A new twist on Stokes’ second problem: Partial penetration of nonlinearity in sheared viscoelastic layers

Purely pulsating flow of a viscoelastic fluid in a pipe revisited: The limit of large Womersley number

“…c ¼ 1), where shear waves are effectively underdamped and thus extend to the whole fluid domain. This behavior has been reported in several viscoelastic fluid flows induced by an oscillating plate (e.g., [15,14,16]; see Discussion below).…”

“…It is interesting to note that this waviness is similar to that found in underdamped (Ferry) shear waves generated by an oscillating plate (see, e.g., Refs. [15,14,16]). In fact, the structure of the solution for the velocity above the oscillating plate in the case of a Maxwell fluid (e.g., Eq.…”

“…It is easily found from (16) that this external solution is f e ¼ Ài in all the orders of the expansion in powers of b. Thus, the external solution for the velocity, valid to any order in b, is, according to (8) and (10),…”

“…Since the blood is known to behave as a non-Newtonian fluid [4], analytical solutions for several non-Newtonian fluid models have also been obtained later for this idealized pipe flow, as well as for some other more general pulsating pipe flows, not only in relation to blood flow, but to some other physiological and industrial processes, many of them in relation to the flow enhancement effect [5][6][7][8][9][10][11][12][13][14]. Some of these works, in addition to other ones for the viscoelastic fluid flow generated by an oscillating plate [15,16], are cited below in connection to the solutions described in the present work. Here we consider the flow in a pipe due to a purely periodic pressure gradient of a fluid modelled by a simple Maxwell model in order to analyse the interesting pulsating behavior of a viscoelastic fluid in the limit of large Womersley numbers, of interest for the blood flow in arteries.…”

Dynamic responses in small intestinal mucus: Relevance for the maintenance of an intact barrier

“…The glycosylated bottlebrush structures of the mucin molecule function well as boundary lubricants and facilitate the sliding of mucin coated surfaces [29]. It is known that within viscoelastic layers, such as mucus, subjected to shear stress the distribution of stress at different depths will vary, a phenomenon known as shear banding [30,31], which would support the formation of a slippage plane. It has also been suggested that two dimensional laminar arrays of mucins could enhance the slippage plane effect [10].…”