Dynamics of thin liquid films on vertical cylindrical fibres

Abstract

Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms, and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of traveling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the traveling wave solution of the model.

Modelling film flows down a fibre influenced by nozzle geometry

“…where the FCM subscript stands for fully nonlinear curvature model. In the low-Reynolds-number limit δ → 0, (3.3b) gives an expression for q in terms of h. Substituting this expression into (3.3a) leads to a single lubrication equation for h, which is equivalent to the model (3.11) studied in Ji et al (2019) and Craster & Matar (2006),…”

“…For the case S < 0, we have Λ < 0 for any k > 0. We follow the approach in Ji et al (2019) and select the stabilization parameter A based on the dimensional thickness p = Hh c of a stable undisturbed layer obtained from experimental observations, where h c is the dimensionless stable coating film thickness. By setting S(h c ) = 0 and using the O(1) equation, we derive a formula for a critical A c :…”

“…This is characterized by the interaction between an azimuthal curvature term in Z(h) and the streamwise curvature terms h xx in (3.3b). Following the approach in Ji et al (2019), we also introduce a film stabilization term Π(h). As a result, the functional Z in (3.3b) consists of a destabilizing azimuthal curvature term β/(α(1 + αh)) and a film stabilization term Π(h),…”

“…Recently, Ji et al. (2019) investigated a full lubrication model that includes slip boundary conditions, nonlinear curvature terms and a film stabilization term. The last term brings to focus the presence of a stable liquid layer that plays an important role in the dynamics.…”

Instabilities and bifurcations of liquid films flowing down a rotating fibre

“…Recently, the problems of coating flows arising in more complex situations, for example in the presence of thermocapillarity (Liu & Liu 2014), subject to electric field (Ding & Willis 2019), in contact with countercurrent gas flow (Dietze & Ruyer-Quil 2015), flowing over a slippery surface (Halpern & Wei 2017; Ji etal. 2019), have been extensively investigated due to their relevance to technological applications. Except for the attempts in the complex situations mentioned above, rotation is an effective way to control the stability and dynamics of coating flows.…”