CCSE Research: Fluctuating Hydrodynamics





Complex Fluids

Using our low Mach number fluctuating hydrodynamics solvers, we have extended the basic formulation for diffusive mixing of multispecies mixtures to include additional physics such as chemistry and charged fluids.

Room Temperature Ionic Liquids

Room temperature ionic liquids are solvent-free electrolytes known to self-assemble into a variety of patterns at the nanoscale. The tuning of these nanoscale-structures affects the mechanical, transport, and charge transfer properties of these materials and thus makes them desirable for a large number of applications where a high charge density is useful such as batteries, solar cells, and supercapacitors. Our fluctuating low Mach number model allows us to understand how the nanoscale structures result from the competition of short-range intermolecular interactions driving phase separation and long-range Coulombic effects.


Our low Mach code can be used for studying electrolyte systems. The animation on the left shows a type of electrokinetic instability that occurs when an electric field is applied to an inhomogeneous solution. The top region is more dilute than the bottom region. Because of the different behavior of positively and negatively charged species in the presence of the electric field, charged layers appear and become unstable. The animation on the right shows fluctuation-enhanced electric conductivity in an electrolyte solution. When an electric field is applied to an homogeneous solution, charged regions spontaneously appear due to fluctuations and couple with the electric field. This results in enhanced velocity fluctuations (as demonstrated by the velocities shown in the animation) as well as enhanced electric transport..

Stochastic Chemistry

As a first step towards incorporating stochastic reactions, we have developed stochastic simulation methods for reaction-diffusion systems. Our approach combines the rigor of the master equation approach for reactions and the efficiency of the fluctuating hydrodynamics approach for diffusion. The animation on the left shows pattern formation. Compared with the widely-used stochastic simulation algorithm (SSA), our method produces the same results much faster. The animation on the right shows front propagation. This example involves the equivalent of 1012 molecules, which cannot be simulated by SSA.

Next, we developed a fluctuating hydrodynamics formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Our new approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. The image on the left shows the growth of convective chemo-hydrodynamic finfigering patters in a Hele-Shaw cell, induced by a double-diffusive instability in the presence of a neutralization reaction. The image on the right is the same simulation without reactions.

Low Mach Number Multispecies Mixtures

Using a low Mach number approach that eliminates fast sound waves (pressure fluctuations) from the full compressible equations, we have obtained a quasi-incompressible formulation and developed a simulation code for multicomponent mixtures. The animation on the left shows the development of a mixed-mode instability as a layer of salty water is placed on top of a horizontal layer of less-dense sweet water. The animation on the right shows a different configuration where the salty water has been further diluted in water so that denser sweet water lies underneath. Here we see the development of a diffusive layer convection instability. The color plots show the vertically averaged density (horizontal plane) and planar slices of density (vertical planes). The observed giant fluctuations are caused by long-range correlations between fluctuations. ☞ For more information, contact Andy Nonaka