Temperature gradient → Electrical 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: MarangoniD.01 × C.12 · Temperature gradient × Triboelectricfamily: Triboelectric

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 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→ 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 [5]
4. 04
   Flow-induced vibration —produces→ Mechanical vibrationestablishedclaim record

   mechanical → mechanical

   refs [5]
5. 05
   Mechanical vibration —drives→ Triboelectric effectestablishedclaim record

   mechanical → electrical · loss to thermal

   • vibration or motion that repeatedly contacts and separates two dissimilar surfaces

   solid · dielectric required

   refs [6] [7]
6. 06
   Triboelectric effect —produces→ Separated surface chargeestablishedclaim record

   electrical → electrical

   refs [6] [8]
7. 07
   Separated surface charge —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes on the charged surfaces connected through a load

   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 · 8

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]
   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
6. [6]
   F.-R. Fan, Z.-Q. Tian, Z. L. Wang. Flexible triboelectric generator (2012)

   Nano Energy 1, 328–334 · doi:10.1016/j.nanoen.2012.01.004 · crossref ✓ 2026-09-19 · record
7. [7]
   C. Wu et al.. Triboelectric nanogenerator: a foundation of the energy for the new era (2019)

   Advanced Energy Materials 9, 1802906 · doi:10.1002/aenm.201802906 · crossref ✓ 2026-09-19 · record
8. [8]
   D. J. Lacks, T. Shinbrot. Long-standing and unresolved issues in triboelectric charging (2019)

   Nature Reviews Chemistry 3, 465–476 · doi:10.1038/s41570-019-0115-1 · crossref ✓ 2026-09-19 · record