6.021/Notes/2006-09-18
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Water Transport
- Cells specific for water transport
- ~15 pounds of water secreted and reabsorbed daily
- hydraulic pressure: blood
- osmosis: cells
Osmosis
- Transport of solvent due to differences in solute concentration
- described by Dutrochet (early 1800s)
- developed 1st osmometer
- Wilhelm Pfeffer
- osmosis can be stopped by hydraulic pressure
- pressure proportional to concentration of solute
- isotonic: concentration at which cells don't change in size
- osmosis is colligative
- depends on molar concentration not chemical properties of solute
Van't Hoff
- Found relationship identical to ideal gas law
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \pi(x,t)= RTC_\Sigma(x,t)}
- Also works for salts if count ions of salt
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle C_\Sigma(x,t)} is called osmolarity in units of (osmol/volume)
- 1 osmol is the same as 1 mol
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \pi} : units of pressure (Pa)
- ocean about 1000 osmol/m^3, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \pi\approx 25\cdot 10^5{\rm Pa}\approx 25{\rm atm}}
Model
- No one really understands osmosis
- requires semipermeable membrane
- solute collides and bounces off membrane
- membrane exerts force due to changing momentum of solute
- solute transfers momentum to solvent
- change in solvent momentum is equivalent to hydraulic pressure
- change in hydraulic pressure is change in osmotic pressure
- momentum of solvent increase away from membrane due to solute bouncing back off membrane
Darcy's Law
- flow through porous medium
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Phi_V(x,t)= -\kappa\frac{\partial p}{\partial x}}
- solvent flux is proportional to hydraulic pressure gradient
- continuity: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle -\frac{\partial}{\partial x}(\rho_m \Phi_V) = \frac{\partial \rho_m}{\partial t}}
- water is incompressible so Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \rho_m} is constant
- Therefore, flux gradient is zero so flux is constant and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle p(x,t)} is a linear function of space