Rise time of spherical intruder in granular fluid

A model is developed to explain rise time of a spherical intruder placed in a granular bed, which is considered as fluid. Phenomenon of rising intruder in a granular bed is well known as Brazil nut effect. Radius of the intruder is varied with $R_n = R_0 n, n = 1 .. 10$. An approximation for $t << \tau$ is chosen in order to simplify the solution of second order differential equation of intruder vertical position to obtain the rise time T. A non-physical parameter $\alpha$ and also transformation from $T$ to $T'$ are needed to be introduced in order to control the results to mimic reported experiment qualitatively. Several forms of rise time $T_n$ and also transformed rise time $T_n'$ against $n$ are presented and discussed.