Inferring the Turbulent Breakup of Colloidal Aggregates Using Graph Neural Networks

TL;DR

The paper tackles predicting the turbulent breakup of colloidal aggregates by using Graph Neural Networks to infer rupture from a graph-based representation of aggregates and the local velocity-gradient field. It presents two models—a classifier and a regressor—trained on ground-truth data generated from DNS and Stokesian Dynamics, including multiple thresholds and unseen geometries to test generalization. Both models achieve high accuracy, with the classifier generally outperforming the regressor and a simple statistical baseline, and they demonstrate strong generalization to new shapes and random rupture thresholds. This approach enables fast, large-scale assessment of fragmentation in complex turbulent suspensions, with potential extensions to more complex flow regimes and heterogeneous aggregates.

Abstract

Solid aggregates in turbulent suspensions may break under the action of shear stresses. We explore the use of Graph Neural Networks (GNN) to infer aggregate fragmentation once the aggregate structure and flow velocity gradients are known. We consider two models: the first GNN is a classifier, trained to distinguish aggregates that break from those that do not; the second GNN is a regression model, trained to predict the maximal tensile force within each aggregate in a given flow condition. We show that both models complete their task with a high statistical accuracy, and generally perform better than the statistical prediction based on mean field quantities. This work paves the way for future use of Graph Neural Networks to quantify aggregate breakup in large population of aggregates suspended in complex flow configurations.

Figures (11)

• Figure 1: Structure of a cluster-cluster aggregate of fractal dimension $D_F=1.9$, made up on $N_M=384$ primary particles of radius $a$, and $N_L=N_M-1$ links among them. The gyration radius of the aggregate scales with the primary particle radius and the number of primary particles as $R \simeq a \,N_M^{1/D_F}$.
• Figure 2: (a) PDF of the tensile force $F$. (b) PDF of the maximal tensile force $F_{\text{max}}$; in the inset, the cumulative distribution of $F_{\text{max}}$(continuous line). The green circles plotted on top of the CFD identify the six threshold values for the maximal tensile force, $F_{th1} = 1052$; $F_{\text{th2}} = 1220$; $F_{\text{th3}} = 1417$; $F_{\text{th4}} = 1653$; $F_{\text{th5}} = 1988$; $F_{\text{th6}} = 2539$, corresponding to the CDF being equal to 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9, respectively.
• Figure 3: PDF of the maximal force $F_{\text{max}}$ for the aggregates having a single bond failing when $F_{\text{max}} \ge F_{\text{threshold}}$, here $F_{\text{threshold}}=F_{\text{th3}}$ (vertical dashed line). Most of the broken aggregates have their maximal force close to the threshold; differently, unbroken aggregates experience any value $F_{\text{max}} < F_{\text{threshold}}$, and exhibit a very broad distribution. This is generally true for all thresholds, and is related to the single-bond rupture mechanism.
• Figure 4: A scheme of the end-to-end prediction task with the GNN classifier producing a binary output; for the regression model, the scheme is very similar, but there is no threshold value given in input, and the output is a positive real number.
• Figure 5: (a) The evolution of success probability (or accuracy) with the number of epochs for the GNN classifier model on the learning dataset (filled circles) and the test Cl-imb dataset (continuous line). (b) The evolution of loss function, $L_{MSE}$, with the number of epochs for the GNN regression model on the learning dataset (filled circles) and the test Cl-rnd dataset (continuous line).