- Mathematical and Stochastic Modelling
- Fluid Dynamics
- Partial Differential Equations
- Stochastic Processes and Applications

- Geothermal Harnessing High-temperature aquifer storage is an important approach to providing heating and cooling in residential and commercial settings with a low-carbon footprint. Predicting the fluid, thermal and solutal transport of these systems over decades of use requires an understanding of the transport processes through low-conductivity regions. While aqueous chemistry takes place on much shorter time scales, surface dissolution, whose rate depends on the pH and temperature in the fluid and the calcite matrix alters the pore geometry and ultimately affects thermal transport on the thermal storage time scale. To better understand these competing processes, we focus on the transport dynamics in a single pore and derive a model in a three-dimensional axisymmetric cylindrical system. Assuming quasi-steady aqueous reactions and a small pore radius compared to the characteristic length of the pore, we derive a system that describes the evolution of the pore shape, thermal and calcium ion transport, and fluid mass conservation. When energy is delivered to the pore, dissolution occurs at the inlet but precipitation is observed near the pore outlet, reducing the net heat flux delivered to the system. When energy is retrieved by reversing the flow direction, precipitation can be observed with a rapid nonlinear pore closure depending on species and thermal profiles, preventing energy harnessing. The results of this work will form the foundation for adaptations for dynamic pore network models (PNM) of geothermal energy harnessing applications.
- Membrane Filtration via Spectral Graph Theory This work considers a membrane network as a weighted random graph. Fouling mechanisms, such as adsorption and sieving, evolve graph operators (e.g. the graph Laplacian) in continuous and discrete, deterministic and random fashion. Various performance metrics can be represented by this theoretical setup and thus analyzed using theory.
- A Flow-guided Weighted Random Walk on a Connected Graph with Blocking This problem arises from the modelling of the sieving fouling mechanism in membrane filtration. Particles of size similar to filter pore size arrive at the membrane surface and traverse the membrane network via fluid flow (that can be modelled by particle-laden flow). We model these particles as consecutive continuous-time random walkers that follow transition matrices induced by relative fluid flux through each pore junction (vertice). In addition to travelling, the random walkers carry size information that may or may not pass through pore throats (edges) and inevitably modify the graph topology. The weight of the graph also evolves due to a slower fouling mechanism -- adsorption. This entire dynamic process on the graph can be modelled by a stochastic temporal graph.
- Tortuosity and Connectivity of Random Media Tortuosity is (in one way) defined by the average distance traversed by a particle in a porous media, relative to porous media thickness. Simulating the paths of a large of number of particles is one way to estimate this quantity. However, if a network is used to represent the media, then this quantity can be explicitly computed using an asymmetric random walk on the network, obviating the simulations and thus reducing computation load.

Fall 2021: Calculus I

Spring 2020: Calculus II

Fall 2020: Calculus II

- On the Influence of Pore Connectivity on Performance of Membrane Filters.
B. Gu, D.R. Renaud, P. Sanaei, L. Kondic, L.J.Cummings

Journal of Fluid Mechanics,

**902**, A5 (2020) - A Graphical Representation of Membrane Filtration.
B. Gu, L. Kondic, L.J. Cummings

SIAM Journal on Applied Mathematics,

**82**, 950-975 (2022). - Network-based membrane filters: Influence of network and pore size variability on filtration performance.
B. Gu, L. Kondic, L.J. Cummings .

Journal of Membrane Science,

**657**, 120668 (2022). - Flow through Pore-Size Graded Membrane Pore Networks
B. Gu, L. Kondic, L.J. Cummings

Physical Review Fluids,

**8**, 044502 (2023). - A Numerical Model for Shear-Thinning Hele-Shaw Flow.
B. Gu, J. Adriazola, L. Kondic, L.J. Cummings (final stage of manuscript prepration).

- Stochastic Modelling of Sieving.
B. Gu, P. Sanaei, L. Kondic, L.J. Cummings (In progress).

- Persistent Homology of Membrane Pore Networks.
M. Illingworth, B. Gu, L. Kondic, L.J. Cummings (In progress).

- Finding the Limits of Machine Learning in Optimization.
D. A. Edwards, B. Gu, K. Jonston, M. Wichman, M. Zyskin, November, 2022.

- On Temperature Effects in Reacting Porous Media Applications.
R.H. Allaire, A.G. Odu, B. Gu, W. Lu, A. Newell, P.J. Paranamana, T. Phan, H. Ruzayqat, June, 2017.