Rectangular Cross-section Microchannels Research Articles

Confined bubble growth during flow boiling in a mini-/micro-channel of rectangular cross-section part II: Approximate 3-D numerical simulation

This Part II of the paper reports the three-dimensional (3-D) numerical modelling on bubbly flow in confined mini-/micro-channels using the volume of fluid (VOF) method in commercial CFD code FLUENT. The numerical simulation aims to provide detailed information of the fields of velocity, temperature and pressure so as to further understand the effect of bubble growth on the flow field and heat transfer from the channel wall. In Part I, the experiment of flow boiling in a mini-/micro-channel of rectangular cross-section was carried out and a simple one-dimensional (1-D) model for the interaction of the pressure fluctuations during the growth of a confined bubble with various kinds of upstream compressibility was developed as an aid to the rational specification of inlet resistance. In Part II, the experimental observers and the theoretical model developed in Part I are tested by performing the 3-D numerical simulation of bubble growth from nucleation to full confinement. The simulation involves some approximations based on a concept of pseudo-boiling to avoid the well-known difficulties of modelling bubble generation and growth. During the simulation, the volumetric growth rate of the bubble is defined to match the experimental observations. At small times prior to bubble detachment, a vapour flow was injected through a small hole in the wall to simulate nucleation. Following partial confinement, vapour injection was stopped and growth was driven by the generation of vapour at a defined rate at the contact area between the bubble and the superheated wall. The 3-D simulation reproduces the experimental observations of the distorted profile of the bubble and its trajectory during partially confined growth and provides information about flow and heat transfer in the bulk liquid outside the thin film region. The 3-D and 1-D predictions of the development of axial pressure distributions during partially and fully confined growth are in satisfactory agreement.

A four-zone model for saturated flow boiling in a microchannel of rectangular cross-section

A four-zone flow boiling model is presented to describe saturated flow boiling heat transfer mechanisms in a microchannel of rectangular cross-section. The boiling process in the microchannel is assumed to be a cyclic passage of four zones: (i) liquid-slug zone, (ii) elongated bubble zone, (iii) partially-dryout zone, and (iv) fully-dryout zone. The existence of the partially-dryout zone in this model is proposed to take into consideration of corner effects on boiling heat transfer in the microchannel. To verify this new model, an experimental study was carried out to investigate flow boiling heat transfer of water in a microchannel having a rectangular cross-section with a hydraulic diameter of 137 μm (202 μm in width and 104 μm in depth) with a length of 30 mm under three-side heating condition. The data for bubble nucleation frequency was correlated in terms of the Boiling number, which was used to determine the heat transfer coefficient. It is found that the present four-zone flow boiling model successfully predicts trends of boiling heat transfer data in a microchannel with a rectangular cross-section, having a sharp peak at low vapor quality depending on the mass flow rate. The predictions of flow boiling heat transfer coefficient in the microchannel are found in good agreement with experimental data with a MAE of 13.9%.

Pressure Drop in Rectangular Microchannels as Compared With Theory Based on Arbitrary Cross Section

Pressure driven liquid flow through rectangular cross-section microchannels is investigated experimentally. Polydimethylsiloxane microchannels are fabricated using soft lithography. Pressure drop data are used to characterize the friction factor over a range of aspect ratios from 0.13 to 0.76 and Reynolds number from 1 to 35 with distilled water as working fluid. Results are compared with the general model developed to predict the fully developed pressure drop in arbitrary cross-section microchannels. Using available theories, effects of different losses, such as developing region, minor flow contraction and expansion, and streaming potential on the measured pressure drop, are investigated. Experimental results compare well with the theory based on the presure drop in channels of arbitrary cross section.

Numerical and experimental study of gas flows in 2D and 3D microchannels

In the experiments conducted at Purdue, the air flow in rectangular cross-section microchannels was investigated using pressure sensitive paint. The high resolution pressure measurements were obtained for inlet-to-outlet pressure ratios from 1.76 to 20 with the outlet Knudsen numbers in the range from 0.003 to 0.4 based on the hydraulic diameter of 151.7 µm and the length-to-height ratio of about 50. In the slip flow regime, the air flow was simulated by the 2D and 3D Navier–Stokes equations with no-slip and slip boundary conditions. For various pressure ratios, the entrance flow development, compressibility and rarefaction effects were observed in both experiments and numerical simulations. It was found that the accurate modeling of gas flows in finite-length channels requires the inlet and outlet reservoirs to be included in computations. Effects of entrance geometry on the friction factor were studied for 3D cases. In both experiments and numerical modeling, significant pressure drop was found starting at the inlet chamber. The numerical modeling also predicted an apparent temperature drop at the channel exit.

Effects of applied electric field and microchannel wetted perimeter on electroosmotic velocity

Parameters which affect electroosmotic flow (EOF) behavior need to be determined for characterizing flow in miniature biological and chemical experimental processes. Several parameters like buffer pH, ionic concentration, applied electric field and channel dimensions influence the magnitude of the electroosmotic flow. We conducted numerical and experimental investigations to determine the impact of electric field strength and wetted microchannel perimeter on EOF in straight microchannels of rectangular cross-section. Deviation from theoretical behavior was also investigated. In the numerical model, we solved the continuity and Navier–Stokes equations for the fluid flow and the Gauss law equation for the electric field. Computational results were validated against experimental data for PDMS-glass channels of different wetted perimeters over a range of applied electric fields. Results show that increasing the applied electric field at constant wetted perimeter caused the electroosmotic mobility, the ratio of electroosmotic velocity to applied electric field, to increase nonlinearly. It was also found that increasing the wetted perimeter at constant applied electric field decreased the electroosmotic flow. These findings will be useful in determining the optimum value of the electric field required to produce a desired electroosmotic flow rate in a channel of a particular dimension. Alternately, these will also be useful in determining the optimum channel dimensions to provide a desired electroosmotic flow rate at a specified value of the electric field.

Gas hold-up and liquid film thickness in Taylor flow in rectangular microchannels

Abstract The gas hold-up in nitrogen/water Taylor flows in a glass microchannel of rectangular cross-section (100 μm × 50 μm) was shown to follow the Armand correlation. The validity of the Armand correlation implies that the liquid film thickness is not a function of the bubble velocity, which was varied between 0.24 and 7.12 m/s. Images of the Taylor flow were captured at a rate of 10,000 frames per second and were used to obtain the bubble and liquid slug lengths, the bubble velocity, and the number of bubbles formed per unit of time. A mass balance-based model was developed for Taylor flow with negligible liquid film velocities. The model describes the gas hold-up as a function of the liquid film thickness, the bubble and liquid slug lengths, the liquid superficial velocity, and the bubble formation frequency.

Experimental investigation of water flow in smooth and rough silicon microchannels

Water flow in smooth rectangular cross-section microchannels and microchannels with discrete rectangle roughness elements was experimentally investigated. The microchannels were microfabricated on silicon wafers and the hydraulic diameter ranged from 153 µm to 191 µm. The rectangle roughness elements mounted on the sidewall of the microchannel were 50 µm high and 50 µm wide. The global pressure drop and velocity field were measured for Reynolds numbers between 100 and 2300. For the smooth rectangular microchannels, the friction factor of the laminar flow agreed with the value predicted by classical theory. The transition from laminar to turbulent flow occurred at about Re = 2100. For the microchannels with roughness elements, the friction factor approaches the conventional value for Re < 900 and is higher than the conventional value when Re > 900. It indicates that the presence of roughness elements leads to the early transition in the microchannels. The streamwise mean velocity profiles and turbulent intensities obtained from microscopic particle image velocimetry (micro-PIV) show that the transition from laminar flow to turbulent flow occurred for Reynolds numbers ranging between 900 and 1100. This result was consistent with the experimental data of the friction factor. The experimental results of flow fields also suggest that the flow became fully developed turbulence for Re > 1400 in the rough microchannel. In the microchannel with roughness elements, large scale coherence structures are observed in the flow fields for Re < 2000.

Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios

Laminar convective heat transfer in the entrance region of microchannels of rectangular cross-section is investigated under circumferentially uniform wall temperature and axially uniform wall heat flux thermal boundary conditions. Three-dimensional numerical simulations were performed for laminar thermally developing flow in microchannels of different aspect ratios. Based on the temperature and heat flux distributions obtained, both the local and average Nusselt numbers are presented graphically as a function of the dimensionless axial distance and channel aspect ratio. Generalized correlations, useful for the design and optimization of microchannel heat sinks and other microfluidic devices, are proposed for predicting Nusselt numbers. The proposed correlations are compared with other conventional correlations and with available experimental data, and show very good agreement.

Thermal performance of silicon micro heat-sinks with electrokinetically-driven flows

A heat sink consisting of microchannels of rectangular or trapezoidal cross-section through which a polar fluid is circulated by means of an electro-osmotic pump was studied numerically. The equivalent pressure head—volume flow rate curve was determined for both geometries and the influence of the aspect ratio was investigated. The dimensionless temperature profile was calculated taking also the effect of Joule heating into account. The cross-sectional Nusselt number was determined for the above conditions and was found to be strongly influenced by the ratio of Joule heating to convective heat flux, M z . The dependence of the Nusselt number on the dimensionless electro-osmotic diameter ( k D h ) was also investigated for the two geometries and for increasing values of M z , and a comparison with the values obtained analytically for slug flow under the same conditions was made. The value of the Nusselt number, as a function of the aspect ratio, was also calculated for increasing values of M z . The numerical data presented in this paper can be useful to optimize silicon micro heat-sinks in terms of thermal performance.

Electroosmotic flow in a rectangular channel with variable wall zeta‐potential: Comparison of numerical simulation with asymptotic theory

Electroosmotic flow in a straight micro-channel of rectangular cross-section is computed numerically for several situations where the wall zeta-potential is not constant but has a specified spatial variation. The results of the computation are compared with an earlier published asymptotic theory based on the lubrication approximation: the assumption that any axial variations take place on a long length scale compared to a characteristic channel width. The computational results are found to be in excellent agreement with the theory even when the scale of axial variations is comparable to the channel width. In the opposite limit when the wavelength of fluctuations is much shorter than the channel width, the lubrication theory fails to describe the solution either qualitatively or quantitatively. In this short wave limit the solution is well described by Ajdari's theory for electroosmotic flow between infinite parallel plates (Ajdari, A., Phys. Rev. E 1996, 53, 4996-5005.) The infinitely thin electric double layer limit is assumed in the theory as well as in the simulation.

Effective heights and tangential momentum accommodation coefficients of gaseous slip flows in deep reactive ion etching rectangular microchannels

The behavior of a rarefied, compressible flow in long, constant cross section channels provides an opportunity to study complex gas dynamics in a simple geometry that allows analytical solutions. The problem of a rarefied, compressible flow in near unity aspect ratio rectangular cross section channels has been all but ignored despite it being a common flow geometry. We present analytical expressions for the mass flow rate in long, straight and uniform rectangular cross section microchannels in the slip flow regime. Using these analytical expressions, we extract the tangential momentum accommodation coefficient (TMAC) as well as the effective channel dimensions to account for a slight curvature of one of the walls of the rectangle. These expressions are effective in near unity aspect ratio rectangular microchannels made by deep reactive ion etching. The dependence of the flow behavior on the channel height to width aspect ratio is discussed as is the effect of the slight deviation from a rectangular cross section. The obtained TMAC results are consistent with values found by previous researchers using similar materials. Finally, a method of determining TMACs in channels consisting of non-homogenous materials or processing methods is presented.

Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces

A series of experiments are presented which study the flow kinematics of water past drag-reducing superhydrophobic surfaces. The ultrahydrophobic surfaces are fabricated from silicon wafers using photolithography and are designed to incorporate precise patterns of micrometer-sized ridges aligned in the flow direction. The ridges are made hydrophobic through a chemical reaction with an organosilane. An experimental flow cell is used to measure the velocity profile and the pressure drop as a function of the flow rate for a series of rectangular cross-section microchannel geometries and ultrahydrophobic surface designs. The velocity profile across the microchannel is determined through microparticle image velocimetry (μ-PIV) measurements capable of resolving the flow down to lengthscales well below the size of the surface features. Through these detailed velocity measurements, it is demonstrated that slip along the shear-free air-water interface supported between the hydrophobic micrometer-sized ridges is the primary mechanism responsible for the drag reduction observed for flows over ultrahydrophobic surfaces. A maximum slip velocity of more than 60% of the average velocity in the microchannel is found at the center of the shear-free air-water interface whereas the no-slip boundary condition is found to hold along the surface of the hydrophobic ridges. The experimental velocity and pressure drop measurements are compared to the predictions of numerical simulations and an analytical theory based on a simple model of an ultrahydrophobic surface composed of alternating shear-free and no-slip bands with good agreement.

Measurement of residence time distribution in microfluidic systems

We present a method for measuring the residence time distribution (RTD) in microfluidic systems. A piezoelectrically actuated sample injector releases approximately 100 nl of tracer liquid into a microchannel of rectangular cross section. The spreading of the tracer pulse in pressure-driven microflows is monitored with fluorescence microscopy measurements. Residence time distributions are determined for single-phase liquid and segmented gas–liquid microflows, with the RTD being significantly narrower for the latter case. The selected flow conditions are relevant to synthesis in microreactors with residence times up to several minutes.

Hydrodynamic control of the interface between two liquids flowing through a horizontal or vertical microchannel.

We derive a Fourier expansion for estimating laminar hydrodynamic spreading when two immiscible liquids flow steadily, side by side, at low Reynolds number, in a horizontal microchannel of rectangular cross-section. When the aspect ratio of the height of the channel to its width is small this expansion can be truncated after a couple of terms and solved to yield the steady-state position of the boundary in terms of the constant volumetric flow rates, the aspect ratio and the viscosities of the two liquids. Our formula shows that we can control the location of the liquid boundary at the outlet of the microchannel by adjusting the relative volumetric flow rates of the two inlet streams. If the microchannel is oriented vertically and the volumetric flow rates are very low, the position of the boundary is also influenced by gravitational forces that depend on the relative densities of the two liquids. We have tested solutions to our analytical expansions by running computational fluid dynamics simulations and have found excellent agreement. When the aspect ratio is 0.01 the leading term in the Fourier expansion for the spreading has an accuracy of about 1%. This accuracy deteriorates to about 12% when the aspect ratio is 0.1. An understanding of these spreading mechanisms is fundamental to the design of T-sensors and related microfluidic devices.

3245 進行波を用いた薄膜バルブレスマイクロポンプの基礎研究

We have developed a novel electrostatic micropump driven by traveling wave using surface micromachining techniques. This micropump can transport the liquid in both directions by only changing the driving signals for the electrostatic actuators without mechanical valves. The traveling wave can be generated by superimposing two standing waves whose phase differs by π/2 in time and space each other. The two standing waves are electrostatically produced along microchannel by comb electrodes which are operated by sine-wave voltages. The rectangular cross-section microchannel is composed of three rigid walls and one flexible wall on which the traveling wave is imposed. This micropump is smaller and simpler than other micropumps and is made of harmless materials (Al, Silicone rubber and Acrylate resin). We show that the developed micropump is suitable for the πTAS product applications.

Time-dependent laminar electrokinetic slip flow in infinitely extended rectangular microchannels

A rectangular microchannel is the most popular shape to be widely used in microelectromechanical devices. However, analytical solutions of flow in this shape of microchannels are seldom reported because of its two-dimensional problem. Furthermore, microflows in microchannels are more difficult to describe. In this paper, we addressed analytically the problem of laminar electrokinetic slip flow in microchannels with a rectangular cross section subjected to a time-dependent pressure gradient and a time-dependent electric field. The analytical solution has been determined based on the Debye–Hückel approximation and its solution is useful to precisely control microflow with slip in rectangular cross-section microchannels.