- #1
tanaygupta2000
- 208
- 14
- Homework Statement
- The concentration p(r,t) of ink diffusing in water is governed by the diffusion equation
∂p/∂t = D∇^2(p)
where D is a parameter known as diffusion constant. What is the average time taken for a molecule of ink to spread by a root mean square distance R?
(a) √(R/D)
(b) R/√D
(c) R^2 /D
(d) RD
- Relevant Equations
- ∂p/∂t = D∇^2(p)
I assumed p(r,t) as p(r,t) = R(r)T(t) as Separation of Variables method. I got the expression of T(t) as
T(t) = C1eC2t
and got a non-linear differential equation in R(r) as
d2R/dr2 + (2/r)dR/dr - (C/D)R = 0
(I assumed r to be the radial distance in spherical coordinates)
Now I'm not getting how to solve this differential equation.
T(t) = C1eC2t
and got a non-linear differential equation in R(r) as
d2R/dr2 + (2/r)dR/dr - (C/D)R = 0
(I assumed r to be the radial distance in spherical coordinates)
Now I'm not getting how to solve this differential equation.