ON TANGENTIAL INTERACTION BETWEEN TWO RIGID SPHERES WITH INTERSTITIAL POWER-LAW FLUID

Discrete Element Modeling for wet particle assembly is based on the interactionsbetween two spheres with an interstitial fluid, when the fluid behaves as non-Newtonian, theanalysis for the tangential interaction becomes much more complicated. Up-to-date there is onlyGoldman's asymptotic solution for Newtonian fluid.In the authors' previous study, an approximate approach for the tangential interaction with aPower-law fluid was proceeded with an additional assumption for velocity, correspondingly anpressure equation was obtained and then solved numerically to get the viscous force and moment.However, its validity has not yet been estimated.In order to get the more accurate expressions, a new approach was carried out based onReynolds lubrication theory without the additional assumption. As a result a pressure equationwas derived and then simplified by using Fourier-series expansion, after the pressure equationwas solved, corresponding results for the viscous force and moment were obtained. Thenumerical results from the proposed equation were compared with those from the previousequation, showing that the additional assumption could be satisfied automatically for aNewtonian fluid, therefore the previous solutions can be applied to a Newtonian-like Power-lawfluid, otherwise the proposed pressure equation is necessary. For a Power-law fluid, the powerindex is a key factor affecting the accuracy. The more deviation of the index from 1, the moreerrors produced. Generally the differences of viscous force and moment between the previousand the proposed schemes are significant less than those of the pressure distribution.Especially when the power index approaches or exceeds 0.8, the previous results are ingood coincidence with the proposed ones, which suggest that the previous is valid with asatisfied accuracy, in this case, the additional assumption could be taken to simplify thederivation.