General criteria for the estimation of effective slip length over corrugated surfaces
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RESEARCH PAPER
General criteria for the estimation of effective slip length over corrugated surfaces Jia Chen1 · Young Ju Kim2 · Wook Ryol Hwang1 Received: 2 January 2020 / Accepted: 20 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we aim to develop an effective hydrodynamic boundary condition over patterned surfaces for the application to microfluidics. Four different criteria to estimate the effective Navier-slip length and their performance are investigated for flows over corrugated surfaces, such as patterned surfaces or porous interfaces, which can be applied for efficient flow simulations. Four distinctive methods were discussed in the estimation of slip length, namely: mass conservation, balance of energy dissipation rate, force balance, and interfacial slip velocity averaging. Expressions of slip length were derived analytically for each criterion in a pressure-driven flat channel flow and the slip length was determined using a combination of analytic and numerical methods. We report that (i) the slip length from force balance appears to be the most accurate and exactly the same as that from interfacial slip velocity averaging, (ii) the slip length from mass conservation deviates from that of force balance, though minor, particularly for a small relative channel height to the length scale of patterns or pores, and (iii) the energy balance yields significantly different slip lengths. The slip length reduces to a single value for a sufficiently large relative channel height, which indicates that it can be considered as a surface property in general, when the pattern dimension is much smaller than the length scale of flow. Keyword Patterned surfaces · Porous interface · Navier slip · Slip length · Conservation equations
1 Introduction Broad interest in modeling hydrodynamic boundary condition has arisen in the microfluidic system (Stone et al. 2004). It is widely recognized that the velocity slip over a solid-fluid interface in a microfluidic device is generated due to the presence of micro-grooved surfaces, which can result in the friction drag reduction (Min and Kim 2004; Fukagata et al. 2006). To quantify such complex microor nano-flow problems with corrugated surfaces, we are motivated to consider a favorable modeling method on the hydrodynamic boundary condition that can be implemented easily and efficiently in flow simulations. In this work, the * Young Ju Kim [email protected] * Wook Ryol Hwang [email protected] 1
School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju 52828, Korea
Extreme Resources Plant R&D, Korea Institute of Geoscience and Mineral Resources, Pohang 37559, Korea
2
effective Navier-slip boundary condition was investigated for the flows over corrugated surfaces, which include the flows over patterned surfaces and that near the interface of porous media. Both interfacial flows are of great interest in nature and industries, and patterned surfaces are often employed to control local flow field
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