Moving contact-line mobility measured

Abstract

Contact-line mobility characterizes how fast a liquid can wet or unwet a solid support by relating the contact angle $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ to the contact-line speed $U_{CL}$. The contact angle changes dynamically with contact-line speeds during rapid movement of liquid across a solid. Speeds beyond the region of stick–slip are the focus of this experimental paper. For these speeds, liquid inertia and surface tension compete while damping is weak. The mobility parameter $M$ is defined empirically as the proportionality, when it exists, between $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ and $U_{CL}$, $M\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}=U_{CL}$. We discover that $M$ exists and measure it. The experimental approach is to drive the contact line of a sessile drop by a plane-normal oscillation of the drop’s support. Contact angles, displacements and speeds of the contact line are measured. To unmask the mobility away from stick–slip, the diagram of $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ against $U_{CL}$, the traditional diagram, is remapped to a new diagram by rescaling with displacement. This new diagram reveals a regime where $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ is proportional to $U_{CL}$ and the slope yields the mobility $M$. The experimental approach reported introduces the cyclically dynamic contact angle goniometer. The concept and method of the goniometer are illustrated with data mappings for water on a low-hysteresis non-wetting substrate.

Droplet motions fill a periodic table

“…For our purposes, Λ may be viewed as a phenomenological parameter. It should be noted that Λ is well defined, has been measured experimentally, and has been related to CL dissipation, independent of any theory (27).…”

Directional motion of vibrated sessile drops: A quantitative study

“…The only fact that remains recurrent in most of the aforementioned experimental studies, is that the relationship between contact-line velocity and dynamical CAs shows complex behaviour taking non-singled values [13,45,46,48,49]. This complexity was included in numerical models [28] and was shown to increase the efficiency of the directional motion, particularly in the presence of CAH.…”

Dissipation of oscillatory contact lines using resonant mode scanning

“…The ISV experiments, to be summarized later, take advantage of larger, slower drops to make measurements of CL and CA motions for evaluation of CL dissipation according to the methods introduced in ref. 19 and demonstrated in this paper. Our apparatus is presently scheduled to be conveyed to the ISS in 2020 for subsequent experiments.…”

“…5a and related plots are discussed in ref. 19 To the authors' knowledge, the derivation of Eq. 7and the resulting relations Eq.…”

“…These correspond to two-and three-layer bouncing modes, respectively, or ½2; 0 and ½4; 0 modes in the nomenclature of, 20 two of some 35 sessile drop modes discovered to date. 21 The relative amplitude of the two prominent peaks may be surprising-the lower (67 Hz) is much lower in amplitude than the higher peak (155 Hz), suggesting greater damping, which 19 attribute to greater CL dissipation owing to greater CL motion. Less prominent peaks (23 Hz, 35 Hz) are subharmonic resonances.…”