Note: I have read similar questions, but since it is not totally what I want, and they are old, I prefered to write a new one.
So, if one aims to work with Navier-Stokes at microscales, the equation that is used is the Stokes equation, where we have neglected the inertia part over the viscous force. This happens when Re << 1, an even one could work with Oseen equation for a better aproximation. Now, my question is regarding to the approximation that gives the Stokes flow. Either in Stokes or Oseen, you neglect/lineralize only: $v\cdot \nabla v$, but not $\partial_t v$. The last is omitted because the flow is steady. And the question is: physically, which is the interpretation of both terms and significance of steady?
I imagine that in a fixed volume V of fluid at a position x, the speed of the fluid will evolve its speed because it is changing by itself (partial), and because it is recieving fluid from outside (convection, inertia). Is that? if you have, say an alive bacterium, that is moving inside the fluid, it can be steady because the speed of fluid around the bacterium changes only by convection? Could it be also a possible scenario where the partial is not 0 at this scale?
I'm basically interested from a physical point of view, because I want to understand the main concepts, not just the math itself.