On the compound sessile drops: configuration boundaries and transitions

Abstract

Abstract

Walking droplets have been halted

“…As observed by Zhang et al. (2023), this result implies that for large drops (and movable CL), non-axisymmetric oscillation will more likely manifest in large drops than in smaller ones.…”

“…Zhang et al. (2023) tackle such a problem through a BEM, which can deal with arbitrary drop geometry, with the advantage of reducing the two-dimensional problem to a boundary integral equation. The modes are then classified by the pair , where the latter is the azimuthal wavenumber and the former indicates the number of vertical layers of the perturbation, which is related to the polar wavenumber of spherical harmonics introduced in (1.1) as .…”

“…The key contribution of the paper by Zhang et al. (2023) lies in a systematic investigation of the effects of gravity on the axisymmetric and non-axisymmetric oscillations of sessile drops over a wide range of static contact angles and Bond numbers , with the characteristic length scale based on the the drop volume . It is shown that the frequency of zonal modes decreases with gravity at small contact angle, but increases when the contact angle exceeds a certain critical value, with larger being more sensitive to the effects of gravity (in agreement with the numerical simulations of Sakakeeny & Ling (2021)).…”

“…The appeal of the approach by Zhang et al. (2023) comes from the effectiveness in solving the small-amplitude dynamics of inviscid drops of arbitrary shape. These results can be of valuable help in several applications, including inkjet printing, additive manufacturing, printed electronic components and circuits, forensic bloodstains, colloidal aggregation and biological flows such as plants transpiration, among many others.…”

“…As the drop shape differs from that of the spherical cap, however, there are no general theoretical models for the natural frequencies, owing to the difficulties in the geometrical treatment of the flattened drop configuration and the motion of the three-phase CL. Thus, the effect of gravity on the natural frequencies and the corresponding modes of a sessile drop had not been tackled until the recent paper of Zhang, Zhou & Ding (2023), where the corresponding eigenvalue problem is solved numerically through a general boundary element method (BEM) for different Bond numbers, CL conditions (either free or pinned) and static equilibrium contact angle.…”