On a New Passive Scalar Equation With Variable Mass Diffusivity

The present work investigates the mass conservation equation of a Newtonian and non-Newtonian fluid in turbulent flow with variable mass diffusivity. The mass conservation equation is considered with the fluctuating terms in the concentration as well as in the mass diffusivity and is written for the average concentration, for the fluctuating concentration one as well as for the square of the fluctuating concentration. A new term appears in the form of product of the fluctuating mass diffusivity to the space gradient of the concentration fluctuation. This new term is interpreted and introduced in the mass conservation equation of the square of the fluctuating concentration where other new terms are also appearing. A possible physical interpretation is given to the different terms. Assuming several relations between mass diffusivity and concentration it is then possible to write expressions for the average and the fluctuating mass concentration which can be simplified on the basis of physical and mathematical considerations. Specifically, the mass flux is then expressed as the product of the derivative of the mass diffusivity to the gradient of the square of the mass fluctuation. Further considerations make possible to write a new mass conservation equation of the average concentration which include a new term which takes into account the space gradient of the mass flux. The mass conservation equation can be solved with the coupled solution of the equation of the square of the concentration fluctuation.