  We present a new mesoscale model for ionic liquids based on a low Mach number
fluctuating hydrodynamics formulation for multicomponent charged species. The
low Mach number approach eliminates sound waves from the fully compressible
equations leading to a computationally efficient incompressible formulation.
The model uses a Gibbs free energy functional that includes enthalpy of mixing,
interfacial energy, and electrostatic contributions. These lead to a new
fourth-order term in the mass equations and a reversible stress in the momentum
equations. We calibrate our model using parameters for [DMPI+][F6P-], an
extensively-studied room temperature ionic liquid (RTIL), and numerically
demonstrate the formation of mesoscopic structuring at equilibrium in two and
three dimensions. In simulations with electrode boundaries the measured double
layer capacitance decreases with voltage, in agreement with theoretical
predictions and experimental measurements for RTILs. Finally, we present a
shear electroosmosis example to demonstrate that the methodology can be used to
model electrokinetic flows.
