Asymptotically exact formulas for channel flows over liquid-infused surfaces

• Published in: IMA journal of applied mathematics Vol. 89; no. 4; pp. 623 - 660
• Main Authors: Rodriguez-Broadbent, Henry, Miyoshi, Hiroyuki, Crowdy, Darren G
• Format: Journal Article
• Language: English
• Published: Oxford University Press 11.12.2024
• Subjects: asymptotic analysis; complex analysis; microfluidics
• DOI: 10.1093/imamat/hxae026
• ISSN: 0272-4960

Analytical formulas are derived describing channel flows over liquid-infused surfaces. The formulas are explicit, asymptotically exact and readily evaluated; no numerical scheme beyond simple quadrature is needed to calculate the flows. The formulas are obtained using a three-stage asymptotic analysis under the assumptions that an array of aligned finite-length grooves on the lower wall of a channel are (i) slender, (ii) well separated from the upper channel wall and (iii) well separated from each other. Despite these apparently limiting assumptions it is found, by comparison with full numerical simulations, that the formulas give excellent approximations to the flow across a much broader range of operating conditions. Useful formulas for the hydrodynamic slip lengths of the liquid-infused surfaces are reported and tested against both numerical simulations and other approximate formulas appearing in the literature. The formulas are also expected to be useful in assessing the possibility of so-called shear-induced failure of liquid-infused surfaces.