Abstract
This work presents a detailed numerical investigation on the required development length (L=L/B) in laminar Newtonian fluid flow in microchannels with rectangular cross section and different aspect ratios (AR). The advent of new microfluidic technologies shifted the practical Reynolds numbers (Re) to the range of unitary (and even lower) orders of magnitude, i.e., creeping flow conditions. Therefore, accurate estimations of L at Re≤O(1) are important for microsystem design. At such low Reynolds numbers, in which inertial forces are less dominant than viscous forces, flow characteristics become necessarily different from those at the macroscale where Re is typically much larger. A judicious choice of mesh refinement and adequate numerical methods allowed obtaining accurate results and a general correlation for estimating L, valid in the ranges 0≤Re≤2000 and 0.1≤AR≤1, thus covering applications in both macro and microfluidics.
Highlights
Over the past two decades, many microfluidic systems have been designed and built for a wide range of applications
The results obtained for Lext considering different aspect ratio (AR) are presented in Table 3, for a number of representative Reynolds numbers (Re) values
It should be remarked that the errors are below 3.5%, within the asymptotic range of convergence
Summary
Over the past two decades, many microfluidic systems have been designed and built for a wide range of applications. Sadri and Floryan [21] presented a linear correlation for the relation of L( Re) ranging from Re = 0.01 to 2200 They relied on a numerical method based on the use of the stream function and vorticity in the flow governing equations, with a compact fourth-order finite-difference scheme. The values of their correlation overpredict the entry length at low. We present a detailed numerical investigation on the development length (L = L/B) in rectangular microchannels by considering the laminar regime (including the limit of creeping flow conditions) and the dependence on the aspect ratio, AR. It should be remarked that preliminary tests with different meshes where conducted initially, in order to select the most appropriate meshes, without compromising the convergence accuracy and the computational time needed to perform the simulations
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