Thermo-driven nanofluidic electrokinetic converter

Matrix context

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

D.01 × C.37 · Temperature gradient × Thermo-osmoticfamily: Thermo-osmoticD.01 × C.23 · Temperature gradient × Electrokineticfamily: Electrokinetic

Measured or reported performance

1. streaming current14 nA at ΔT = 47.5 °Cdevice2020
   track-etched polyimide membrane, 0.5 cm² exposed area, between hot and cold reservoirs; current rising linearly with ΔT, direction set by the surface charge (pH) — a measured short-circuit current; the electrical power (25.48 pW per channel at ΔT = 40 °C in the paper) is calculated, not delivered to a load
   refs [3]

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
• Onsager–Casimir reciprocity · constitutive-relation · listed, never decisive
  L_ij(B) = ε_i ε_j L_ji(−B): the cross-coefficients of coupled linear transport are equal up to the time-reversal parities ε of the variables and reversal of the magnetic field; L_ij = L_ji is the zero-field, even-parity case

Steps

1. 01
   Temperature gradient —drives→ Thermo-osmosisestablishedclaim record

   thermal → kinetic · loss to thermal

   • a membrane separating two reservoirs of the same liquid at different temperatures; the flow direction depends on the membrane–liquid interaction

   selective membrane required · temperature gradient required · liquid

   refs [1] [2]
2. 02
   Thermo-osmosis —couples to→ Streaming potentialdemonstratedclaim record

   kinetic → electrical · loss to thermal

   • a charged, ion-selective nanochannel or nanoporous membrane contains an electrolyte
   • a sustained temperature difference drives thermo-osmotic liquid motion along the charged interface
   • electrical-double-layer counter-ions are preferentially transported by that flow
   • no external electrical bias is required for the measured short-circuit current
   • pressure-driven current is absent, negligible or separately controlled when the thermo-driven contribution is attributed

   aqueous medium required · selective membrane required · temperature gradient required · bulk flow required

   One physical experiment (Zhao et al. 2020): a track-etched polyimide membrane between hot and cold reservoirs gave a streaming current rising linearly with ΔT to 14 nA at 47.5 °C over 0.5 cm², direction set by the surface charge (pH). One paper is demonstrated, not established.

   refs [3]
3. 03
   Streaming potential —produces→ Ionic currentestablishedclaim record

   electrical → electrical

   refs [4] [5]
4. 04
   Ionic current —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes exchange the ionic current for an electronic current through the external load

   refs [6]

Evidence for the complete composition · 1

1. [3]
   X. Zhao et al.. pH-regulated thermo-driven nanofluidics for nanoconfined mass transport and energy conversion (2020)

   Nanoscale Advances 2, 4070–4076 · doi:10.1039/D0NA00429D · crossref ✓ 2026-09-20 · record

Evidence for the constituent relations · 6

1. [1]
   V. M. Barragán, S. Kjelstrup. Thermo-osmosis in Membrane Systems: A Review (2017)

   Journal of Non-Equilibrium Thermodynamics, 42 · doi:10.1515/jnet-2016-0088 · crossref ✓ 2026-09-20 · record
2. [2]
   S. R. de Groot, P. Mazur. Non-Equilibrium Thermodynamics (1962)

   North-Holland · book, no DOI · record
3. [3]
   X. Zhao et al.. pH-regulated thermo-driven nanofluidics for nanoconfined mass transport and energy conversion (2020)

   Nanoscale Advances 2, 4070–4076 · doi:10.1039/D0NA00429D · crossref ✓ 2026-09-20 · record
4. [4]
   J. Yang et al.. Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena (2003)

   Journal of Micromechanics and Microengineering 13, 963 · doi:10.1088/0960-1317/13/6/320 · crossref ✓ 2026-09-19 · record
5. [5]
   R. J. Hunter. Zeta Potential in Colloid Science: Principles and Applications (1981)

   Academic Press · doi:10.1016/C2013-0-07389-6 · crossref ✓ 2026-09-19 · record
6. [6]
   A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications (2nd ed.) (2001)

   Wiley · book, no DOI · record