In Classical fluid mechanics, according to Navier-Stokes equation, the main forces acting on a flowing continuum include convection, molecular transport, and external forces. In the case of fluid flow in reservoir, gravity, capillary, and buoyant forces are active as well. My question is how we can connect these forces to those mentioned in Navier-Stokes equation? What role will gravity, capillary, and buoyant forces play if they are included in the Navier-Stokes equation?
I am not sure to understand fully your question ... In term of the mathematical model of the PDE, they all enter into the momentum equation as additional terms to convection, pressure and diffusion (that are surface-based forces). Many of them requires coupling with the internal energy equation. Yould could find useful the example of Marangoni flows model where you can see how work the forces acting in micro-gravity conditions.
A further classical example is buoyancy, modelled by Bousinnesq in such a way that small temperature gradients enter into density variation
Dear Filippo
I am looking for the origin or nature of forces which occur in reservoir. That is, convection,molecular transport, and external forces are normally observed in any fluid continuum, including oil reservoir. Each force may have been originated from a specific source. For example, the gravity drainage caused by differences in oil reservoir may be regarded as an external force. What about the other forces? For instance, how can we interpret capillary force in terms of three basic forces in a continuum?
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