Concentration gradient → Mechanical work

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.03 × C.22 · Concentration gradient × Osmotic / salinity-gradientfamily: Osmotic / salinity-gradientD.03 × C.24 · Concentration gradient × Turbomachineryfamily: Turbomachinery

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

• Free energy of mixing · resource-bound · listed, never decisive
  W ≤ −ΔG_mix ≈ 0.8 kWh per m³ of fresh water into seawater
• Betz limit · upper-bound · hard, filtered out by its applicability
  C_p ≤ 16/27 ≈ 59.3% of the kinetic power through the rotor disc

Steps

1. 01
   Concentration gradient —drives→ Osmosisestablishedclaim record

   chemical → osmotic

   aqueous medium required · selective membrane required

   refs [1]
2. 02
   Osmosis —produces→ Osmotic pressure differenceestablishedclaim record

   osmotic → osmotic

   refs [2] [1]
3. 03
   Osmotic pressure difference —drives→ Pressure-retarded osmosisestablishedclaim record

   osmotic → mechanical · loss to thermal

   aqueous medium required · selective membrane required

   refs [2] [3]
4. 04
   Pressure-retarded osmosis —produces→ Hydraulic pressureestablishedclaim record

   mechanical → mechanical

   refs [2] [3]
5. 05
   Hydraulic pressure —drives→ Aerodynamic and hydrodynamic liftestablishedclaim record

   mechanical → mechanical · loss to thermal

   • pressurised water expanded through a reaction or impulse turbine

   liquid · bulk flow required

   refs [4]
6. 06
   Aerodynamic and hydrodynamic lift —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [4]
7. 07
   Mechanical motion —converts into→ Mechanical workestablishedclaim record

   mechanical → mechanical · loss to thermal

   refs [5]

Evidence for the complete composition · 0

No source on record for this exact composition. The sources below support the individual steps, not the route as a whole.

Evidence for the constituent relations · 5

1. [1]
   A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications (2nd ed.) (2001)

   Wiley · book, no DOI · record
2. [2]
   S. Loeb. Osmotic power plants (1975)

   Science 189, 654–655 · doi:10.1126/science.189.4203.654 · crossref ✓ 2026-09-19 · record
3. [3]
   B. E. Logan, M. Elimelech. Membrane-based processes for sustainable power generation using water (2012)

   Nature 488, 313–319 · doi:10.1038/nature11477 · crossref ✓ 2026-09-19 · record
4. [4]
   S. L. Dixon, C. A. Hall. Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.) (2014)

   Butterworth-Heinemann · doi:10.1016/C2011-0-05059-7 · crossref ✓ 2026-09-19 · record
5. [5]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record