# Professor Simon Brandon

**Research Fields**

Crystal Growth Science and Technology

Batteries and Fuel Cells

Transport Phenomena

Interfacial Phenomena

**Research Topics**

**Sophisticated Computational Tools**

We have developed sophisticated computational tools for multiple-dimensional, multiple-length-scale analysis of combined transport phenomena and interface attachment kinetics (associated with facetted growth) in large scale melt and solution growth systems. In addition we have developed a user-friendly and flexible multi-dimensional tool for design and analysis of Thermal Batteries and are currently working on the preparation of algorithms for the analysis of Fuel Cell Systems. Specific numerical and modeling techniques include the Finite Element and Finite Difference Methods, Lattice Boltzmann Methods and Phase Field Modeling. Recent efforts include implementing some of these algorithms on Graphic Processing Units (GPUs). In addition to these in-house codes we often apply public-domain and commercial software packages to problems of interest. These include the Surface Evolver (for analysis of wetting phenomena) and FLUENT (for various problems involving transport phenomena).

**Crystal Growth**

One example involves defects developing during growth of large-scale crystals from solution. These are, in many cases, associated with non-uniform and/or time varying distribution of solute near the growing interfaces. Previous analyses of simplified model crystalline surfaces have yielded suggestions for ways to avoid such problems. We have shown that more realistic models of systems involving the entire crystal geometry predict, under certain conditions, interactions between faces as well as between different parts of a face and the flow-and-solute field. Such interactions may complicate the situation, e.g. by creating additional avenues for the development of defects.

**Thermal Batteries**

Thermal batteries operate using a molten salt electrolyte. This is achieved (once only per battery) by igniting pyrotechnic material which raises the temperature above the electrolyte's melting point thus facilitating battery discharge. The life-time of the battery is often determined by the ability of thermal insulation to keep the system's temperature above the melting point of the salt. We (in collaboration with a colleague from industry) have developed a versatile simulator for the analysis and design of thermal batteries. This can be applied to a wide range of cylindrical geometries with flexible inner structure related to the number and type of electrochemical cells as well as insulating material geometries. Thus far, our thermal model has predicted realistic operating times while accounting for phase-change effects in the eutectic electrolyte material. We have achieved (for the first time) a quantitative analysis of the importance of heat of solidification release during cool down as well as the relative importance of joule heating and (endothermic) heats of reaction during the operation of a typical battery.

**Liquid bridges**

Liquid bridges are typically formed by small volumes of water joining two solid surfaces. Resultant forces of cohesion (or adhesion) can be surprisingly large as can be observed when trying to lift a flat glass plate (e.g. a microscope slide) placed on a wet kitchen counter. We have investigated a number of systems involving liquid bridges. In one case we have looked at cylindrical-shaped fibers joined by liquid bridges. Interesting observations in this system include the existence of torques which in certain cases act to align fibers one with another.

** Selected Publications**

N. Haimovich, D.R. Dekel and S. Brandon, A simulator for system-level analysis of heat transfer and phase-change in thermal batteries II: Multiple-cell simulations, submitted.

A. Virozub and S. Brandon, Three-dimensional simulations of liquid bridges between two cylinders: forces, energies, and torques, Langmuir, 25(22), 12837-12842 (2009)

I.G. Rasin, O. Weinstein and S. Brandon, `Modeling the impact of flow modulation on surface structure during the growth of potassium dihydrogen phosphate single crystals from solution, Int. J. Multiscale Comp. Eng. 6(6), 585-601 (2008).

S. Brandon, P. Katsonis, and P.G. Vekilov, Multiple extrema in the intermolecular potential and the phase diagram of protein solutions, Phys. Rev. E., 73(6-1), 061917/1-061917/9 (2006).

O. Weinstein and S. Brandon, Dynamics of partially faceted melt/crystal interfaces III: three-dimensional computational approach and calculations,' J. Crystal Growth, 284, 235-253 (2005).

S. Brandon and J.J. Derby, Heat transfer in vertical Bridgman growth of oxides: effects of conduction, convection and internal radiation, J. Crystal Growth, 121(3), 473-494 (1992)