Mechanical properties momentum balance

Free-radical high-pressure LDPE tubular reactors can be modelled in terms of a system of non-linear differential equations. Over the past twenty years, several modelling studies have been reported in the literature (Thies and Schoenemann I 1Agrawal and Han I 2j, Chen et al. 1 3H, Thies 1 4], Lee and Marano l5J, Donati et al. 1 6J, Goto et al. 7J, Yoon and Rhee [ S y Gupta et al. 9 ). In the present work, a detailed mathematical model is developed for an LDPE tubular reactor. The variation of the physical properties of the reaction mixture with position is accounted for. The elements of the model are the reaction mechanism, the mass, energy and momentum balances, and the moments of live and dead polymer distributions. Polyethylene is produced via the following set of elementary reactions k. 

Summary. The first three balance equations are formulated in this section. The balances are necessary conditions to be fulfilled not only in thermodynamics but generally (in continuum mechanics). The balance of mass was formulated locally in several alternatives—(3.62), (3.63), or (3.65). The most important consequence of the balance of momentum is the Cauchy theorem (3.72), which introduces the stress tensor. The local form of this balance is then expressed by (3.76) or (3.77). The most relevant outcome of the balance of moment of momentum is the symmetry of the stress tensor (3.93). Note that in this section also an important class of quantities— the specific quantities—was introduced by (3.66) note particularly their derivative properties (3.67) and (3.68). 

Based on continuum mechanics, the motion of fluid particles is modeled as a two-phase flow with phase boundary represented by a sharp interface. More precisely, we consider isothermal flows of two fluids of constant material properties each, which are immiscible on the molecular scale. Within each phase, the balance equations of mass and momentum read... 

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