A Stokesian analysis of a submerged viscous jet impinging on a planar wall

Abstract

The wall pressure and wall shear stress of a submerged viscous jet impinging on an infinite planar wall are derived. The whole creeping flow of semi-infinite extent is generated via distributions on a cylindrical pipe of tangentially and normally directed Stokeslets which are modified to achieve no-slip at the wall in two stages. First the pressure and vorticity jumps associated with the Poiseuille flow upstream in the pipe are readily forced, and then further distributions, of zero density far upstream but with square-root density singularity at the orifice z = h, are added to achieve no-slip on the pipe wall. Thus the adjustment of the interior pipe flow from its upstream parabolic profile to its exit profile is fully included in -and a major feature of -this creeping flow analysis. The maximum plane wall pressure is always located on the axis r = 0, and decreases as h increases to alleviate the obstruction effect of the wall. The interaction of the inflow with the ambient fluid in the neighbourhood of z = 0 causes the wall stress to rise rapidly to a maximum and then decay with the radial position of this maximum increasing as h increases. This behaviour is discussed in the context of physiological experiments on auditory sensory hair cells that motivated this study.

Jet‐Printing Microfluidic Devices on Demand

“…The aqueous phase is confined by fluid walls-media:FC40 interfaces-which are robust yet easily pierced (so liquids can be added/removed through them at any preselected point) whilst being transparent. The physics underlying flow during such jetting is complex; [12][13][14][15] therefore, we establish appropriate conditions. We then exploit jetting to "beat" the Poisson limit to clone single mammalian cells, subculture them (again using a contactless method), and perfuse them steadily with fresh media for a week.…”

The Stokesian flow field of an oscillatory submerged viscous jet impinging on a planar wall

“…It extends the steady case of Davis et al [2] by involving a periodic version of Stokeslets imposed along the pipe wall and the plane wall. A more detailed description of the flow field is thus presented, in order to display the periodic streamfunction through instantaneous level curves during a half cycle.…”

“…The steady limit studied by Davis et al [2] can be recovered from these and subsequent expressions by use of the formulae…”

“…All rights reserved. sensitivity of mammalian hearing, Davis et al [2] developed a model of a submerged viscous fluid jet impinging on an infinite planar wall and identified non-uniformities in the wall pressure and wall shear stress. This leads to the question of whether modelling the periodic case would be helpful in understanding the experiments by Canlon et al [3], Canlon & Brundin [4], Brundin & Russell [5] and Rybalchenko & Santos-Sacchi [6], in which the lateral wall of the OHC was subjected to an oscillatory fluid jet.…”

Jet-printing microfluidic devices on demand

“…The aqueous phase is confined by fluid wallsmedia:FC40 interfaces -which are robust yet easily pierced (so liquids can be added/removed through them at any preselected point) whilst being transparent. The physics underlying flow during such jetting is complex (Glauert, 1956;Deshpande and Vaishnav, 1982;Phares et al, 2000;Davis et al, 2012); therefore, we establish appropriate conditions. We then exploit jetting to 'beat' the Poisson limit to clone single mammalian cells by limited dilution, sub-culture them (again using a contactless method), and perfuse them steadily with fresh media for a week.…”