can potentially be used for flow gating in portable lab-on-a-chip systems where minimal energy consumption is desired. The microvalve innovatively exploits paraffin wax of low melting point, whose solid–liquid phase changes allow the closing and opening of fluid flow through deformable microchannel ceiling. The latchable phase-change actuation scheme can be used in an active valve to shut off and open fluid flow. Valve switching is initiated by melting of paraffin through heating, with an additional pneumatic pressure used for valve switching from open to closed state. Energy consumption is only required during the valve switching. After paraffin solidifies the switched state is subsequently maintained passively without further consumption of energy. The microvalve can be fabricated from PDMS through the multilayer soft lithography technique. Testing results demonstrate that the valve has response times of 60 s for closing and 100 s for opening; when closed, the valve can passively withstand a pressure up to 35 kPa without significant leakage. The relatively slow time response of the proof-of-concept device can be readily improved by integrating on-chip heaters, while the latchability of the microvalve can be improved by optimizing the wax chamber and membrane design. Compared to existing latchable phase-change valves, the thin compliant channel ceiling of the valve separates the fluid channel from the wax chamber. Therefore, the microvalve is free of potential contamination of the fluid by the paraffin wax. In addition, the improved sealing offered by the compliant membrane makes the valve robust and flexible in operation, allowing large ranges of initiation pressure generated from various actuation schemes.