Rough curved microchannel slip flow
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Rough curved microchannel slip flow Nnamdi Fidelis Okechi1,a
, Saleem Asghar2
1 Mathematics Programme, National Mathematical Centre, Abuja, Nigeria 2 Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
Received: 20 January 2020 / Accepted: 28 July 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper models a slip flow through a curved microchannel. The curved walls confining the flow have surface roughness of small amplitude. Through domain perturbation analysis, the analytical expression of the volumetric flow rate is obtained as a function of the Knudsen number of the slip flow, the channel radius of curvature and the parameters characterising the surface roughness. It is found that the surface roughness effect is decreased in the slip regime compared to the continuum case. The study further shows that the volumetric flow rate can be enhanced, depending on roughness parameters. The channel radius of curvature has a significant effect on the entire flow.
1 Introduction Flow dynamics in microchannels have been studied by researchers, diversely and intensively, due to the developments in the area of microfabrication technology. The advancement in this research field is well accompanied by many significant applications, including microsensors and microdevices [1–5], biofluid mechanics [6, 7], and vacuum technology [8]. The understanding of the flow behaviour in microchannels is central to the design of microelectromechanical systems (MEMS). Studies have shown that the behaviours of flow in microdomains are considerably distinct from those observed in macrodomains [9–14]. For microchannel flows, the mean free path is comparable to the characteristic dimension of the channel. Thus, the microscopic effect is significant, compared to macrochannel flows. In a microchannel, the fluid–wall interactions exhibit non-continuum phenomena, due to rarefaction effect. Consequently, a slip regime exists, where velocity slip for isothermal flows [14, 15] and temperature jump for nonisothermal flows [16] are encountered at the flow walls. In the slip regime, the non-continuum phenomenon at the walls can be described by slip wall conditions expressed using the Knudsen number (Kn), where the Knudsen number denotes the ratio of mean free path to characteristic length scale of the microchannel. For low Knudsen number (0.001 < Kn ≤ 0.1), the flow in the microchannel is reasonably governed by continuum conservation equations, whereas the wall conditions are modelled by a non-continuum approach to describe the fluid–wall interactions [17]. The limitations in macrofabrication technology lead to the presence of distributed roughness on the walls of microchannels, fabricated via several micromachining techniques. The
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
(2020) 135:685
wall roughness alters the flow geometry, such that the flow characteristics are modified depen
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