A relatively heavy, non-Newtonian power-law fluid of flow behavior index n is released from a point source into a saturated porous medium above an horizontal bed; the intruding volume increases with time as t^alpha . Spreading of the resulting axisymmetric gravity current is governed by a nonlinear equation amenable to a similarity solution, yielding an asymptotic rate of spreading proportional to t^((alpha+n)/(3+n)). The current shape factor is derived in closedform for an instantaneous release (alpha= 0 ), and numerically for time-dependent injection ( alpha different 0 ). For the general case alpha different 0 , the differential problem shows a singularity near the tip of the current and in the origin; the shape factor has an asymptote in the origin for n >=1 and alpha different 0 . Different kinds of analytical approximations to the general problem are developed near the origin and for the entire domain (a Frobenius series and one based on a recursive integration procedure). The behavior of the solutions is discussed for different values of n and alpha. The shape of the current is mostly sensitive to alpha and moderately to n ; the case alpha=3 acts as a transition between decelerating and accelerating currents.
Spreading of axisymmetric non-Newtonian powerlaw gravity currents in porous media / V. Di Federico; R. Archetti; S. Longo. - In: JOURNAL OF NON-NEWTONIAN FLUID MECHANICS. - ISSN 0377-0257. - 189-190(2012), pp. 31-39. [10.1016/j.jnnfm.2012.10.002]
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