Temperature gradient → Mechanical work

Matrix context

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

D.01 × C.34 · Temperature gradient × Marangonifamily: Marangoni

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).

• Carnot limit · formula-bound · hard, applies to this route
  η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c

Steps

1. 01
   Temperature gradient —drives→ Marangoni effectestablishedclaim record

   thermal → kinetic · loss to thermal

   • thermocapillary case: surface tension falls with temperature, so a temperature gradient along the interface drives flow toward the cold side

   liquid · temperature gradient required

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

   kinetic → kinetic

   refs [1] [2]
3. 03
   Fluid flow —drives→ Flow-induced vibrationestablishedclaim record

   kinetic → mechanical · loss to thermal

   • a bluff or flexible body in the produced stream at a Reynolds number where vortex shedding locks to a structural mode

   bulk flow required

   refs [3]
4. 04
   Flow-induced vibration —produces→ Mechanical vibrationestablishedclaim record

   mechanical → mechanical

   refs [3]
5. 05
   Mechanical vibration —drives→ Resonant vibrationestablishedclaim record

   mechanical → mechanical · loss to thermal

   • a cantilever or seismic mass with natural frequency near the excitation

   solid

   refs [4] [5]
6. 06
   Resonant vibration —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [6] [5]
7. 07
   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]
   H. B. Radousky, H. Liang. Energy harvesting: an integrated view of materials, devices and applications (2012)

   Nanotechnology 23, 502001 · doi:10.1088/0957-4484/23/50/502001 · crossref ✓ 2026-09-19 · record
4. [4]
   S. Roundy, P. K. Wright, J. Rabaey. A study of low level vibrations as a power source for wireless sensor nodes (2003)

   Computer Communications 26, 1131–1144 · doi:10.1016/S0140-3664(02)00248-7 · crossref ✓ 2026-09-19 · record
5. [5]
   A. Erturk, D. J. Inman. Piezoelectric Energy Harvesting (2011)

   Wiley · doi:10.1002/9781119991151 · crossref ✓ 2026-09-19 · record
6. [6]
   S. P. Beeby, et al.. A micro electromagnetic generator for vibration energy harvesting (2007)

   Journal of Micromechanics and Microengineering 17, 1257 · doi:10.1088/0960-1317/17/7/007 · 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