capillaryrise

Capillary rise is the movement of a liquid within narrow spaces, such as a thin tube or porous material, driven by capillary forces that arise from liquid–solid adhesion and surface tension. The phenomenon occurs when the liquid wets the solid surface, producing a curved meniscus and a capillary pressure that pulls the liquid upward against gravity.

In a cylindrical capillary of radius r, the equilibrium rise height h is given by Jurin’s law: h = (2 γ cos θ) / (ρ g r). Here γ is the liquid–air surface tension, θ is the contact angle between liquid and solid, ρ is the liquid density, and g is the acceleration due to gravity. Wetting liquids (θ < 90°) rise; non-wetting liquids (θ > 90°) may not rise or may depress the liquid level.

Dynamic behavior: Rise is time-dependent in many systems. Washburn’s equation describes capillary infiltration into a tube or porous medium: L^2 = (r γ cos θ / (2 η)) t, where η is the dynamic viscosity. This form neglects inertia and gravity at early times; real systems may deviate due to inertia, evaporation, and pore structure.

Factors and limitations: The radius r strongly controls height (smaller r yields higher rise). Temperature changes γ, θ, and ρ; surface roughness, contamination, and chemical interactions affect wettability. Gravity limits the maximum height for a given liquid and capillary, and in porous media a distribution of pore sizes and tortuosity modifies the flow.

Applications: Capillary rise influences soil moisture, inkjet printing, textile wicking, paper products, and microfluidic devices, where capillary transport enables passive liquid movement.

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