Laminar flow of some inelastic time-dependent fluids in pipes

The paper presents some modification of the previously published model of thixotropic fluids for the case of fluids with irreversible destruction of the structure. In the second part of the paper the laminar flow of this kind of fluids in pipes is discussed. A simple method of determining the initial value of the structural parameter at the inlet to the pipe is proposed. D pipe diameter, m - k ₁,k ₂ rheological parameter in eq. (5), Nsⁿ/m² - L pipe length, m - m ₁,m ₂ rheological parameter in eq. (5) - n ₁,n ₂ rheological parameter in eq. (6) - p pressure, Pa - v mean linear velocity in the pipe, m/s - rheological parameter in eq. (2), = 1 s - shear rate, s^–1 - structural parameter - ₀ initial value of structural parameter - ₁, ₂ mean value of natural time for breakdown and build-up of the structure, respectively, s - shear stress, Pa - fluid density, kg/m³ - mean value of the friction factor - De modified Deborah number defined by eq. (11) - Re _m generalized Reynolds number defined by eq. (16) - Re _n generalized Reynolds number defined by eq. (10) - Se structural numbers defined eq. (12)