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Apr
12
awarded  Yearling
Feb
26
accepted Dependance of diffusion coefficient on size?
Feb
23
comment Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?
@lemon Let's say the fluid is water.
Feb
23
comment Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?
@lemon I am aware of this equipartition theorem. But I am worried that the mean deviation along a single dimension, $\langle x_j (t) ^ 2 \rangle$, changes with the number of dimensions, due to a change in effective viscosity, for example. This would make your argument invalid.
Feb
23
comment Dependance of diffusion coefficient on size?
Yes, now I get it, $u$ is $\sqrt(T/M)$ (which the typical velocity in Maxwell-Boltzmann distribution, up to some constant factors).
Feb
23
comment Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?
@lemon So $\langle x(t)^2 \rangle$ is proportional to $n$? I know about the equipartition theorem, but maybe other things change when going from 3-dimensions to 2-dimensions, like the effective viscosity.
Feb
23
comment Dependance of diffusion coefficient on size?
Sorry I missed your edits for the last 5 days, but please @notify me in comments. Thanks :)
Feb
23
revised Dependance of diffusion coefficient on size?
added 59 characters in body
Feb
23
asked Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?
Feb
23
comment Dependance of diffusion coefficient on size?
Your $Re$ is a Reynold's number? So $u$ is not the instantaneous velocity of the sphere, it is just an estimate of the maximum magnitude of this velocity, which is a constant. If I am correct, you should maybe clarify this a bit in your answer
Feb
23
comment Dependance of diffusion coefficient on size?
So $u$ is the drift velocity? I don't understand why there is a drift velocity here. There isn't a drift velocity in 3-dimensions. Basically this is saying that the diffusion coefficient depends on the velocity of motion of the particles, i.e., it is not a constant, so Fick's law doesn't apply in 2-dimensions? I don't understand this
Feb
16
comment Dependance of diffusion coefficient on size?
What is $u$, in the last line?
Feb
16
comment Dependance of diffusion coefficient on size?
What is the paper by Oseen with the 2-dimensional drag coefficient?
Feb
14
comment Dependance of diffusion coefficient on size?
No, in your expressions $\eta_D$ increases with $a$ in 3D, but decreases with $a$ in 2D.
Feb
14
comment Dependance of diffusion coefficient on size?
hmmm, also, the diffusion coefficient decreases with $a$ in three dimensions, but increases with $a$ in three dimensions... that's weird. Are you sure?
Feb
10
asked Dependance of diffusion coefficient on size?
Jan
25
comment Why are four-legged chairs so common?
What if you take into account the error in leg lenghts? In 4-legs, one of the legs can be shorter/longer than the others.
Jan
25
comment Why are four-legged chairs so common?
Moreover, 4-legs have the problem that when one leg is a bit shorter/larger, it will be unstable
Jan
7
awarded  Nice Question
Dec
27
awarded  Nice Question