Permeability of a polymer film

permeability_of_polymer_film

from numpy import array, ones
from numpy.linalg import inv
import matplotlib.pyplot as plt

# Ref. E. L Cussler - Diffusion mass transfer in fluid systems 2009

m = array([14])

text_data = """
0 14.0153
1 13.9855
4 13.9104
7 13.8156
8 13.7710
12 13.6492
14 13.5830
16 13.5256
"""

t,m = array(
    [x.split(' ') for x in text_data.split('\n') if len(x)>0],
    dtype=float
).T

plt.plot(t,m,'o')
h = array([t,ones(len(t))]).T
y = inv(h.T.dot(h)).dot(h.T).dot(m)

sstot=(m-sum(m)/len(m)).dot((m-sum(m)/len(m)))
eTe =(m - h.dot(y)).dot((m - h.dot(y)))
r2 = 1-eTe/sstot

plt.plot(t, h.dot(y), 
         '-', color='gray', 
         label='{:0.4g}(g/d) t + {:0.4g}g  '.format(*y)+
        r'$R^2={:0.4g}$'.format(r2))
plt.xlabel('t / d')
plt.ylabel('m / g')
plt.legend()

plt.show()