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Effect of Interfacial Properties on Viscoelastic Behavior of High- Temperature Multi-Phase System

This study reveals that in high-temperature granular systems with poor wettability, viscoelastic behavior is governed by interfacial rotational mechanics at gas–liquid interfaces rather than conventional capillary bridge scaling laws, as liquid phases occupy larger voids and avoid solid–solid contacts.

Original authors: Kento Nakanishi, Takehiro Sumita, Noritaka Saito

Published 2026-08-13

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CC BY 4.0

Original authors: Kento Nakanishi, Takehiro Sumita, Noritaka Saito

Original paper licensed under CC BY 4.0 (https://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 sand doesn't just sit there; it flows, sticks, and snaps back like a rubber band. This is the fascinating realm of granular materials—think of piles of sand, coffee grounds, or even snow. Usually, when you add a little water to dry sand, it becomes "wet sand," which can hold a castle shape. This happens because tiny bridges of liquid form between the grains, pulling them together like invisible magnets. Scientists have spent years studying this "wet sand" behavior at room temperature, creating rules (called scaling laws) to predict how stiff or squishy the mixture will be based on how sticky the liquid is.

But what happens when you turn up the heat? In high-temperature industries like making steel or glass, the "sand" is mixed with molten metal or rock-melt (magma-like liquid). Here, the rules might change completely. The liquids are incredibly hot, and they often hate touching the solid grains (a property called poor wettability), unlike water loving sand. The big question for scientists is: Do the old rules about sticky liquid bridges still work when the liquid is a scorching hot metal that refuses to hug the solid particles? Understanding this is crucial because if the rules are wrong, engineers might struggle to control how these hot mixtures flow in furnaces, potentially ruining the final product.

Enter a team of researchers from Kyushu University who decided to test the limits of these old rules. They mixed tiny ceramic beads (acting as the "sand") with various molten metals like tin, copper, and iron, as well as a molten rock mixture, heating them up to temperatures where the metals are liquid but the beads stay solid. They wanted to see how these hot, messy mixtures behaved when they were wiggled back and forth, measuring how "springy" (storage modulus) they were.

Here is the twist: The old rules predicted that the stiffness of the mixture should depend heavily on the surface tension of the liquid, assuming that tiny liquid bridges were holding the beads together. But when the researchers looked closely, they found something surprising. The old rules were completely off. Their measurements showed that the stiffness didn't follow the expected pattern at all.

To solve the mystery, they used a special X-ray camera (like a super-powered CT scan) to take 3D pictures of the hot mixture while it was still molten. The images revealed a secret: the liquid wasn't forming bridges between the beads at all! Because the liquid and the solid beads didn't get along (poor wettability), the liquid actively avoided the spots where the beads touched each other. Instead, the liquid hid in the big empty gaps between the beads, forming isolated, floating droplets. It was like a game of musical chairs where the liquid refused to sit on the same seat as the beads, leaving the beads to touch each other directly while the liquid floated in the voids.

So, if there are no liquid bridges, what makes the mixture stiff? The researchers discovered that the stiffness comes from a different kind of dance. The beads, trapped at the edge of the floating liquid droplets, act like tiny pivots. When the mixture is wiggled, the beads try to rotate, and the surface of the liquid droplet resists this rotation, acting like a spring. The researchers found that the stiffness of the whole system scales with how hard it is to rotate these beads at the liquid's surface, not with the strength of liquid bridges.

In short, this study shows that in high-temperature systems where the liquid and solid don't mix well, the old idea of "sticky bridges" is a myth. Instead, the behavior is governed by how the particles rotate against the surface of the liquid droplets. This finding suggests that to control these hot industrial processes, we need to stop thinking about bridges and start thinking about the rotational mechanics of particles trapped at liquid surfaces. It's a new way of looking at a very hot, very complex problem.

Technical Summary: Effect of Interfacial Properties on Viscoelastic Behavior of High-Temperature Multi-Phase System

Problem Statement
The viscoelastic behavior of granular materials containing liquid phases is critical to high-temperature metallurgical processes, such as blast furnace operations and liquid phase sintering. While the mechanical response of conventional "wet" granular systems (studied at room temperature) is well-understood—governed by capillary forces arising from liquid bridges between particles—high-temperature systems present a distinct challenge. These systems often involve molten metals or oxides with high surface tensions (0.4–1.8 N/m) and poor wettability (contact angles > 90°) against solid particles. Under these conditions, the formation of liquid bridges is thermodynamically unfavorable, rendering the established scaling laws for the storage modulus ( $G'$ ), which rely on capillary-mediated interactions, potentially invalid. The specific role of interfacial properties (surface tension and contact angle) in determining the viscoelasticity of poorly wetted, high-temperature granular systems remains unexplored.

Methodology
To investigate these phenomena, the authors conducted a systematic study using mixtures of alumina ( $Al_2O_3$ ) beads (mean diameter 0.5 mm) and various liquid phases: molten tin (Sn), copper (Cu), iron (Fe), and a calcium aluminosilicate oxide melt. The experimental design isolated the effects of surface tension and contact angle by selecting specific combinations where these variables varied independently.

The methodology comprised three primary components:

Rheological Measurements: A custom-built high-temperature rheometer (capable of reaching 2023 K) was used to perform oscillatory shear tests. Samples were pre-sheared to establish a steady-state structure, followed by measurements of the storage modulus ( $G'$ ) and loss modulus ( $G''$ ) across a range of strain amplitudes ( $10^{-4}$ to $10^{-1}$ ) at a fixed frequency (10 rad/s).
Microstructural Characterization: To visualize the spatial distribution of the liquid phase, samples were rapidly quenched after rheological testing and analyzed using X-ray micro-computed tomography (micro-CT). This allowed for 3D reconstruction of the liquid morphology within the granular packing.
Theoretical Evaluation: The experimental data were compared against conventional scaling laws (specifically the model by Møller et al., which predicts $G' \propto \sigma_{liquid}^{1/3}$ ) and various theoretical models for interfacial deformation, including lateral capillary interactions and vertical interfacial restoring forces.

Key Results

Viscoelastic Behavior: All systems exhibited solid-like behavior at low strains, with $G'$ significantly exceeding $G''$ . However, the dependence of $G'$ on surface tension and contact angle deviated significantly from conventional scaling laws. Specifically, $G'$ did not follow the predicted $1/3$ power law dependence on surface tension.
Microstructural Observations: X-ray CT analysis revealed that in systems with poor wettability, the liquid phase does not form bridges at solid-solid contact points. Instead, the liquid preferentially occupies larger voids, forming isolated, nearly spherical droplets. This configuration maintains direct solid-solid contacts while creating gas-liquid interfaces adjacent to the particles.
Deformation Mechanism: The study evaluated potential mechanisms for the observed elasticity. Models based on lateral capillary forces and vertical interfacial restoring forces showed weak correlations with the experimental data. However, the authors found that the storage modulus scales with the effective spring constant associated with particle rotation at the gas-liquid interface.
Wettability Impact: The storage modulus was observed to increase as the contact angle decreased (improving wettability), but the magnitude of $G'$ in high-temperature systems was consistently lower than predictions from room-temperature capillary models, even for systems with relatively good wettability.

Significance and Claims
The paper claims to provide a new framework for understanding the rheology of high-temperature granular systems where liquid bridges are absent. The primary contribution is the demonstration that under poor wettability conditions, viscoelasticity is not governed by capillary bridges but by interfacial rotational mechanics involving the gas-liquid interface.

The authors conclude that the conventional scaling laws for $G'$ are inapplicable to these high-temperature, poorly wetted systems because the fundamental assumption of capillary-mediated particle contacts is invalid. Instead, the mechanical response is dictated by the stiffness associated with particle rotation at the gas-liquid interface. This finding offers a revised theoretical basis for controlling and predicting the mechanical behavior of multi-phase systems in metallurgical processes, moving beyond the limitations of room-temperature wet granular models.

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