Shear-thinning effects on cone-jet electrospray dynamics: a lattice Boltzmann study

Shear-thinning fluids are widely used in electrospray applications, yet the coupling between shear-rate-dependent viscosity and electrohydrodynamics remains insufficiently characterised. To clarify how viscosity and shear-thinning affect cone-jet electrospray, we develop a unified, axisymmetric charge-transport phase-field lattice Boltzmann framework for inelastic generalized-Newtonian shear-thinning fluids that enables a systematic investigation of cone-jet evolution and breakup. The formulation allows free charge to exist in the bulk; during electrospray startup, charge is often enhanced near the diffuse liquid-gas interface, while finite transient bulk charge can persist when charge relaxation lags rapid interface deformation. Using this model, we investigate electrospray evolution from Taylor-cone formation to the first-drop pinch-off under a broad range of operating conditions. We find that Newtonian and shear-thinning fluids share common features during the initial jetting stage. For example, reducing viscosity promotes inertia-dominated abrupt breakup, accompanied by rapid ligament retraction, whereas increasing viscosity slows the necking process and delays breakup. Specifically, the breakup morphology can be described by an effective apparent viscosity associated with an effective local shear rate. When expressed in the normalized variables proposed by Gañán-Calvo et al. (2016), the tip kinematics collapse approximately onto the reported parabolic trend, and the first-drop size follows an approximately linear scaling law. Under capillary-dominated conditions, shear-thinning can reduce the jet length at first pinch-off compared with Newtonian cases. Finally, we propose a new scaling correlation for the first-drop charge that incorporates charge-relaxation effects for the electrospray process.