General microscopic balance
The general microscopic balance gives pointtopoint variations of a specific (intensive) property in a defined space. Properties of interest include momentum (velocity), internal energy (temperature), and mass or mole fraction of a species in a multicomponent mixture.
Introduction
The microscopic balance is formulated as a differential equation on a "per volume" basis of a transport quantity . If we specify as the value of the transport quantity per unit volume, and the convective flux of as , then the differential equation describing how varies in a continuum has the general form

(1) 
where
 is the Del or nabla operator
 is the time variation of the transport quantity per unit volume
 is the net convective flow per unit volume of the transport quantity due to both advective (bulk flow) and molecular (diffusive) mechanisms.
 is the generation/consumption of the transport quantity per unit volume.
Convective flux and flow rate
Convective flux is the movement of a property due to both advective and molecular mechanisms. It has dimensions of "property per unit time per unit area" and has the general form

(2) 
where
 is the advective flux of due to a velocity field
 is the molecular flux of due to the gradient in .
The flow rate of the transport property, or , is related to the convective flux by

(3) 
where
 is the unit normal that defines
Molecular flux
The different types of molecular flux are
Type of transfer  Notes  

Mass  Fick's law of diffusion  
Momentum  Newton's law of viscosity  
Energy  Fourier's law of conduction 
Types of microscopic balances
The most common types of microscopic balances include total mass, component mass in a mixture, momentum, and internal energy. The various parts of Eq. 1 are provided in the table below
Property  Notes  

Total mass  0  Also known as the continuity equation.  
Mass (of component in a mixture)  Also known as the convection–diffusion equation. The generation/consumption term is the rate of chemical reaction.  
Momentum  Also known as the equation of motion. The generation/consumption term is the conversion of hydrostatic pressure to momentum.  
Internal energy  Also known as the heat equation. The generation/consumption term is reversible generation/consumption of internal energy due to compression/expansion plus the irreversible generation of internal energy due to viscous dissipation. 
It is to be noted that the continuity equation and the convection diffusionequation can also be expressed on a mole basis. Here, Eq. (1) becomes

(4) 
Property  Notes  

Total moles  The generation/consumption term is nonzero as the number of moles in not necessarily conserved in a reaction, i.e. if  
Moles (of component in a mixture) 