Dukhin Number¶
A dimensionless electrokinetic ratio comparing conduction along a charged interface with conduction through its surrounding electrolyte.
Core Idea¶
The Dukhin number compares electrical conduction along a charged interface with conduction through the neighboring bulk electrolyte. In one charged-particle convention, Du = K_s/(K_b a): specific surface conductance K_s (S) divided by bulk conductivity K_b (S/m) times particle radius a (m). Bolève and colleagues instead define effective macroscopic surface conductivity σ_S with geometry already incorporated and use Du = σ_S/σ_f; both conductivities are S/m, so no extra length divides this granular-medium ratio.[ref-a9a0ed7d53a9][ref-a65940cdc3db]
Scope of Application¶
For colloidal particles, Du helps assess whether surface conduction can affect electrophoretic mobility. In granular porous media, Bolève's effective surface-versus-pore-water conductivity comparison enters streaming-potential models along with Reynolds number and texture. The ratio transfers; the particle's explicit radius and response equation do not automatically transfer to a pore network.[ref-a9a0ed7d53a9][ref-a65940cdc3db]
Clarity¶
Du is not zeta potential, mobility or a surface-charge measurement. It isolates one possible reason a bulk-only model can mislead. Small Du only reduces the importance of surface conduction under the stated setup; it does not certify every other double-layer, hydrodynamic or geometry assumption.[ref-a9a0ed7d53a9][ref-a65940cdc3db]
Manages Complexity¶
The number compresses surface and bulk paths under a unit-compatible geometry convention into one interpretable comparison. That can prioritize whether an interface-current correction matters, while leaving other regime variables explicit. Bolève and colleagues need both small Dukhin and Reynolds numbers for their familiar streaming-potential limit.[^ref-a65940cdc3db]
Abstract Reasoning¶
At fixed particle properties, shrinking radius a raises K_s/(K_b a); raising bulk conductivity lowers it. These are deductions about the relative conduction paths, not universal predictions for measured mobility. Before carrying them to a porous sample, determine whether geometry is explicit or already absorbed into effective σ_S; Bolève's σ_S/σ_f needs no second length factor.[ref-a9a0ed7d53a9][ref-a65940cdc3db]
Knowledge Transfer¶
The colloid and porous-medium cases share a surface/bulk/unit-compatible-ratio structure. The particle radius is explicit in one convention; granular geometry is absorbed in the other. Their observables and validity assumptions differ. A proposed strict subsumption edge to live Dimensionless Quantity captures the physical normalized-number genus; prime Ratio supplies a broader ordered-comparison pattern. No canonical DAG edge was changed.[ref-a9a0ed7d53a9][ref-a65940cdc3db]
[^ref-a9a0ed7d53a9]: Todd M. Squires and Martin Z. Bazant, “Induced-charge electro-osmosis”, Journal of Fluid Mechanics 509 (2004), 217–252, especially §2.2, eqs. (2.7)–(2.10). [^ref-a65940cdc3db]: Arnaud Bolève et al., “Streaming potentials of granular media: Influence of the Dukhin and Reynolds numbers”, Journal of Geophysical Research: Solid Earth (2007), abstract and model-parameter sections.
Relationships to Other Abstractions¶
Current abstraction Dukhin Number Domain-specific
Parents (1) — more general patterns this builds on
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Dukhin Number is a kind of Dimensionless Quantity Domain-specific
The Dukhin number is a dimension-one physical comparison of interface with bulk electrical conduction.
Hierarchy path (1) — routes to 1 parentless root
- Dukhin Number → Dimensionless Quantity → Physical quantity → Measurement
Neighborhood in Abstraction Space¶
Dukhin Number sits in a sparse region of the domain-specific corpus (85th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Electromagnetic Fields & Responses (11 abstractions)
Nearest neighbors
- Sintering — 0.83
- COSMO solvation model — 0.82
- Oncotic Pressure — 0.81
- Adsorption — 0.81
- Diffuson — 0.81
Computed from structural-signature embeddings · 2026-10-08