Relaxation of liquid bridge after droplets coalescence

Jiangen Zheng,Hua Wei,Weijia Wen,Guo Chen,Shuxia Wang,Yingzhou Huang,Haiyang Shi

doi:10.1063/1.4967883

Abstract

We investigate the relaxation of liquid bridge after the coalescence of two sessile droplets resting on an organic glass substrate both experimentally and theoretically. The liquid bridge is found to relax to its equilibrium shape via two distinct approaches: damped oscillation relaxation and underdamped relaxation. When the viscosity is low, damped oscillation shows up, in this approach, the liquid bridge undergoes a damped oscillation process until it reaches its stable shape. However, if the viscous effects become significant, underdamped relaxation occurs. In this case, the liquid bridge relaxes to its equilibrium state in a non-periodic decay mode. In depth analysis indicates that the damping rate and oscillation period of damped oscillation are related to an inertial-capillary time scale τc. These experimental results are also testified by our numerical simulations with COMSOL Multiphysics.

Highlights

Similar oscillation cycles of h with gradually reduced vibration strength repeat multiple times until excess of surface energy has been dissipated and the bridge approaches a static equilibrium state around t = t5. These specific times are: t0 = 0 ms, t1 = 1 ms, t2 = 11 ms, t3 = 20 ms, t4 = 27 ms, t5 = 170 ms. We classify this case into the first kind of relaxation of liquid bridge-damped oscillation relaxation, which is similar to the general comprehension.[25,27]
We investigate the relaxation behaviour of the liquid bridge after the fusion of two sessile droplets sitting on an organic glass substrate with a fast camera
The liquid bridge is illustrated to relax to its equilibrium state via two distinct approaches: damped oscillation relaxation and underdamped relaxation

Summary

Introduction

Coalescence of droplets is very common in daily life, and the scientific and systematic study on this phenomenon for the first time can be dated back to the 19th century to our knowledge.[1,2,3,4,5]In the last decade, the fusion of droplets has been actively studied due to the emergence of new ideas and research approaches, like the coalescence of liquid droplets with equal or unequal size caused by collision,[6,7] or fusion of droplets induced by an electric field,[8,9,10] or merging of droplets in microfluidic channel.[11,12,13] the coalescence is fundamentally interesting, and may find broad applications in many important areas such as ink printing,[14] fuel injection,[15] and even dew water collection.[16,17] A comprehensive understanding about it is still lacking.Beysens and co-workers investigated the coalescence of two sessile droplets experimentally and theoretically,[18,19] and they divided the coalescence process into three stages:[20] an initial stage where a liquid bridge nucleates and grows, followed by an intermediate stage where the bridge relaxes exponentially and an ellipsis like drop forms, and the droplet slowly relaxes to a circular shape. The first stage process has been extensively studied[21,22,23] and is revealed to be started from a regime controlled by inertial, viscous and surface tension forces and followed by either a viscous or an inertial regime.[21] Relatively speaking, the second and the third stages, during which the liquid bridge relaxes to its equilibrium state, are of equal importance but do not get enough attentions.[24] A quite recent study by Chireux and co-workers revealed that the liquid bridge undergoes weakly damped oscillations until it reaches its equilibrium shape after the coalescence of two inviscid droplets.[25]

Methods

Results

Conclusion