Surface energy difference → Mechanical work

Matrix context

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

D.15 × C.34 · Surface energy difference × Marangonifamily: MarangoniD.15 × C.24 · Surface energy difference × 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).

• 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
   Surface energy difference —drives→ Marangoni effectestablishedclaim record

   surface → kinetic · loss to thermal

   • a gradient of surface tension along a free liquid interface, from composition (solutocapillary) or temperature (thermocapillary)

   liquid

   refs [1] [2]
2. 02
   Marangoni effect —produces→ Fluid flowdemonstratedclaim record

   kinetic → kinetic · loss to thermal

   • thermocapillary pumping of a liquid plug or droplet confined in a microchannel; the surface-tension gradient translates the plug rather than producing only local interfacial circulation

   Thermocapillary pumping (TCP) of a discrete droplet in a closed microchannel: the plug's displacement and velocity were measured on the PZT device of Odukoya & Naterer 2013 and in their 2010 experiments. The confined translating plug is bulk, loadable flow; that fact must not leak onto open-surface Marangoni circulation, which keeps its own claim and tokens.

   refs [3] [4]
3. 03
   Fluid flow —drives→ Aerodynamic and hydrodynamic liftestablishedclaim record

   kinetic → mechanical · loss to thermal

   • a rotor or vane in the produced stream at a working angle of attack; the driven flow must carry a directed momentum flux for a blade to load

   bulk flow required

   refs [5] [6]
4. 04
   Aerodynamic and hydrodynamic lift —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [6]
5. 05
   Mechanical motion —converts into→ Mechanical workestablishedclaim record

   mechanical → mechanical · loss to thermal

   refs [7]

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 · 7

1. [1]
   L. E. Scriven, C. V. Sternling. The Marangoni Effects (1960)

   Nature 187, 186-188 · doi:10.1038/187186a0 · crossref ✓ 2026-09-20 · record
2. [2]
   Q. Dai et al.. Directional interfacial motion of liquids: Fundamentals, evaluations, and manipulation strategies (2021)

   Tribology International 154, 106749 · doi:10.1016/j.triboint.2020.106749 · crossref ✓ 2026-09-20 · record
3. [3]
   P. S. Glockner, G. F. Naterer. Surface tension and frictional resistance of thermocapillary pumping in a closed microchannel (2006)

   International Journal of Heat and Mass Transfer 49(23–24), 4424–4436 · doi:10.1016/j.ijheatmasstransfer.2006.05.005 · record
4. [4]
   A. Odukoya, G. F. Naterer. Transient response of thermocapillary pumping of a droplet in a micro heat engine (2013)

   International Journal of Heat and Mass Transfer 58, 202–212 · doi:10.1016/j.ijheatmasstransfer.2012.11.009 · record
5. [5]
   A. Betz. Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren (1920)

   Zeitschrift für das gesamte Turbinenwesen 26, 307–309 · paper, no DOI · record
6. [6]
   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
7. [7]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

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