Unsteady flows of a viscoplastic medium in channels

Building on Oldroyd’s viscoplastic legacy: Perspectives and new developments

“…the solution in y < 0 can be obtained by symmetry, w(x, y) being an odd function of y. For large y, we neglect all but the first term of the sum to find w−1 ∼ −e − π 2 y sin π 2 x; this can be matched with the far-field hodograph solution with m = 1 quoted in (47) by taking A = − 2 π Bi, X = 1 and Y = (2/π) log(2Bi −1 ), ignoring the unit wall speed, which can be added as an additional hodograph solution owing to the linearity of (31). The yield surface in (49) with these values must therefore characterize the remote plug when Bi 1, as illustrated in figure 5, which shows numerical solutions for low Bi that converge to the asymptotic result as Bi is reduced.…”

“…In many ways, the papers set the stage for later work on viscoplastic flow down conduits of arbitrary cross section (e.g. [23,24,25,26,27,28,29,30,31,32]).…”

The Effect of Microstructure on Models for the Flow of a Bingham Fluid in Porous Media: One-Dimensional Flows

“…The computation of pipe flow in more complicated geometries, such as square cross sections, is hindered by the need to find the yield surfaces numerically. Considerable progress has been made on this aspect, and we refer the reader to the work of Mosolov and Miasnikov (1966), Saramito and Roquet (2001), Huilgol (2006) and Muraleva and Muraleva (2009). It is worth mentioning that Saramito and Roquet (2001) show that the Buckingham-Reiner law for a circular tube may be used with minimal error for a square tube after rescaling.…”

Application of machine learning to viscoplastic flow modeling

“…This problem has been solved numerically in many papers (both for steady [14][15][16][17][18][19][20] and unsteady 21,22 cases). Wall slip boundary conditions were considered in [23][24][25] .…”