PhD Studentship: Modelling the Dynamics of Surfactant-laden Droplets for Sustainable Design of Emulsions

Emulsions, which consist of dispersed droplets of one liquid in another immiscible liquid, are critical components in a wide range of applications, from personal care products and pharmaceuticals to food, agrochemicals, and lubricants. These emulsified systems exhibit complex behaviours near solid substrates, influencing key functionalities such as cleaning, thin-film formation, and agent deposition. Understanding and controlling these interactions is crucial for designing formulations that are both high-performing and sustainable.

The intricate dynamics of emulsified droplets near substrates arise from the interplay of interfacial forces at different scales. At the microscale, surfactants—amphiphilic molecules that stabilise emulsions—modulate the droplets’ interfacial properties, influencing adhesion, cohesion, and spreading. At the mesoscale, irreversible interactions such as droplet coalescence, breakup, and thin-film formation occur as droplets encounter solid surfaces. These phenomena, in turn, impact the macroscale rheological properties of the emulsion, affecting its flow behaviour and overall performance.

Despite the significance of these processes, achieving a comprehensive understanding of the fluid-fluid interactions involved remains a challenge. Experimental methods are often limited by the fast timescales and small length scales of these interactions, while conventional computational fluid dynamics (CFD) approaches struggle to resolve large deformations and complex interfacial phenomena associated with emulsified droplets.

Aims, Objectives, and Approach

This project aims to develop a hybrid computational model to resolve the micro- and meso-scale interfacial dynamics of emulsified droplets. Understanding the underpinning fluid-fluid dynamics facilitate the sustainable design and development of the next generation of green emulsions. Accordingly, the main research objectives are:

• Droplet Formation near Surfaces: Understanding how surfactants encapsulate a tiny amount of a foulant/soul from the surface.
• Droplet Dynamics: Understanding the role of surfactants on the dynamics and deformation of droplets.
• Droplet Cohesion and Coalescence: Understanding how droplets merge and form larger structures, which can alter the emulsion’s internal structure and optical properties.
• Droplet Breakup: Investigating how droplets split under shear or impact forces, critical for processes like emulsion stability and delivery of active agents.

The insights gained will enable the formulation of emulsions tailored for specific applications, reducing chemical consumption and environmental impact. This research aligns with global sustainability goals and the UK’s Net Zero strategy, addressing the dual challenges of high market demand and environmental responsibility.

The numerical model will combine a group of particle-based methods including Smoothed Particle Hydrodynamics (SPH), Mass-Spring Models (MSM), and Dissipative Particle Dynamics (DPD).

Applicant’s profile

Applicants are expected to:

1. Have a background in mechanical engineering, chemical engineering, applied mathematics, chemistry, physics, or a related discipline.
2. Have a good mathematical background and familiarity with ODEs and PDEs.
3. Be familiar with at least one of the following:

• • fluid dynamics and multiphase flows,
  • numerical modelling,
  • one of the programming languages such as C++, Python, and MATLAB.

Support and training

The PhD student will be supported through extensive training on numerical modelling, parallel computing, programming languages, and utilising High-Performance Computing (supercomputer) facilities. The student will gain hands-on experience in developing hybrid numerical codes and will develop experience and expertise in multiphase systems and fluid dynamics. The student will work directly with a team of researchers in the area, will have access to experimental facilities and extensive experimental data, and have the opportunity to attend career development workshops.

For details of the funding available, advice on making your application, and informal enquires, please contact a.rahmat@bham.ac.uk.

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