L06 Diffusion 2011

L06 Diffusion 2011 - COPYRIGHT Mammalian Physiology BIOAP...

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1/10 COPYRIGHT Prof. Beyenbach Mammalian Physiology BIOAP 4580 2011 DIFFUSION 1) Fundamental equations in physiology. There are two basic concepts that describe physiological processes suitable for quantitative treatment. One concept relates one force to another, as for example the Nernst equation which equates a concentration difference of an ion (a chemical force) with a voltage (electrical force), akin to exchanging $ for Euro or Yen. Eq. 1 is the Nernst equation that states the equivalence of a chemical concentration ration and a voltage. Force = Force, (eq. 1) where V is the voltage, [ ] indicates the concentration of the ion of interest in compartments 1 and 2, and where R, T, z, and F have their usual meaning: gas constant, temperature, valence of ion, and Faraday constant, respectively. Other examples of conversions abound: hydrostatic pressure/osmotic pressure, volume/size, specific gravity/osmolarity, calories/joules, pressure/tension, etc. The other equation sets flow proportional to a driving force, where the driving force can be a concentration difference. In particular, a chemical concentration difference drives diffusion; a voltage difference drives current. In both cases, the fundamental equation relates potential energy (a force) to kinetic energy (a movement). The equation comes in many variations of the same theme: Kinetic Energy = (k) Potential Energy Movement = (k) Force where k is a proportionality constant: a hydraulic conductance, an electrical conductance, or a permeability , and ∆Force is the difference between two forces. One well known example relates flow to pressure proportional to the constant k. Flow = (k) Pressure, where flow takes place from a high pressure to a low pressure; (Poiseuille equation) (eq. 2) where BP is the blood pressure. Note that the constant k includes 1) the radius r and the length (L) of the blood vessel, and 2) the viscosity (η) of blood. Together these variables combine to yield the hydraulic conductance g h = k. In general, conductance is the inverse of resistance, which is be st illustrated in Ohm’s Law.
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2/10 (Ohm's Law) (eq. 3) where I is current, g is electrical conductance, V is voltage, and R is electrical resistance. 2) Diffusion of solute and water. Diffusion is driven by a concentration difference (eq. 4) Flux = (P) Concentration (Fick's Law of Diffusion) (eq. 4) where P is the permeability. (Electrodiffusion is driven by both concentration difference and voltage.) Similarly, osmotic water flow is driven by the concentration difference for water. Osmosis is simply the diffusion of water down its own concentration gradient. Water flux = (P) Water concentration (Osmosis) (eq. 5) where P is again the permeability. 3) The diffusion of solute. Flux = (P) Concentration (Fick's Law of Diffusion) (eq. 4) (eq. 6) where J diff is the diffusive flux, D x is the diffusion coefficient of substance x, A is area available to diffusion, L is the diffusion distance (length of the pathway), and [x] is the concentration difference, [x] 1 [x] 2 , separated by L.
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