N spherical particles of radius R are diffusing in water in a container, as shown in...

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N spherical particles of radius R are diffusing in water in a container, as shown in the Figure. The depth of water is L. The mass of each particle is m and the drag applied on a particle by water is given by the Stokes equation Fa- 6πμRV Where u is the viscosity of water and V is the relative velocity between the particle and water. Assume that the side walls of the container do not affect the diffusion of the particles and the buoyancy force is neglected. In steady state, it is known that the number density of the particles is a function of x. (a) Build a model for the number density of the particles and solve the model for the number density distribution. N spherical particles of radius R are diffusing in water in a container, as shown in the Figure. The depth of water is L. The mass of each particle is m and the drag applied on a particle by water is given by the Stokes equation Fa- 6πμRV Where u is the viscosity of water and V is the relative velocity between the particle and water. Assume that the side walls of the container do not affect the diffusion of the particles and the buoyancy force is neglected. In steady state, it is known that the number density of the particles is a function of x. (a) Build a model for the number density of the particles and solve the model for the number density distribution.