Mass conservation equations, continuous media

Continuum mechanics, one of our most successful physical theories, is readily applicable to the process industries. In continuum mechanics, the existence of molecules is ignored, and matter is treated as a continuous medium. The continuum hypothesis is valid, provided the equations of continuum mechanics are applied at sufficiently large length scales and time scales that the properties of individual molecules are not noticed. The mapping of the laws of mass, momentum, and energy conservation to the continuum results in field equations that describe the dynamics of the continuum. These field equations, variously known as the equations of motion, the equations of change, or simply the conservation equations, are nonlinear, partial differential equations that can be solved, in principle, when combined with the appropriate constitutive information and boundary conditions. 

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