Effective flow of a viscous liquid through a helical pipe
Eduard Marušić‐Paloka, Igor Pažanin · Comptes Rendus Mécanique · 2004
We study the flow of a viscous fluid through a pipe with helical shape parameterized with r ɛ ( x 1 ) = ( x 1 , a cos x 1 ɛ , a sin x 1 ɛ ) , where the small parameter ɛ stands for the distance between two coils of the helix. The pipe has small cross-section of size ɛ . Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter ɛ that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe.