Modelling of electrosprays of ionic liquids including dissipation and self-heating

This study investigates the effects of dissipation and the associated self-heating in cone jets of ionic liquids with high electrical conductivities. A numerical model based on the leaky-dielectric formulation that incorporates conservation of energy and temperature-dependent properties (restricted to the viscosity and the electrical conductivity) is developed and compared with isothermal numerical solutions and experimental data for four ionic liquids. The numerical solutions show that self-heating leads to significant temperature increases (up to 446 K) along the cone jet, dramatically enhancing the electrical conductivity and reducing the viscosity. The model reproduces the experimental values of the current for the ionic liquids studied. While isothermal solutions follow established scaling laws, the solutions including self-heating exhibit liquid-specific behaviours due to the unique temperature dependencies of the conductivity and viscosity. Self-heating creates a strong positive feedback between the electric current and the electrical conductivity, resulting in much higher electrospray currents compared with the isothermal solution. Ohmic dissipation dominates over viscous dissipation. Strong self-heating and the opposite effects of temperature on the electrical conductivity and the viscosity, increase the disparity between the two dissipation modes. This work demonstrates the importance of accounting for self-heating in the modelling and analysis of experimental data of cone jets of ionic liquids and other highly conductive liquids. First-principles modelling and case-specific experimental characterisation are necessary to describe these systems, as the traditional scaling laws break down when self-heating is significant.