Laminar Fully Developed Flow in Periodically Converging-diverging Microtubes

Laminar fully developed ow and pressure drop in linearly varying cross -section converging-diverging microtubes have been is investigated in this work. These microtubes are formed from a series of converging-diverging modules. An analytical model is developed for frictional ow resistance assuming parabolic axial velocity pro le in diverging and converging sections. Frictional ow resistance is found to be only a function of the geometrical parameters. To validate the model, a numerical study is carried out for the Reynolds number ranging from 0.01 to 100, for various taper angles and maximum-minimum radius ratios ranging from 0.5 to 1. Comparisons between the model and numerical results show that the proposed model predicts the axial velocity and the ow resistance accurately. As expected, the ow resistance is found to be effectively independent of the Reynolds number from numerical results. Parametric study shows that the effect of radius ratio is more signi cant than the taper angle. It is also observed that for small taper angles, ow resistance can be determined accurately by applying the local Poiseuille ow approximation. Assistant Professor and Mem. ASME. Corresponding author. E-mail: [email protected]. †PhD Candidate ‡Assistant Professor Nomenclature a(z) = radius of tube, m a0 = maximum radius of tube, m a1 = minimum radius of tube, m Ac = cross-sectional area, m2 L = half of module length, m m = slope of tube wall, [ ] Q = volumetric ow rate, m3=s r;z = cylindrical coordinate, m Re = Reynolds number, 2ρum;0a0=μ R f = frictional resistance, m 1s 1 R f = normalized ow resistance, R f =R f ;0 um = mean uid axial velocity, m=s u;v = velocity in z and r directions, m=s Greek β = a0=a(z) η = r=a(z) ε = a1=a0 ρ = uid density, kg=m3 μ = uid viscosity, kg=m:s φ = angle of tube wall, [ ] ∆P = pressure gradient, Pa