It is know, that when one consider a suspension of particles. The motion of a given particle induces a flow field in the solvent, which will be felt by all the other particles. As a result these particles experience a force which is said to result from hydrodynamic interaction with the original...
If we consider a system of N suspended particles diffusing through a narrow channel. What happened if the hydrodynamic interactions are neglected? Is there only flow? How can the particles diffusse without flow?
Sorry, I forgot to said that I am considering a incompresible and viscous flow with very small Reynolds numbers.
\mathbf{\nabla}\times\textbf{u} is the curl for u, that you can become from the properties of the laplacian operator:
\mathbf{\nabla}^2 \mathbf{u} = \mathbf{\nabla} (...
My attempt following the case of 3 dimensions that I found in the book Fluid Mechanics by Kundu.
First of all, I have to obtain the stream function, for that we now
\vec{u} = \nabla \times \phi
in cartesians coordinates:
u_x = \frac{\partial \phi}{\partial y}
u_y =...
Homework Statement
hello everybody,
I am trying to obtain the flow velocity in two dimensions u(x,y) for the case of a flow past a circle. The equations to solve are:
\vec{\nabla} p = \mu \vec{\nabla}^2 u
\vec{\nabla} \cdot \vec{u} = 0
I am very blocked at the moment and I...