Viscous energy dissipation in slender channels with porous or semipermeable walls

Hanna Rademaker, Kaare H. Jensen, Tomas Bohr

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We study the viscous dissipation in pipe flows in long channels with porous or semipermeable walls, taking into account both the dissipation in the bulk of the channel and in the pores. We give simple closed-form expressions for the dissipation in terms of the axially varying flow rate Q(x) and the pressure p(x), generalizing the well-known expression W˙=QΔp=RQ2 for the case of impenetrable walls with constant Q, pressure difference Δp between the ends of the pipe and resistance R. When the pressure p0 outside the pipe is constant, the result is the straightforward generalization W˙=Δ(p-p0)Q. Finally, applications to osmotic flows are considered.

Original languageEnglish
Article number033108
JournalPhysical Review E
Issue number3
Number of pages5
Publication statusPublished - 2021

Bibliographical note

Funding Information:
We are grateful for support from the Danish Council for Independent Research–Natural Sciences (Grant No. 12-126055) and from Villum Fonden through Research Grant No. 13166.


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