  In this work, we extend the analyses devoted to Newtonian viscous fluids
previously reported by Ribe [Physical Review E 68, 036305 (2003)], by
investigating shear thickening (dilatant) and shear thinning (pseudoplastic)
effects on the development of folding instabilities in non-Newtonian viscous
sheets of which viscosity is given by a power-law constitutive equation. Such
instabilities are trigged by compression stresses acting on viscous sheets that
leave a channel at a very small initial velocity, fall, and then hit a solid
surface or a fluid substrate. Our study is conducted through a mixed approach
combining direct numerical simulations, energy budget analyses, scaling laws,
and experiments. The numerical results are based on an adaptive variational
multi-scale method for multiphase flows, while Carpobol gel sheets are
considered for the conducted experiments. Two folding regimes are observed: (1)
the viscous regime; and (2) the gravitational one. Interestingly, only the
latter is affected by shear thinning/thickening manifestations within the
material. In short, when gravity is balanced by viscous forces along the
non-Newtonian viscous sheet, both the folding amplitude and the folding
frequency are given by a power-law function of the sheet slenderness, the
Galileo number (the ratio of the gravitational stress to the viscous one), and
the flow behaviour index. Highly shear thickening materials develop large
amplitude (and low frequency) instabilities, which, in contrast, tend to be
suppressed by shear thinning effects, and eventually cease. Lastly,
nonNewtonian effects on folding onset/cessation are also carefully explored. As
a result, non-Newtonian folding onset and cessation criteria are presented.
