Diffusion, osmosis. Physics-Biophysics 1. I. Diffusion Medical Biophysics book: chapter III/ October Tamás Huber

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1 Diffusion, osmosis Physics-Biophysics October Tamás Huber I. Diffusion Medical Biophysics book: chapter III/2. 1

2 Experiment 1: add a droplet of ink to a glass of water Observation 1: the stain spreads and eventually colours the entire fluid Experiment 2: add a droplet of ink to HOT and COLD water Observation 2: the stain spreads faster in hot water than in cold water 2

3 BIOLOGICAL IMPORTANCE OF DIFFUSION microscopic matter transport processes transport through the cell membrane metabolism gasexchangebetweenbloodand thelungs stimuli absorption of medicines chemical reactions MOLECULAR MOTION most of the particles of biological systems are in constant motion fluid phase aqueous medium (50 60 % of the human body consists of water) lipid phase cell membrane Brownian motion Robert Brown (scottish botanist, 1827) experiment: microscopic investigation of pollen in water observation: random, zig-zag motion of pollen particles explanation? 3

4 Brownian motion WHAT IS THE REASON OF BROWNIAN-MOTION? MACROSCOPIC VIEW MICROSCOPIC VIEW continuous collision between the particles random motion of particles depends on the temperature (T): thermal motion kinetic theory of gases model of the perfect/ideal gas 4

5 DIFFUSION due to the non-uniform (inhomogeneous) distribution of particles net transport* of the particles occurs from regions of higher concentration to regions of lower concentration which continues until the distribution of the particles is uniform (homogeneous) * Brownian motion DIFFUSION QUANTIFYING DIFFUSION IN SPACE FICK S 1 ST LAW For simplicity, let s investigate diffusion in 1D ( along the x axis) t = 0 s t inhomogeneous distribution DIFFUSION t = homogeneous distribution x 5

6 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 constant due to diffusion through a surface of A (perpendicular to the direction of matter flow) during t time n amount of particles (mole fraction) travels through 6

7 Diffusion described by the flow of the amount of substance in time amount of particles time MATTER FLOW RATE: I v (unit: mol/s) depends on the surface (A) matter flow rate surface MATTER FLOW DENSITY: J (unit: mol/m 2 s) 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 General description of transport processes: Onsanger s linear equation the matter flow density of the extensive quantity(amount of particles) is linearly proportional to the gradient of the intensive quantity(concentration) FICK 1 st LAW spatial description matter flow density is linearly proportional to the drop in concentration! negative sign: particles diffuse from the high concentration regions to the low concentration regions! D: DIFFUSION COEFFICIENT 7

8 DIFFUSION COEFFICIENT characterises the mobility of a diffusing particle- tells us how fast a given substance diffuses symbol: D unit:m 2 s -1 gives the amount of substance that diffuses through a surface unit duringatimeunitiftheconcentrationdropwasunity depends on both the diffusing particle and the medium in which the particle diffuses For shperical particles(r: radius) in a viscous medium(η) at T temperature: 6 STOKES-EINSTEIN EQUATION temperature (T) the higher the temperature, the stronger the thermal motion geometry/shape of the particle (r) small/globular particle diffuse more easily than big/fibrillar particle molecular weight of the particle (M) heavier particles diffuse more slowly than the lighter ones viscosity of the medium (η) diffusion is faster in low viscosity media than in hign viscosity media gases > liquids k: Boltzmann constant k = joule/kelvin 6 8

9 WHAT ELSE? concentration gradient (force) diffusion (matter flow) homogeneous distribution (equilibrium) we quantitated diffusion considering the spatial variations in the concentration FICK S 1st LAW (spatial description) but we have not considered that the concentration changes with time, too: c (x, t) FICK S 2 nd LAW (spatial & temporal description), Fick s II. Law Time and space dependence of diffusion For simplicity, let s investigate diffusion in 1D ( along the x axis) The change in concentration over time is proportional to the change in the concentration-gradient along the x axis D: DIFFUSION COEFFICIENT 9

10 II. Osmosis Medical Biophysics book: chapter III/2.2 Experiment 1: place a dried leaf of salade in water before after (3-4 hours) Observation 1: the leaf of salad becomes bigger and looks fresh again 10

11 Experiment 2: place an egg into corn syrup then water corn syrup water Observation 2: the egg shrinks Observation 2: the shrinked egg gains its original size, and it continues to get bigger and bigger SEMIPERMEABLE MEMBRANE Erythrocyte, Red Blood Cell Albumin, as Example of a Big Protein Molecule Electrolytes Bacteria Medium sized Molecules, e.g. b2- Microglobulin Water Flow is Easily Possible The semipermeable membrane functions similar to a fine sieve, only molecules that are small enough can pass. 11

12 QUANTIFICATION OF OSMOSIS low solute high solute solvent solvent + solute mixture semipermeable membrane concentration difference semipermeable membrane: allows solvent molecules to pass through, but not the larger solute molecules QUANTIFICATION OF OSMOSIS low solute high solute J OUT J IN solvent + solute solvent mixture semipermeable membrane solvent molecules flow through the semipermeable membrane 12

13 QUANTIFICATION OF OSMOSIS low solute JOUT high solute h J IN solvent solvent + solute mixture semipermeable membrane the volume of the solvent + solute mixture increases (h) QUANTIFICATION OF OSMOSIS low solute JOUT high solute h J IN ρ: density h: height of theliquid g= 10 m/s 2 solvent solvent + solute mixture semipermeable membrane HYDROSTATIC PRESSURE (p h ) 13

14 QUANTIFICATION OF OSMOSIS low solute JOUT high solute J OUT h J IN J IN r: density h: height of theliquid g= 10 m/s 2 solvent solvent + solute mixture semipermeable membrane thesolventflow slowsdown 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 14

15 VAN T HOFF s LAW for dilute solutions and perfect semipermeable membranes using the equation of state of the ideal gas V volume n: mole fraction T temperature c concentration R universal gas constant Notice ~ the osmotic pressure is linearly proportional to the concentration upon OSMOSIS the net particle transport occurs from the low-concentration regions (low osmotic pressure) to the high-concentration regions (high osmotic pressure) it is always the more dense solution which becomes diluted! solvent solute opposite what we observe during DIFFUSION: net transport of the particles occurs from the high-concentration regions to the lowconcentration regions 15

16 RED BLOOD CELLS IN DIFFERENT ENVIRONMENT HYPERTONIC (more concentrated: 10% NaCl) IZOTONIC (0.87 % NaCl) HYPOTONIC (less concentrated: 0.01% NaCl) p > p x p = p x p < p x net water OUTflux NO net water flux net water INflux HYPERTONIC IZOTONIC (0.87 % NaCl) HYPOTONIC 16

17 OSMOSIS IN THE MEDICAL PRACTICE INJECTION, INFUSION drugs are dissolved in physiological saline solution isotonic environment (compared to the body fluid) TREATMENT OF OEDEMAS, INFLAMED AREAS abnormal accumulation of fluid beneath the skin or in one or more cavities of the body that produces swelling (fluid accumulation) dextran-solution/bitter salt (MgSO 4 -solution)-based treatment hypertonic environment is created (compared to the swollen areas) induces water outflow from the swollen areas reduces swelling water influx water outflow hypertonic TREATMENT OF CONSTIPATION - LAXATIVE SALTS laxative salts are not absorbed by the large intestine hypertonic environment is created in the large intestine results in water influx into the large intestine dilution of colonic content, facilitate excretion hypertonic DIALYSIS different (macro)molecules can be sorted by semipermeable membranes pore size of the membrane determines which molecules can pass through the membrane dialysis bag semipermeable membrane concentrated solution t = 0 s t 17

18 HEMODIALYSIS treatment for serious kidney illnesses remove soluble chemicals toxic for the body protein products toxins other waste products The End! 18