Frequency-Dependent Behavior of Electrostatic Forces Between Human Finger and Touch Screen Under Electroadhesion

The existing lumped parameter circuit models do not capture the true (experimentally observed) behavior of electrostatic forces between human finger and a touch screen under electroadhesion, changing as a function of stimulation frequency. In order to address this problem, we first conducted an experiment to measure the voltage-induced frictional forces acting on the finger of a user sliding on a touch screen under constant normal force for stimulation frequencies ranging from 1 to 10 $^6$ Hz. The steady-state values of coefficient of sliding friction for those frequencies and the value for voltage-free sliding (no electroadhesion) were utilized to estimate the magnitude of electrostatic force as a function of frequency. The experimental data shows that electrostatic force follows an inverted parabolic curve with a peak value around 250 Hz. Following the experimental characterization of electrostatic forces, an electro-mechanical model based on the fundamental laws of electric fields and Persson's multi-scale contact mechanics theory was developed. Compared to the existing ones in the literature, the proposed model takes into account the charge accumulation and transfer at the interfaces of finger and touch screen. The model is in good agreement with the experimental data and shows that the change in magnitude of electrostatic force is mainly due to the leakage of charge from the Stratum Corneum (SC) to the touch screen at frequencies lower than 250 Hz and electrical properties of the SC at frequencies higher than 250 Hz.