4719.sagews

# (c - c0) / (c∞-c0) = erf(z/sqrt(4Dt))
#  where:
#	c = concentration of the diffusing substance, at a position within the slab
#	c0 = concentration of the diffusing substance, at the slab’s surface
#	c∞ = concentration of the diffusing substance, deep within the slab
#	z = depth within the slab at which ‘c’ is measured
#	D = diffusion coefficient of the substance within the slab
#	t = time since diffusion began

var('c c0 cinf z D t')

c0 = 1          # arbitrary units; saturation
cinf = 0        # system is initially anaerobic
D  = 0.00002    # O2 in H2O; cm2/s

a = plot([])
for i in range(1,20):
    t = i*86400/4    # in seconds; 86400s/day
    c = (cinf-c0)*erf(z/sqrt(4*D*t))+c0
    a += plot(c, z, (0,10))

show(a)

t = i*86400/4    # in seconds; 86400s/day
    c = (cinf-c0)*erf(z/sqrt(4*D*t))+c0

int(integrate(c,z,0,10))

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