Influence of Ribbon Structure Rough Wall on the Microscale Poiseuille Flow

Abstract

The regular perturbation method is introduced to investigate the influence of two-dimensional roughness on laminar flow in microchannels between two parallel plates. By superimposing a series of harmonic functions with identical dimensional amplitude as well as the same fundamental wave number, the wall roughness functions are obtained and the relative roughness can be determined as the maximal value of the product between the normalized roughness functions and a small parameter. Through modifying the fundamental wave number, the dimensionless roughness spacing is changed. Under this roughness model, the equations with respect to the disturbance stream function are obtained and analyzed numerically. The numerical results show that flowing in microchannels are more complex than that in macrochannels; there exist apparent fluctuations with streamlines and clear vortex structures in microchannels; the flow resistances are about 5–80% higher than the theoretical value under different wall-roughness parameters. Furthermore, analysis shows that the effect of roughness on the flow pattern is distinct from that on the friction factor.

Fluid Mechanics, Heat Transfer and Thermodynamic Issues of Micropipe Flows

“…The growing impact of surface roughness on friction coefficient at higher Reynolds numbers and lower micropipe diameters can evidently be inspected from these figures. Similar to the present findings, the augmenting role of roughness on friction coefficient with Reynolds number was as well documented by Vicente et al (2002), Guo & Li (2003), Engin et al (2004), Wang et al (2005), Petropoulos et al (2010) and Almeida et al (2010). On the other hand, with the increase of Reynolds number the variation rates in C f , at different micropipe diameter cases, become stronger with the particular values of 3.4→4.2% (d=1.00→0.50 mm), 6.6→8.1%, 9.6→11.9% and 12.4→15.2% for Re=500, 1000, 1500 and 2000.…”

Effects of gas compressibility and surface roughness on the flow in microfluidic devices

“…However, all of them are about the incompressible flow, with nearly no reports on the compressible flow so far. Wang et al [7,8] introduced the boundary perturbation method to study the two-dimensional wall roughness on the microscale plane Poiseille flow. In the study made by Hu [9], Rawool [10] and Du et al [11], a simplified roughness-element model was proposed.…”

Influence of three-dimensional wall roughness on the laminar flow in microtube

“…Kleinstreuer and Koo (2004) introduced a porous medium layer (PML) mode to simulate several kinds of microscale flow. Wang et al (2005) introduced a kind of regular perturbation method to study two-dimensional wall roughness on the microscale plane Poiseuille flow. Hu et al (2003) numerically simulated laminar flow in rough microtube to study the mechanism of the roughness effect.…”

“…In this method, a rough wall surface is converted into a smooth one and the physical quantities of flow field are expanded into perturbation series. The regular perturbation method was used in other literatures including Lesson andHuang (1976), Tö eren (1983), Bontozoglou and Papapolymerou (1996) and Cable et al (2001) as well as Wang et al (2005), and so on.…”