I Numerical Solution to the Rayleigh Plesset Equation

[KDPhysics]

TL;DR Summary

I have been trying to find a numerical solution to the Rayleigh Plesset equation (for a sonoluminescing bubble) using a Python code. Read up here if you need to refresh on this (surprisingly) unknown field: https://en.m.wikipedia.org/wiki/Sonoluminescence
However, the python code seems to give a strange output. Please, gods of computational physics help me...

I have been trying to numerically solve the Rayleigh Plesset equation:

$R\ddot{R} + \frac{3}{2}(\dot{R})^2=\frac{p_g-p_0-p(t)}{\rho_l}-4\mu\frac{\dot{R}}{R}-\frac{2\gamma}{\rho_lR}$

using the odeint python function. The code is given below:

import numpy as np
from matplotlib import pyplot as plt
from scipy.integrate import odeint

# define equations
def equation(y0, t):
    R, u = y0
    return u, (P_g-P_0-1317000*np.sin(2*np.pi*26500*t)-2*sigma/R)/(R*rho)-4*miu*u/(R**2)-3*u**2/(2*R)

def plot_results(time, R):
    plt.plot(time, R)

    s = " for R0=" + str(R_0*1000) + "mm"
    plt.title("Oscillations in Bubble Radius" + s)
    plt.xlabel("Time")
    plt.ylabel("Radius of bubble")
    plt.grid(True)
    plt.show()

# parameters
time = np.arange(0, 0.0005, 0.000000025)
rho = 1000
sigma = 0.0725
miu = 8.9*10**(-4)
P_g = 2330
P_0 = 10000

# initial conditions
R_0 = 0.0001
u_0 = 0

R_1 = odeint(equation, [R_0, u_0], time)

R = R_1[:,0]

plot_results(time, R)

Wh

en i run the code, I get a very strange output.

It should look more like this:

[1]: https://i.stack.imgur.com/aTc3j.png
[2]: https://i.stack.imgur.com/fQ9J8.gif

EDIT:
Ok, I've been working on the code for a while, and I think I have found the mistake. I was using an approximate form of the equation. For anyone interested in the correct code, here it is (feel free to edit it if you want, I am bad at writing efficient code XD).

import numpy as np
from matplotlib import pyplot as plt
from scipy.integrate import odeint

# define equations
def equation(y0, t):
    R, u = y0
    return u, (P_g-P_0-1317000*np.cos(2*np.pi*26500*t)-2*sigma/R-4*miu*u/R+(2*sigma/R_0+P_0-P_g)*(R_0/R)**(3*k))/(R*rho)-3*u**2/(2*R)

#define plot
def plot_results(mtimes, R):
    plt.plot(mtimes, R)

    s = " for R0=" + str(R_0*10**6) + "$\mu$m"
    plt.title("Oscillations in Bubble Radius" + s)
    plt.xlabel("T/$\mu$s")
    plt.ylabel("R/$\mu$m")
    plt.grid(True)
    plt.show()

# parameters
time = np.arange(0, 0.00002, 0.00000000025)
rho = 1000
sigma = 0.0725
miu = 8.9*10**(-4)
P_g = 2330
P_0 = 10000
k = 1.33

# initial conditions
R_0 = 0.0000026
u_0 = 0

R_1 = odeint(equation, [R_0, u_0], time)

R = R_1[:,0]*10**6
mtimes = time*10**6

#plot the results
plot_results(mtimes, R)

I rescaled the axes so that the marks wouldn't overlap, and the results should coincide with past literature.

 

[vacuum]

Thanks for your help!Great job on finding and fixing the mistake in your code! It's always important to double check and make sure that your equations are accurate, especially when working with numerical solutions. Keep up the good work!