Diffusion, osmosis
Biophysics seminar
Szilvia Barkó
I.
Diffusion
Book of Medical biophysics: chapter III/2.
Brownian-motion
What is the reason of Brownian-motion?
Diffusion: The particles of the material spread in the medium via Brownian-motion
Important rule: it goes from higher concentrations to lower concentrations
DIffusion
Diffusion described by the flow of the amount of substance
in time
MATTER FLOW RATE: Iv (unit: mol/s)
depends on the surface (A)
MATTER FLOW DENSITY: J (unit: mol/m2s)
independent from the surface (A)
MATTER FLOW DENSITY
number of moles of substance travelling through a unit surface during a
time interval of unity
≈
„STRENGTH” OF DIFFUSION
Diffusion described by the spatial distribution of concentration
spatial variation of the concentration (c)
along the x axis
CONCENTRATION GRADIENT
ratio of the change in the concentration (∆
∆c)
and the distance (∆
∆x) between two points
for simplicity:
the concentration changes linearly
decreasing!
Summary of the previously mentioned equations:
Fick’s First law
where D: DIFFUSION COEFFICIENT
Stokes-Einstein relationship describes
Example : FREE DIFFUSION IN 1D
How far does a particle get from its initial position during t? R(t) = ?
y
x
Example: FREE DIFFUSION IN 1D
How far does a particle get from its initial position during t? R(t) = ?
the diplacement of particles (R(t)) can be described with a
distribution function (Gaussian function)
the average value of R(t) is linearly proportional to the square-root of
time
Notice…
the diffusion time (t) is proportional to the square of the diffusion
distance (R)
2
time (t)
t~R
distance (R)
Diffusion
relatively fast (< seconds) over a short distance (100 mm)
exeptionally slow (> days) over a long distance (1 cm)
Example: GAS EXCHANGE BETWEEN BLOOD AND THE LUNGS
obstacles
LUNGS
O2 uptake
CO2 discharge
BLOOD CIRCULATION
diffusional gas
exchange
Simplified scheme.
time spent by the red blood
cell
t ≈ 0.5 s
R
≈ 1 µm
molecule
diffusion distance diffusion coefficient
[R]
[D], m2s-1
time needed
[t], s
O2
1 µm = 10-6 m
2 ∙ 10-9 m2s-1
500 ∙10-6 s = 500 µs << 0.5 s
CO2
1 µm = 10-6 m
1.2 ∙ 10-8 m2s-1
80 ∙10-6 s = 80 µs << 0.5 s
Effectivity of gas exchange:
short diffusional distance (µ
µm), large diffusion speed (µ
µs).
II.
Osmosis
Book of Medical biophysics: chapter III/2.2
Semipermeable Membrane
Erythrocyte,
Red Blood Cell
Bacteria
Albumin, as
Example of a Big
Protein Molecule
Medium sized
Molecules, e.g.
b2Microglobulin
Electrolytes
Water Flow is
Easily
Possible
The semipermeable membrane functions similar to a fine sieve,
only molecules that are small enough can pass.
QUANTIFICATION OF OSMOSIS
low solute
solvent
high solute
solvent + solute
mixture
semipermeable membrane
concentration difference
semipermeable membrane: allows solvent molecules, but not solute
molecules to pass through
QUANTIFICATION OF OSMOSIS
low solute
high solute
J OUT
J IN
solvent
solvent + solute
mixture
semipermeable membrane
solvent molecules flow through the semipermeable membrane
QUANTIFICATION OF OSMOSIS
low solute
high solute
J OUT
h
J IN
solvent
solvent + solute
mixture
semipermeable membrane
the volume of the solvent + solute mixture increases (h)
QUANTIFICATION OF OSMOSIS
low solute
high solute
J OUT
h
J IN
ρ: density
h: height of the liquid
g = 10 m/s2
solvent
solvent + solute
mixture
semipermeable membrane
HYDROSTATIC PRESSURE (ph)
QUANTIFICATION OF OSMOSIS
low solute
high solute
J OUT
J OUT
J IN
J IN
h
r: density
h: height of the liquid
g = 10 m/s2
solvent
solvent + solute
mixture
semipermeable membrane
the solvent flow slows down
dynamic equilibrium: OSMOTIC EQUILIBRIUM
OSMOTIC PRESSURE
J OUT
J OUT
J IN
J IN
OSMOTIC PRESSURE
pressure that has to be exerted on the solution connected to pure solvent by a
semipermeable membrane to reach dynamic equilibrium, to counteract osmosis
pressure that inhibits the solvent flow
Osmosis
Time
Different to diffusion the dissolved particles cannot pass the
membrane, nevertheless the concentrations tend to equal out,
thus water passes the membrane
Reverse Osmosis
Time
Pressure
Similar to ultrafiltration pressure is applied to one side of the membrane.
Reverse osmosis is especially important for the purification
of water for the production of dialysate.