[CIG-LONG] Re:Re: Re: Cumulative strain history in Gale et alia - Stokes, example (Walter Landry)

[Walter Landry]

Christoph Schrank <schrank at geology.utoronto.ca> wrote:
> Hi, Walter,
> 
> I wanted to simulate the classical simple Physics experiment with a
> solid ball falling in a fluid in a pipe where the frictional force
> is given by:
> 
> F_r = 6phrv,
> 
> lifting force by: F_l = -r_fluid V_ball g,
> 
> and Fg=r_ball V_ball g. Adding these up to zero for constant sinking
> velocity leads to: v_sink =(2/9)(r_ball - r_fluid )r^2 g/h.

These calculations are for a sphere.  However, the simulation is in
2D, so we need to use calculations for a cylinder.  That changes the
drag force to 

  4*pi*viscosity*velocity/log(3.70*viscosity/(velocity*radius*density))

The buoyancy force is

  pi*radius^2 * (density_ball - density_fluid)*gravity

Doing a nonlinear solve for the velocity gives

 velocity=0.0026914

which is almost ten times larger than the case for the sphere.  The
number you were getting (about 0.0004) is off because of the proximity
of the boundary.  As you increase the distance from the cylinder to
the boundaries, you get larger velocities.  However, running the code
in 3D should give you the lower velocity (0.00027778).  I am wrestling
with my supercomputer account, but when I get that fixed, I will run
2D and 3D cases.

Cheers,
Walter Landry
walter at geodynamics.org