Effect of a DC electric field on a meniscus in a square groove

The present study aims at investigating the deformation of a liquid-gas meniscus across a square groove when submitted to an electric field. Two numerical methods are developed: a first one (in-house) consists in solving the strong coupling between the Laplace-Young equation and the Laplace equation for the electric potential; the latter equation being required to get the distribution of the normal electric stress along the meniscus while the first equation is used to calculate the meniscus shape. The Laplace-Young equation is accordingly modified in order to take into account the added contribution of the normal electric stress. A second method based on the phase-field approach is developed for sake of comparison. The results demonstrate a fair agreement between both methods: the electric stress is found to be mostly focused on the top edges of the side walls, which pulls up the interface and yields higher curvatures for a same pressure jump. The in-house method is found to be significantly fast and to accommodate well with realistic boundary conditions, compared to the phase-field method which does not comply with the contact angle. The results, as obtained from the in-house method, are analysed based on non-dimensional numbers whose respective effects on the shape of the interface are properly investigated. A significant impact of the electric field near the triple contact line and at the centre of the groove is made evident. These effects can be described by considering an apparent angle near the triple contact line, or by considering the elevation of the meniscus centre. These results can be used in order to optimise an electrocapillary enhanced structure whose groove geometry is given.