The project relates to pattern formation in a microfluidic network due to reacting and diffusing species. The objective is to estimate conditions under which Turing instabilities emerge in microfluidic networks. It involves mathematical modeling and computation. 

Reference: Van Gorder RA. 2021 A theory of pattern formation for reaction–diffusion systems on temporal networks. Proc.R.Soc.A477: 20200753. https://doi.org/10.1098/rspa.2020.0753 

In this project, the student will model the deposition process of nanoparticles onto surface of hydrogel microbeads. The deposition and synthesis is based on droplet coalescence within a microchannel. The project will involve theory and simulations.

This project will model and simulate the a radial flow chromatographic column, which has advantages of high throughput over axial column chromatography. The project will benchmark with axial chromatography to compare their performances. 

Problem Statement: Battery modules composed of series–parallel cell assemblies exhibit non-uniform ageing due to current imbalance, thermal gradients, and heterogeneous operating histories. Conventional models used in battery management systems inadequately capture coupled electrochemical–thermal degradation across cells under realistic, variable charge–discharge cycles. This limits accurate life prediction, safe operation, and degradation-aware control at the module level.

Problem Statement: Industrial BESS energy management systems typically rely on simplified aging assumptions, treating battery degradation as proportional to energy throughput and neglecting operating-condition dependence. Such simplifications lead to aggressive charging and discharging strategies that reduce battery lifetime and distort the true economic value of storage, particularly under variable tariffs, temperatures, and industrial load profiles.

Enzymatic cascades are conserved set of biochemical reactions, ubiquitously found in many systems. The goal of this project is to develop a suitable machine learning model to predict the reaction structure and kinetics of an enzymatic cascade. The project will involve use of systematic kinetic model simulations of a repertoire of cascades in the context of machine learning models. Candidate is expected to have a strong interest in reaction engineering and have basic training in python programming.

The goal is to develop a general lattice Boltzmann model for high (~10^{-3}) Knudsen numbers flow in porous media. The challenges involve maintaining numerical stability at high Knudsen numbers in complex geometries. Focus will be on specular boundary conditions. The project will involve building and testing a mathematical model with C++/Python code. 

This project will exclusively use dynamic models identified using data for MPC of the underlying process. The data based models will be either directly identified as state space models or state space models realized from input-output models. We will start with toy examples to understand the pipeline but eventually apply it to a process of industrial scale. 

Dealloyed gold nanoparticles can be synthesized by selectively dissolving Ag from gold-silver alloy nanoparticles through the well-known process of dealloying. These nanoparticles exhibit remarkable catalytic activity towards the CO oxidation reaction owing to their large specific surface area, presence of rough surfaces that contain a high density of catalytically-active sites, and synergistic effects arising from the residual Ag leftover from the dealloying process.

Microkinetic modeling is powerful tool in heterogeneous catalysis, as it quantitatively merges fundamental surface chemistry principles with experimental data, avoiding the need for prior assumptions about rate-determining steps (RDS), quasi-equilibrated steps, or most abundant reaction intermediates (MARI). This project focuses on modeling of green, heterogeneously catalyzed reactions that generate H2 and syngas (H2 + CO), such as dry reforming of methane (DRM).