Finite wavelength selection for the linear instability of a suspension of settling spheroids
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 689, 183-202 p.Article in journal (Refereed) Published
The instability of an initially homogeneous suspension of spheroids, settling due to gravity, is reconsidered. For non-spherical particles, previous studies in the literature report that normal-mode density perturbations of maximum growth rate are those of arbitrarily large, horizontal wavelength. Using the 'mixture theory' for two-phase flow we show that the maximum growth rate for horizontal density perturbations is obtained for a finite wavelength if the inertia of the bulk motion associated with the normal-mode density perturbation is accounted for. We find that for long wavelengths, lambda -> infinity, the growth rate approaches zero as lambda(-2/3). The maximum growth rate is obtained for lambda similar to d/root alpha(0)Re(L)(1/2), where d is the axis perpendicular to the axis of rotational symmetry of the spheroid, alpha(0) is the undisturbed volume fraction of particles and Re(L), typically << 1, is a Reynolds number of the bulk motion on a typical length scale L similar to d/p root alpha(0) and a velocity scale on the order of the undisturbed settling speed. The theoretical results for the wavelength selection agree qualitatively well with previous experimental results in the literature of measured correlation lengths of vertical streamers in settling fibre suspensions.
Place, publisher, year, edition, pages
Cambridge University Press, 2011. Vol. 689, 183-202 p.
instability, particle/fluid flow, suspension
Engineering and Technology Fluid Mechanics and Acoustics
IdentifiersURN: urn:nbn:se:kth:diva-47800DOI: 10.1017/jfm.2011.410ISI: 000298802800008ScopusID: 2-s2.0-84855806386OAI: oai:DiVA.org:kth-47800DiVA: diva2:456273
FunderSwedish Research Council, 621-2008-3854
QC 201111142011-11-142011-11-142012-02-06Bibliographically approved