I am now facing a fluid-particle interaction problem. I would like to simulate particle motion in a fluid.
I do know the external force acting on a particle (dielectrophoretic force in this case) and gravity and buoyancy forces. The assumption is the particle reaches its terminal velocity in zero time.
The thing I am not really sure about is the drag force. My particle is surrounded by fluid of certain viscosity and density. The problem is the "velocity field", if I can describe it in this way, is not isotropic - the fluid velocity might have (and has) different magnitude as well as orientation on different sides of the particle. (My problem is 2D only.)
The question I am asking is how can I add the velocities around the particle to get the total drag force affecting the particle in a physically correct way?
edit 1: Clarification. I only have one particle in the fluid and the fluid itself is already moving which causes the particle to move according to the drag force affecting it. I am aware of Brownian motion, but I have neglected it for now. The particle is significantly larger than water molecules, so I take water as a bulk and the particle as some sort of object which is moving through the bulk.
edit 2: Picture. I have made a simple drawing of my problem. The particle is significantly larger than the water molecules. The flow in the fluid is anisotropic. My question is how can I determine the final velocity = the final drag force. In another words where exactly would my particle move in next "time step"?