🔬 condensed matter

From suspensions to porous multilayers: microstructure formation and particle packing in drying colloidal films

This study numerically investigates how particle-particle interactions govern microstructure formation in drying colloidal films, revealing that weak interactions lead to hexagonal layer-by-layer assembly while strong interactions induce network-like porous structures, with a theoretical model identifying three distinct packing regimes based on the adhesion parameter.

Original authors: Qingguang Xie, Jens Harting

Published 2026-08-17

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CC BY 4.0

Original authors: Qingguang Xie, Jens Harting

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where the way things dry out isn't just about water disappearing, but about how tiny, invisible building blocks decide to stack up. This story lives in the realm of soft matter physics, a branch of science that studies materials that are somewhere between a solid and a liquid, like gels, foams, and the suspensions used to make everything from battery parts to medical coatings. At the heart of this research are two main characters: the "particles," which are microscopic solid bits floating in a liquid, and the "drying process," which is simply the liquid evaporating away. When the liquid leaves, these particles are left behind to form a film. The big question scientists have always asked is: will these particles line up neatly like soldiers, or will they clump together in a messy pile? The answer matters because the final structure determines how well a device works. If you are building a fuel cell or a battery, you need the particles to be arranged just right to let electricity or chemicals flow through easily. If they are too messy, the device might fail.

In this study, researchers Qingguang Xie and Jens Harting decided to play the role of digital architects. Instead of mixing chemicals in a lab, they built a virtual world inside a computer to watch how these tiny particles behave as their liquid home evaporates. They used a powerful simulation method that acts like a high-speed camera, tracking every single particle and the fluid around it. Their main discovery is that the "personality" of the particles—specifically how strongly they stick to each other—dictates the entire outcome.

When the particles have a weak attraction to one another, they behave like polite dancers. As the liquid level drops, the particles get pushed up to the surface. There, they arrange themselves into perfect, honeycomb-like hexagonal layers. As more liquid leaves, new layers form on top of the old ones, creating a neat, stacked tower of particles. The researchers even created a simple math formula to predict how thick these layers get as time passes, and their computer simulations matched this prediction perfectly.

However, the story changes dramatically when the particles are "sticky." If the attraction between them is strong, they don't wait to be pushed into neat rows. Instead, they grab onto each other early on, forming messy, tangled clusters and web-like networks. As the liquid drains away, these sticky clumps hold their shape, creating a structure that is full of holes and very porous. The researchers found that the amount of empty space (porosity) in these sticky structures follows a specific mathematical rule: as the stickiness increases, the porosity grows rapidly, following a power-law relationship.

By tweaking a single number that represents the balance between the particles' stickiness and the squeezing force of the liquid's surface tension, the team identified three distinct "neighborhoods" where the particles can end up. First, there is the "Hexagonal Close Packing" zone, where particles are perfectly ordered. Second, there is "Random Close Packing," a middle ground where things are a bit jumbled but still fairly dense. Finally, there is "Cohesive Packing," where strong stickiness leads to a loose, sponge-like network with large gaps.

The paper suggests that by carefully controlling how much the particles like to stick together—perhaps by changing the liquid's chemistry or the particle size—scientists can design materials with exactly the right amount of porosity. This isn't just a theoretical game; it offers a practical guide for engineers who need to create specific types of porous layers for things like filters, catalysts, or energy storage devices. While the results are currently based on computer simulations, they provide a clear roadmap for how to manipulate the microscopic world to build better macroscopic tools.

Technical Summary: From Suspensions to Porous Multilayers

Problem Statement
The drying of particle suspensions is a fundamental process for assembling functional porous layers used in electrochemical devices (e.g., electrolyzers, fuel cells, batteries) and printable electronics. The performance of these devices is critically dependent on the microstructural properties of the deposited films, specifically particle packing and porosity. However, controlling these microstructures remains a significant challenge due to the complex, coupled physical processes involved, including evaporation-induced flows, interparticle interactions, and particle–substrate interactions. While experimental studies have explored the effects of evaporation rates and particle properties, directly monitoring microstructural evolution is hindered by material opacity and measurement constraints. Existing numerical models often simplify particle interactions (e.g., using only repulsive potentials) or neglect critical hydrodynamic and capillary interactions at the interface, limiting their predictive capability for structure formation.

Methodology
This work employs a coupled Lattice Boltzmann–Discrete Element Method (LB-DEM) framework to numerically investigate the drying dynamics of thick colloidal films.

Fluid Dynamics: The Lattice Boltzmann Method (LBM), specifically the pseudopotential multicomponent model (Shan-Chen), is used to resolve fluid flow and evaporation-driven transport. A D3Q19 lattice is utilized with a diffuse interface approach to naturally avoid stress singularities at the moving contact line. Evaporation is modeled by imposing a constant density boundary condition, driving diffusion-dominated mass transfer.
Particle Dynamics: Colloidal particles are modeled as rigid spheres coupled to the fluid via a modified bounce-back boundary condition. Particle motion is governed by classical equations of motion, accounting for hydrodynamic forces (drag, lift, and lubrication corrections) and interparticle interactions.
Interactions: The model incorporates van der Waals forces (approximated via a Hamaker constant with short- and long-range cutoffs), a Hertz potential to prevent overlap, and a Lennard-Jones potential for particle–substrate interactions.
Simulation Conditions: Simulations are conducted in the fast-evaporation limit (high Péclet number, $Pe \gg 1$ ), where Brownian motion and gravitational settling are neglected. The study systematically varies a dimensionless adhesion parameter, $\chi = |F^*_{vdW}|/\gamma R$ , which compares the characteristic van der Waals attractive force to the capillary force scale.

Key Contributions and Results
The study identifies three distinct packing regimes determined by the strength of particle–particle interactions relative to capillary forces:

Weak Interactions ( $\chi \approx 0.02$ ):
- Mechanism: Capillary forces dominate. As the liquid interface descends, particles are absorbed and reorganize into a hexagonal arrangement at the interface.
- Structure: This ordered top layer acts as a template, triggering a layer-by-layer assembly process. The result is a well-ordered, multi-layer hexagonal close-packed (HCP) structure with minor defects.
- Modeling: A simple theoretical model based on mass conservation and liquid diffusion is developed to predict the time evolution of the layer thickness. The model shows good agreement with simulation data for this regime.
Intermediate Interactions ( $\chi \approx 0.2 - 1.0$ ):
- Mechanism: Van der Waals forces begin to compete with capillary compression. Particles in the subsurface region aggregate into small clusters before reaching the interface.
- Structure: These clusters destabilize the ordered arrangement of upper layers, leading to a Random Close Packing (RCP) regime. The final structure exhibits periodicity but with larger amplitude fluctuations and increased disorder compared to the weak interaction case.
Strong Interactions ( $\chi \approx 10.0 - 14.0$ ):
- Mechanism: Strong attractive forces cause rapid aggregation into large clusters early in the drying process. These clusters form a network that resists the compressive effects of capillary pressure.
- Structure: The system fails to form close-packed layers, instead developing a highly porous, network-like solid structure (Cohesive Packing, CP). The coordination number drops significantly (to 3–5), and the structure is characterized by large pores and weak connectivity.

Quantitative Findings

Porosity Scaling: The porosity ( $\psi$ ) of the final deposit follows a power-law relationship with the adhesion parameter: $\psi \sim \chi^{2/3}$ . At low $\chi$ , porosity is low and varies smoothly; as $\chi$ increases, porosity rises rapidly, eventually approaching a saturation limit at high adhesion.
Coordination Number: The average coordination number decreases progressively from $\approx 12$ (HCP) to $\approx 6-8$ (RCP) and finally to $\approx 3-5$ (CP) as the adhesion parameter increases, reflecting the transition from ordered crystalline-like structures to disordered, weakly connected networks.

Significance
The paper demonstrates that particle–particle interactions play a decisive role in determining the final porous structure of drying colloidal films. By systematically varying the adhesion parameter, the authors map a continuous transition between hexagonal close packing, random close packing, and cohesive packing. These findings provide practical guidance for tailoring functional layers through the controlled manipulation of particle interactions (e.g., via particle size, material choice, or medium properties like pH and salt concentration). The results offer a predictive framework for optimizing microstructures in applications where transport properties and electrochemical activity are governed by porosity and packing density.

Technical Summary: From Suspensions to Porous Multilayers

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