Transient elastohydrodynamic drag on a particle moving near a deformable wall

Abstract

Naire, Shailesh, and Oliver E. Jensen. Epithelial cell deformation during surfactant-mediated airway reopening: a theoretical model. J Appl Physiol 99: 458 -471, 2005. First published March 31, 2005 doi:10.1152/japplphysiol.00796.2004.-A theoretical model is presented describing the reopening by an advancing air bubble of an initially liquid-filled collapsed airway lined with deformable epithelial cells. The model integrates descriptions of flow-structure interaction (accounting for nonlinear deformation of the airway wall and viscous resistance of the airway liquid flow), surfactant transport around the bubble tip (incorporating physicochemical parameters appropriate for Infasurf), and cell deformation (due to stretching of the airway wall and airway liquid flows). It is shown how the pressure required to drive a bubble into a flooded airway, peeling apart the wet airway walls, can be reduced substantially by surfactant, although the effectiveness of Infasurf is limited by slow adsorption at high concentrations. The model demonstrates how the addition of surfactant can lead to the spontaneous reopening of a collapsed airway, depending on the degree of initial airway collapse. The effective elastic modulus of the epithelial layer is shown to be a key determinant of the relative magnitude of strains generated by flow-induced shear stresses and by airway wall stretch. The model also shows how epithelial-layer compressibility can mediate strains arising from flow-induced normal stresses and stress gradients. recruitment; atelectrauma; volutrauma; fluid-structure interaction; surface tension SUCCESSFUL RECRUITMENT OF liquid-filled airways is a process of fundamental importance in human respiration, from the first breath onward, and is critical in the treatment of conditions such as infant or acute respiratory distress syndrome (ARDS). It is of particular current interest in the context of ARDS, where atelectrauma [damage to airway epithelium through the repeated opening and closing of airways and alveoli (9, 13, 43)], volutrauma [airway overdistension (56, 58)], and biotrauma (inflammatory airway insult secondary to mechanical injury) are candidate mechanisms of ventilator-induced lung injury (49, 53). Mechanisms of atelectrauma, for example, involve processes interacting over widely varying length scales: at the scale of the whole lung (involving forced inflation of a heterogeneous airway network); at the scale of an individual airway (where surface tension, airway compliance, and airway liquid viscosity are significant); at the scale of an airway epithelial cell (deforming in response to its local mechanical environment); and at the scale of individual molecules (for example epithelial-cell mechanosensors such as stretchactivated ion channels). Mathematical and computational models provide powerful tools with which to integrate descriptions of processes operating across such disparate scales. This paper seeks to contribute to the development of a theoretical framework for airway recruitment and specifically aims ...

Elastohydrodynamics induced by a rapidly moving microscopic body

“…Both led to an evolution equation that is integro-differential in form, which reflects the fact that linearized unsteady Stokes flow, present in the lubrication region, has long been known to possess memory effects (Boussinesq 1885;Basset 1888). In the absence of inertia, the integro-differential equation was seen to reduce down to the linearized form of the well-known partial differential equation that governs the quasi-steady regime (Lighthill 1968;Weekley et al 2006;Balmforth et al 2010), as expected.…”

“…(Of course, convective inertia is also negligible in this inner region, since the nonlinear terms are now multiplied by D 2 Re 1.) Whereas earlier studies (Lighthill 1968;Weekley et al 2006) considered the regime where unsteady inertia is unimportant (a → ∞), table 1 suggests that we find ourselves in the novel regime where a ∼ 1 (i.e. If the body's surface in the lubrication region (II) is designated as lying at z = −s 1 (x) when stationary, we note that the body shape can be represented locally as a power series expansion about x = 0, i.e.…”

Porous squeeze-film flow

“…However, Weekley et al (2006), who considered the approach of a parabolic surface towards a flat surface coated with a thin elastic layer through a thin layer of Newtonian fluid, found that the elastic layer deforms in such a way as to create a fluid layer of approximately uniform thickness, with the consequence that the approach is qualitatively the same as that of two flat rigid surfaces. Since the femoral condyles are roughly parabolic and cartilage is poroelastic, we anticipate qualitatively similar behaviour in the knee, and thus modelling the femoral condyles as a flat bearing is not an unreasonable first model.…”

Influence of non-hydrodynamic forces on the elastic response of an ultra-thin soft coating under fluid-mediated dynamic loading

“…The motion of an object close to a wall with intervening fluid is one of the cornerstones of lubrication studies, where an established finding is the growth in lift generated on the object upon approach, enabling the design of robust and effective bearing setups [2][3][4]. Furthermore, there is rich literature on 'soft lubrication' too, where either the approaching object or the wall or both are deformable [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], which finds applications in topics ranging from biotransport modelling [25][26][27][28] to tool design and analysis [29][30][31]. Such soft-lubrication setups are wide-spread in both natural and man-made world, examples being scanning probe microscope (SPM) and surface force apparatus (SFA) setups [32][33][34][35][36][37][38][39][40][41] and motion of biological entities like red blood corpuscles (RBCs) in fluidic environments [42][43][44].…”