Why the shape of a channel changes how liquid is pulled in
Capillary flow is the spontaneous creep of a wetting liquid into a narrow space, driven by surface tension—the same pull that draws water up a thin straw. The classic picture assumes a smooth, round tube, and for that regular case the behavior is well understood and comparatively easy to model [1].
Irregular geometry breaks that simplicity because the liquid no longer meets the wall at one uniform angle everywhere. Corners and angular cross-sections give the liquid extra pathways, and the review of corner-containing geometries notes that most attention historically went to round cylindrical capillaries, leaving the physics of flow in corners comparatively unexplored [4]. In other words, the shape itself becomes an active part of the flow, not just a container.
What irregular flow actually looks like
The most distinctive feature is corner flow: in channels with angular cross-sections, liquid can advance along the corners ahead of the main body of fluid. A review of corner geometries treats isolated corners, rectangular channels, and confined angular geometries as their own cases, precisely because the wetting behavior there differs from a round tube [4].
Cross-sectional shape matters even without sharp corners. A study of oval (elliptical) tubes under microgravity derived a flow equation for that shape and found that the liquid's rise over time splits into distinct phases—early on, inertia dominates; later, resistance from the tube and reservoir takes over [5]. That staged behavior is a property of the specific geometry, which is why the authors emphasize that their equation is for elliptical tubes rather than a universal one.
Can one model cover every shape?
A century of work has produced separate models for circular and non-circular capillaries, open and closed channels with triangular or rectangular cross-sections, and channels whose width changes along their length [1]. Rather than leaving these as disconnected cases, that review proposes a universal model built on a dynamic wetting condition and an equivalent cylindrical geometry, intended to describe imbibition across many solid shapes [1].
A coupled analytical–numerical framework has also been developed for wick structures with arbitrary cross-sectional geometries, aimed at capturing how geometric variation influences capillary performance [2]. These efforts suggest convergence toward general descriptions, but the review itself flags open questions—corner-flow dynamics, snap-off of the wetting fluid, and capillary rise of non-Newtonian fluids—as areas still needing work [1]. So the honest answer is that irregular geometries are increasingly modelable, but not yet fully captured by a single settled theory.
Where the difference between regular and irregular channels matters
The stakes are practical. The same review opens by pointing to plant roots taking up water, reservoir rocks absorbing brine, and tissue paper wiping up stains as everyday examples of capillary imbibition [1]. Rocks and paper are full of irregular pores and corners, so models built only on round tubes would misrepresent how quickly and how far the liquid travels in them.
In engineered settings, the geometry-driven framework for wick structures targets exactly this problem: wicks with arbitrary cross-sections need flow predictions that account for their shape [2]. Separately, work on building capillary-scale vessels in hydrogels found that vessel formation succeeded in 50-micrometer channels but failed in 20-micrometer channels under static conditions, and that flow stimulation promoted vessel formation [3]. That result concerns living cells lining manufactured channels rather than the physics of capillary-driven liquid alone, so it should not be read as evidence about irregular versus regular flow—but it illustrates why precise channel geometry matters when capillaries are engineered rather than found in nature.
Sources used in this answer
Capillary imbibition and flow of wetting liquid in irregular capillaries: A 100-year review
A 100-year review catalogs capillary imbibition models for circular and non-circular capillaries, open and closed triangular/rectangular channels, and axially varying geometries, and proposes a universal model based on dynamic wetting and equivalent cylindrical geometry.
Geometry-driven analysis of capillary flow in wick structures using a coupled analytical–numerical framework
A coupled analytical–numerical framework was developed to analyze capillary-driven flow in wick structures with arbitrary cross-sectional geometries and how geometric variation affects flow behavior.
Flow-driven construction of capillary-scale vessels with predefined geometries in natural hydrogels
In hydrogel microchannels, luminal vascular structures formed readily in 50-micrometer channels but failed in 20-micrometer channels under static conditions, and flow stimulation promoted vessel formation.
Capillary-driven flow in corner geometries
A review of capillary-driven flow in corner geometries covers isolated corners, rectangular channels, and confined angular geometries, noting that corner physics has received far less attention than capillary rise in cylindrical tubes.
Capillary driven flow in oval tubes under microgravity
For capillary-driven flow in elliptical tubes under microgravity, the derived flow equation shows three time domains at low Ohnesorge numbers (rise proportional to t², t, and t) but only two regions at high Ohnesorge numbers.