Computational Modelling of Thixotropic Multiphase Fluids

TL;DR

This paper develops a Smoothed Dissipative Particle Dynamics (SDPD) approach to model thixotropic multiphase fluids by coupling interfacial tension, phase separation dynamics, and time-evolving viscosity due to microstructure. The authors implement a thixotropic viscosity law, a pairwise interfacial force, and a stabilizing background pressure, and they validate the framework through static and dynamic benchmarks (surface tension, contact angles, Poiseuille and shear flow) as well as thixotropic-specific tests. They then apply the model to liquids undergoing LLPS, emulsions with thixotropic components, and microfluidic geometries (periodic constrictions and pillar-based merging), revealing how competing time scales—interfacial, viscous, and thixotropic—govern droplet morphology, coalescence, and transport. The results demonstrate the method’s ability to capture time-dependent rheology and interface evolution, offering a versatile tool for soft matter, biological, and microfluidic applications that involve complex phase interactions and aging phenomena.

Abstract

Multiphase systems are ubiquitous in engineering, biology, and materials science, where understanding their complex interactions and rheological behavior is crucial for advancing applications ranging from emulsion stability to cellular phase separation. This study presents a numerical methodology for modeling thixotropic multiphase fluids, emphasizing the transient behavior of viscosity and the intricate interactions between phases. The model incorporates phase-dependent viscosities, interfacial tension effects, and the dynamics of phase separation, coalescence, and break-up, making it suitable for simulating systems with complex flow regimes. A key feature of the methodology is its ability to capture thixotropic behavior, where viscosity evolves over time due to microstructural changes induced by shear history. This approach enables the simulation of aging and recovery processes in materials such as gels, emulsions, and biological tissues. The model is rigorously validated against benchmark cases, demonstrating its accuracy in predicting multiphase systems under static and dynamic conditions. Subsequently, the methodology is applied to investigate systems with varying levels of microstructural evolution, revealing the impact of thixotropic dynamics on overall system behavior. The results provide new insights into the time-dependent rheology of multiphase fluids and highlight the versatility of the model for applications in industrial and biological systems involving complex fluid interactions.

Figures (15)

• Figure 1: Validation of the methodology for multiphase static cases of (a) droplet surface tension, (b) retraction of a stretched droplet and (c) static contact angle between different phases.
• Figure 2: Validation of the methodology for multiphase Poiseuille flows using (a) a channel with two phases at different viscosity ratios, (b) Taylor deformation vs Capillary number for a droplet under a shear flow and (c) droplet break-up.
• Figure 3: Thixotropic model validation for a simple shear flow for $\alpha$ range of (1,2,4)). Model parameters are based on the validation process developed by rossi2022sph
• Figure 4: Phase separation evolution from the initial homogeneous state to the final phase-separated state.
• Figure 5: KDE comparison for the different properties analyses including the PID value. Inside snapshot illustrate the final configuration for two different system, where droplets are depicted in different colors for clarity. We employ the properties values for (a) $\lambda_{\text{thix}}/\tau_{\sigma}$ with $\sigma =[0.1, 0.5, 1.0, 2.0]$, $\alpha = 1$ (i.e. $\eta_{\text{max}}/\eta_{\infty}=2$), $k_BT=0$, for (b) initial-to-final viscosity with $\sigma =2.0$, $\alpha = [1,4,9,99]$, $k_BT=0$ and for (c) Thermal fluctuations with $\sigma =2.0$, $\alpha = 1$ (i.e. $\eta_{\text{max}}/\eta_{\infty}=2$), $k_BT = \{0, 0.05, 0.1\}$. For all simulations we use a fixed protein phase $\phi_p = 0.25$, viscosity of the solvent phase as $\eta_{s}=1$, thixotropic time scale $\lambda_{thix} = 1$ and $f_0=0$