Numerical prediction of hetero-aggregate composition from electrospray processes and their product-oriented optimization

Introduction

Functional mixing of different particle types, or hetero-aggregation, is a critical unit operation in process engineering for creating novel materials across various industries. The bipolar electrospray (ES) is a versatile method for producing these hybrid particles, leveraging electrostatic attraction to form hybrid particles with diverse properties. However, predicting the final aggregate properties is challenging due to their sensitivity to operational conditions and complex, difficult-to-observe micro-scale phenomena. Given these experimental difficulties, the development of a comprehensive numerical simulation tool is essential for the accurate prediction of the bipolar electrospray process.

Figure  1: Schematic diagram of hetero-aggregate synthesis via the bipolar electrospray process. 

Project Aim and Numerical Approach

The primary aim of this project is to develop a predictive multi-scale simulation tool for the bipolar electrospray process, enabling the accurate prediction and product-oriented optimization of hetero-aggregate composition. The simulations will be performed using the OpenFOAM® C++ toolbox.

The multi-scale physics of the problem—simultaneously tracking micro-sized droplets and the nano-sized particles within them—is computationally infeasible. To address this, the overall problem is decomposed into the main electrospray model utilizing the Euler/Lagrange approach and a detailed sub-model for suspension droplet collision using the Volume of Fluid (VoF) method coupled with Lagrangian particles.

Electrospray Model

The main electrospray model captures the full coupling between the flow field, the electrostatic field and the droplets. The gas flow field computation will be based on the Large Eddy Simulation (LES) approach. Since droplet evaporation is considered, additional transport equations for enthalpy and species must be solved. The electric potential is calculated through the Poisson’s equation, taking into account the ionic space charge left behind by fully evaporated droplets whose transport follows the current continuity equation. Droplet dynamics are governed by drag and electrostatic forces, including Coulomb fission when the Rayleigh limit is exceeded.

Suspension Droplet Collision

The suspension droplet collision simulations, will be used to quantify agglomeration in dependence of impact parameters (Weber number, droplet size ratio, impact angle). The results from these simulations will be used to derive an efficient agglomeration model that describes the post-coalescence state for the main electrospray simulations. Particle tracking within the droplets is conducted by considering hydrodynamic forces (drag, pressure gradient, added mass) and a capillary force acting near the interface. Particle-particle collisions will be handled in a deterministic manner and agglomeration will be modeled through an energy balance on the basis of the DLVO theory.

Figure 2: Initial setup for suspension droplet collision simulation. The figure shows two liquid droplets (red) suspended in air (blue) with embedded particles, and the adaptive mesh refinement at the droplet interfaces.

Conclusion

This project addresses a critical gap in particulate system processing by delivering a robust, multi-scale computational framework for the bipolar electrospray process. The resulting model will be instrumental for the rational design and optimization of novel dispersed products.

This work is part of the Priority Programme (SPP) 2289, funded by the German Research Foundation (DFG), focusing on “Creation of synergies in tailor-made mixtures of heterogeneous powders”.