Linear transport equations, liquid phase

Secondly, the standard single phase -equation was adopted to describe the shear induced turbulence. Third, by adding these two transport equations, assuming that the bubble and shear induced turbulent kinetic energy contributions can be linearly superimposed, they obtained the following -equation for the liquid phase ... 

With the presence of the liquid-phase and interphase mass, momentum, and energy transport, additional source terms are added into the continuity, momentum, and scalar transport equations. As the droplets evaporate the heat of vaporization is taken from the gas phase and there is evaporative cooling of the surrounding gas. This gives rise to a sink term in the energy equation. By assuming adiabatic walls and unity Lewis number, the energy and scalar equations have the same boundary conditions and are linearly dependent [5]. 

All voltammetric equations obtained at the moment by solving simple problems of linear semi-infinite diffusion (in particular, the well-known Randles-Sevcik equation) do not take into account the specific characteristics of anodic selective dissolution of a homogeneous alloy solid phase segregation of an alloy components, initial roughness of an electrode, coupled solid-liquid phase transport, displacement of an alloy/solution interface, concentration dependence of the interdiffusion coefficient, presence of the vacancy sinks and relaxation of the non-equilibrium vacancy subsystem. 

The linear driving force (LDF) model can be classified in the group of equilibrium transport dispersive models (Fig. 9.5). For this model it is no longer assumed that the mobile and the stationary phases are permanently in equilibrium state, so that an additional mass-balance equation for the stationary phase is required. Assuming a linear concentration gradient an effective mass-transfer coefficient keff is implemented, where all mass-transfer resistances and the diffusion into the pores of the particle are lumped together. In this model a constant local equilibrium between the solid and the liquid in the pores is assumed. 

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