Meniscus Formation in a Vertical Capillary Tube

Abstract

In this theoretical work, the energies associated with the formation of a meniscus in a small diameter capillary tube are analyzed. A mechanism for meniscus creation and an associated energy balance are proposed. Equations for work of wetting, surface energy, gravitational energy, and dissipation are derived. The relative magnitude of these quantities is compared, first to each other and then to energies from capillary rise. In capillary rise, the energy released as work of wetting is evenly split between gravitational energy stored in the liquid column and heat dissipated there. The analysis performed here suggests that meniscus formation is energetically distinct and more complex than capillary rise. In meniscus formation, most of the energy released as work of wetting is stored in the stretched air–liquid interface or dissipated in the bulk liquid; their relative distribution depends on the properties of the liquid and the tube.

Energies Associated with a Meniscus along a Flat Vertical Wall

“…For capillary rise, the work of wetting is evenly split between stored gravitational energy and dissipated heat energy . For meniscus formation in a capillary tube, almost none of the wetting energy is transferred to the bulk liquid; instead, roughly half is stored in the air–liquid interface and the remainder is dissipated as heat . For meniscus formation along a completely wetted flat wall, one-fifth of the wetting energy ends up in the bulk liquid, two-fifths is in the air–liquid interface, and the remainder is dissipated.…”

“…40 For meniscus formation in a capillary tube, almost none of the wetting energy is transferred to the bulk liquid; instead, roughly half is stored in the air−liquid interface and the remainder is dissipated as heat. 54 For meniscus formation along a completely wetted flat wall, one-fifth of the wetting energy ends up in the bulk liquid, two-fifths is in the air−liquid interface, and the remainder is dissipated. Menisci in partially wetted tubes or along partially wetted walls are expected to give similar results.…”

“… a D is the inner diameter of a completely wettable capillary tube, and b is the unit width of a meniscus along a wettable wall. Values for the risen column inside a tube were estimated using eqs , , , and found in ref , and values for the meniscus inside a tube were estimated using eqs , , , , , and from ref . Values for the meniscus along a wall were estimated from eqs , , , , , and . …”

“…Heights, Volumes, and Energies for Water Inside a Completely Wettable Vertical Capillary Tube (θ = 0°) or Along a Completely Wettable Vertical Flat Wall (θ = 0°) a type h (mm)V (μL) w (μJ) −ΔΓ/w −ΔU/w Q/wrisen column inside a tube D = is the inner diameter of a completely wettable capillary tube, and b is the unit width of a meniscus along a wettable wall. Values for the risen column inside a tube40 were estimated using eqs 2, 6, 8, and 11 found in ref13, and values for the meniscus inside a tube54 were estimated using eqs 9, 10, 14, 16, 18, and 19 from ref16. Values for the meniscus along a wall were estimated from eqs 7, 17, 27, 30, 33, and 35. h i b i t e d .…”

Deep understanding of the dependence between capillary adhesion behavior and meniscus Kelvin radius or interface micromorphology

“…In this method the pressure differential equation at the gas-liquid-solid interfaces is transformed into a functional representation tied to variables like distance and contact angle. The second approach centers on a modeling technique rooted in the total energy analysis of the meniscus [17][18][19][20] . The meniscus is amalgamated with the Derjaguin approximation, a framework verified to be suitable for thermodynamic non-equilibrium conditions 21,22 .…”