Microchannels Of Arbitrary Cross-section Research Articles

A generalization of the Lucas–Washburn–Rideal law to composite microchannels of arbitrary cross section

Capillary microfluidics or capillarics has been lately gaining importance in the biotechnological and biological domains. In these domains where biological and chemical targets are transported by fluids, it has been shown that capillary actuation of fluids does not require bulky pumps or syringes and produces microsystems with a low cost of fabrication, which are user-friendly, portable and compatible with telemedicine. Capillary systems for biotechnology can be confined or open; i.e., the fluid moves inside a closed channel or in a channel with a boundary with air. In this work, we propose a general expression for the determination of the velocities of spontaneous capillary flows in composite, confined microchannels of arbitrary shapes. This expression generalizes the conventional Lucas–Washburn model which is valid for cylindrical channels. It is shown that the use of an equivalent hydraulic diameter in the Lucas–Washburn–Rideal model introduces a bias when the shape of the channel cross section differs notably from a circle. The approach also shows that relatively large velocities—at the scale of microsystems—can be reached by capillary microflows, depending on the shape of the channel, and that transport distances can be important.

On Laminar Flow in Microfabricated Channels with Partial Semi-Circular Profiles

Soft and hard micromachining techniques used to develop microfluidic devices can yield microchannels of many different cross-sectional profiles. For semi-circular microchannels, these techniques often produce only partialsemicircular (PSC) cross-sections. This study investigated fully developed laminar flow in PSC microchannels as a function of a circularity index, κ, defined as the ratio of the radiuses along the curved and flat surfaces of the PSC profile. A correction factor, K, to the Hagen-Poiseuille relation was determined and was well-fitted by the power-law relationship K=5.299/κ2.56. Actual correction factors were compared to estimates based on several hydraulic models for flow in microchannels of arbitrary cross-section, as well as the half-ellipsoid cross-section. The level of wall shear stress, when normalized by the pressure drop per unit length, increased approximately linearly with increase in the circularity index, κ.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross Section with Constant Axial Heat Flux

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly connected cross sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully developed, laminar flow in microchannels of arbitrary cross sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross sections with a maximum difference on the order of 9%.

Slip-Flow Pressure Drop in Microchannels of General Cross Section

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

Pressure Drop of Fully-Developed, Laminar Flow in Microchannels of Arbitrary Cross-Section

Abstract The pressure drop of fully developed, laminar, incompressible flow in smooth mini- and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes. Also, the comparison of the model with experimental data, collected by several researchers, shows good agreement.