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 [$\mathrm{DMPI}+$][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.

中文翻译：

---

离子液体的低马赫数波动流体力学模型

我们提出了一种基于低马赫数波动的多组分带电物质流体动力学公式的离子液体的新中尺度模型。低马赫数方法从完全可压缩的方程式中消除了声波，从而产生了计算上高效的不可压缩公式。该模型使用了吉布斯自由能函数，该函数包括混合焓，界面能和静电贡献。这些导致质量方程式中出现新的四阶项，而动量方程式中产生可逆应力。我们使用[$\mathrm{DMPI}+$] [F6P-]是经过广泛研究的室温离子液体（RTIL），并在数值上证明了在二维和三维平衡状态下介观结构的形成。在带有电极边界的模拟中，测得的双层电容随电压降低，这与RTIL的理论预测和实验测量一致。最后，我们提供了一个电渗剪切实例，以证明该方法可用于模拟电动流动。