Universal dynamics in the onset of a Hagen-Poiseuille flow

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dc.creatorMortensen, Niels Asger
dc.creatorBruus, Henrik
dc.date2005-11-07
dc.date2006-06-09
dc.date.accessioned2026-07-07T06:52:14Z
dc.date.available2026-07-07T06:52:14Z
dc.descriptionThe dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results to channels of arbitrary cross section. We find that the steady state is reached after a characteristic time scale tau = (A/P)^2 (1/nu) where A and P are the cross-sectional area and perimeter, respectively, and $ν$ is the kinematic viscosity of the liquid. For the initial dynamics of the flow rate Q for t<<tau we find a universal linear dependence, Q(t)= Q_oo(alpha/C)(t/tau), where Q_oo is the asymptotic steady-state flow rate, alpha is the geometrical correction factor, and C=P^2/A is the compactness parameter. For the long-time dynamics Q(t) approaches Q_oo exponentially on the timescale $τ$, but with a weakly geometry-dependent prefactor of order unity, determined by the lowest eigenvalue of the Helmholz equation.
dc.description4 pages including 1 figure
dc.identifierhttps://arxiv.org/abs/physics/0511056
dc.identifierhttp://arxiv.org/abs/physics/0511056
dc.identifierPhys. Rev. E 74, 017301 (2006)
dc.identifierdoi:10.1103/PhysRevE.74.017301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105239
dc.subjectFluid Dynamics
dc.subjectSoft Condensed Matter
dc.titleUniversal dynamics in the onset of a Hagen-Poiseuille flow
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