Mass-conserving kinematic equation

The mass-conserving kinematic equation for this system is of the form [32]... 

Via Eq. (136) the kinematic condition Eq. (131) is fulfilled automatically. Furthermore, a conservative discretization of the transport equation such as achieved with the FVM method guarantees local mass conservation for the two phases separately. With a description based on the volume fraction fimction, the two fluids can be regarded as a single fluid with spatially varying density and viscosity, according to... 

In summary, we have so far seen that there are two types of boundary conditions that apply at any solid surface or fluid interface the kinematic condition, (2-117), deriving from mass conservation and the dynamic boundary condition, normally in the form of (2-122), but sometimes also in the form of a Navier-slip condition, (2-124) or (2-125). When the boundary surface is a solid wall, then u is known and the conditions (2-117) and (2-122) provide a sufficient number of boundary conditions, along with conditions at other boundaries, to completely determine a solution to the equations of motion and continuity when the fluid can be treated as Newtonian. 

An additional inadequacy of equation (B2.3.12) is the assumption of an isotropic Mj distribution of product molecules in the detected rotational level. The product could be aligned because of the dynamics of the reaction. An extreme case is that of alignment imposed by kinematics for the mass combination H + HL -> HH+L, where if and L represent heavy and light atoms, respectively. From angular momentum conservation, we have + /j = Lj-+ Jj-, where is the total angular momentum of the system. Here, the vectors L... 

When a singular surface involves field variables that are affected by the motion and deformation of the medium, the geometrical and kinematical compatibility conditions should be supplemented by restrictions originating from the local balance equations. These conditions are called the dynamical conditions of compatibility. The dynamical conditions of compatibility are due to the local conservation of mass, balance of linear and angular momenta, balance of energy, and the local Clausius-Duhem inequality on ait). 

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