LucasWashburn

LucasWashburn refers to the Lucas–Washburn model, a foundational concept in fluid dynamics and material science that describes capillary-driven infiltration of liquids into porous media or narrow tubes. The model is named after researchers credited with its development in the early 20th century and is commonly invoked in studies of capillary action, ink infiltration, paper wetting, and microfluidics.

The core idea is that capillary pressure pulls liquid into a narrow space while viscous forces resist the flow. Under a set of simplifying assumptions—laminar flow, negligible inertial effects, and a constant contact angle—the model yields a simple time dependence for the penetration length. In a circular capillary of radius r, the advancement length x satisfies x^2 proportional to t, reflecting a diffusion-like behavior of capillary rise.

The standard form for a capillary tube is x^2 = (r γ cos θ / (2 μ)) t, where γ is the liquid surface tension, θ is the contact angle, and μ is the dynamic viscosity. In porous media, the same scaling holds with an effective pore size and permeability, giving x^2 ∝ t with material-specific constants. The model is particularly accurate for short times or small heights where inertia and gravity are negligible.

Limitations and extensions include the influence of gravity, which eventually limits rise and leads to deviations from the pure x^2 ∝ t law; inertial effects may matter at very short times or in very rapid infiltration; and real porous structures often require effective parameters or numerical treatment. Despite these caveats, the Lucas–Washburn relation remains a widely used starting point for analyzing capillary infiltration in coatings, paper, soils, and microfluidic devices.