Integral equation for calculation of distribution function of activation energy of shear viscosity

A new technique of calculation of a distribution function of activation energy (f(E)) of shear viscosity based on a regularization procedure applied to the Fredholm integral equation of the first kind has been developed using the Baxter-Drayton and Brady model for concentrated and flocculated suspensions. This technique has been applied to the rheological data obtained at different shear rates for aqueous suspensions with fumed silica A-300 and low-molecular (3,4,5-trihydroxybenzoic acid and 1,5-dioxynaphthalene) or high-molecular (poly(vinyl pyrrolidone) of 12.7 kDa and ossein of 20-29 kDa) compounds over a wide concentration range (up to 25 wt% of both components) and at different temperatures. Monomodal f(E) distributions are observed for the suspensions with individual A-300 or A-300 with a low amount of adsorbed organics. In the case of larger amounts of nanosilica and organics the f(E) distributions are multimodal because of stronger structurization and coagulation of the systems that require a high energy to break the coagulation structures resisting to the shear flow.