Viscous energy dissipation in slender channels with porous or semipermeable walls

نویسندگان

چکیده

We study the viscous dissipation in pipe flows long channels with porous or semipermeable walls, taking into account both bulk of channel and pores. give simple closed-form expressions for terms axially varying flow rate $Q(x)$ pressure $p(x)$, generalizing well-known expression $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{W}=Q\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}p=R{Q}^{2}$ case impenetrable walls constant $Q$, difference $\mathrm{\ensuremath{\Delta}}p$ between ends resistance $R$. When ${p}_{0}$ outside is constant, result straightforward generalization \.{}\fi{}}{W}=\mathrm{\ensuremath{\Delta}}\left[(p\ensuremath{-}{p}_{0})\phantom{\rule{0.16em}{0ex}}Q\right]$. Finally, applications to osmotic are considered.

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ژورنال

عنوان ژورنال: Physical review

سال: 2021

ISSN: ['0556-2813', '1538-4497', '1089-490X']

DOI: https://doi.org/10.1103/physreve.103.033108