Why pillar spacing and height set the energy barrier
The Cassie-Baxter state is not a true minimum of energy; it is a metastable perch. The droplet sits on the tops of the pillars, and a composite interface of solid and trapped air supports it. To collapse into the Wenzel state, the liquid must push down into the gaps and eventually touch the base. That requires crossing an energy barrier, and the size of that barrier is set by the pillar layout. A model of electric-field-triggered transitions finds that for a fixed droplet volume, the critical voltage needed to force the transition increases with surface roughness on micropillar-patterned surfaces [1]. In plain terms, rougher pillar textures—more or taller pillars per unit area—make the Cassie state harder to knock over.
A separate simulation-based study of periodically pillared surfaces derived an improved transition criterion from the Cassie-Baxter equation. It predicts, for a given pillar geometry, equilibrium contact angle, and droplet volume, when the Cassie state switches from metastable to unstable [3]. The criterion was tested against lattice Boltzmann simulations across different pillar distances, two contact angles, and two droplet volumes, with good agreement [3]. The practical takeaway is that pillar spacing is not a cosmetic detail: it directly controls how much energy is needed to break the Cassie state.
A smaller droplet can be harder to collapse
Droplet volume changes the transition condition in a way that may seem counterintuitive. For a fixed surface roughness, a small droplet tends to ease the critical electrowetting condition for the transition—meaning it takes less voltage to trigger collapse [1]. The same model shows that the critical electrowetting number (voltage) increases with roughness on micropillar surfaces, so geometry and volume trade off against each other [1]. The three-dimensional phase diagrams in that work map out exactly this interplay between voltage, roughness, and volume [1].
This matters for real surfaces because a droplet does not need to be large to be stable. A small droplet on a densely pillared surface can remain in the Cassie state under conditions that would collapse a larger one, because the pressure it exerts and the length of the contact line it maintains are different. The transition criterion developed for periodic pillars explicitly includes droplet volume as a variable alongside pillar geometry and contact angle [3], which is why two surfaces with identical pillars can behave differently depending on the droplet sitting on them.
Not all textures collapse the same way
The shape and arrangement of the texture—not just the pillar spacing—changes how the transition proceeds. On pillar-arrayed surfaces, the free energy during the Cassie-to-Wenzel transition follows the classical pathway: it first rises as water intrudes into the asperities, then falls once the water film touches the basal surface [4]. On striped surfaces, by contrast, there are multiple partial wetting states, each a local energy minimum, so the water film must overcome several energy barriers rather than one [4]. That means a striped texture can hold the droplet in intermediate configurations that a pillar array would not.
The same study examined how aspect ratio and intrinsic wettability affect the transition on both pillar-arrayed and striped surfaces [4]. The implication is that pinning—the resistance of the contact line to moving over a sharp edge—behaves differently depending on whether the texture is a grid of isolated pillars or a set of continuous stripes. A pillar array offers a single main barrier; a striped surface offers a series of smaller ones, which can either stabilize or destabilize the Cassie state depending on how the droplet sits.
The classical models describe the endpoints, not the motion
The Wenzel and Cassie-Baxter equations describe equilibrium contact angles, but they say nothing about how a droplet actually moves from one state to the other. A continuum-level simulation of droplets on laser-textured titanium surfaces showed that spreading dynamics on flat, triangular-relief, and multi-period surfaces cannot be captured by the classical models alone [2]. The evolution of the spreading parameter depends on the specific relief geometry, which is why the authors argue that complex reliefs offer a route to efficient wettability control [2].
A mathematical treatment goes further by treating Wenzel and Cassie-Baxter states as basis states that can be combined into a continuous spectrum of intermediate states [5]. That framework reproduces roughness-dependent apparent contact angles and shows that drop size and contact-line shape—including oval contact lines on inclines—affect the measured angle [5]. It does not address pillar geometry or pinning limits directly, but it reinforces the broader point: the sharp Cassie-versus-Wenzel dichotomy is an idealization, and real droplets can sit in between.
Sources used in this answer
Electric field-triggered Cassie-Baxter-Wenzel wetting transition on textured surface
A theoretical model shows that an applied electric field lowers the energy barrier for the Cassie-Baxter to Wenzel transition, and that for fixed droplet volume the critical voltage increases with roughness on micropillar surfaces while a small droplet eases the critical condition.
Numerical study of the wetting dynamics of droplet on laser textured surfaces: Beyond classical Wenzel and Cassie-Baxter model
Continuum-level simulations of droplets on laser-textured titanium surfaces show that spreading dynamics depend on relief geometry and are not described by the classical Wenzel and Cassie-Baxter models alone.
Validating the Transition Criteria from the Cassie–Baxter to the Wenzel State for Periodically Pillared Surfaces with Lattice Boltzmann Simulations
An improved transition criterion derived from the Cassie-Baxter equation predicts when the Cassie state becomes unstable for given pillar geometry, contact angle, and droplet volume, with good agreement against lattice Boltzmann simulations across different pillar distances.
The Cassie-to-Wenzel wetting transition of water films on textured surfaces with different topologies
On pillar-arrayed surfaces the Cassie-to-Wenzel transition follows a single classical energy pathway, while on striped surfaces multiple partial wetting states create multiple energy barriers.
Beyond the Wenzel and Cassie–Baxter world: Mathematical insight into contact angles
Treating Wenzel and Cassie-Baxter states as basis states yields a continuous spectrum of intermediate contact angles, and drop size and contact-line shape are shown to affect the apparent contact angle.