Surfactant influence on rivulet droplet flow in minitubes and capillaries and its downstream evolution

Abstract

During our investigations of two-phase flow in long hydrophobic minitubes and capillaries, we have observed transformation of the main rivulet into different new hydrodynamic modes with the use of different kinds of surfactants. The destabilization of rivulet flow at air velocities <80 m/sec occurs primarily due to the strong branching off of sub-rivulets from the main rivulet during the downstream flow in the tube. The addition of some surfactants of not-so-high surface activity was found to increase the frequency of sub-rivulet formation and to suppress the Rayleigh and sinuous instabilities of the formed sub-rivulets. Such instabilities result in subsequent fragmentation of the sub-rivulets and in the formation of linear or sinuous arrays of sub-rivulet fragments (SRFs), which later transform into random arrays of SRFs. In the downstream flow, SRFs further transform into large sliding cornered droplets and linear droplet arrays (LDAs), a phenomenon which agrees with recent theories. At higher surface activity, suppression of the Rayleigh instability of sub-rivulets with surfactants becomes significant, which prevents sub-rivulet fragmentation, and only the rivulet and sub-rivulets can be visualized in the tube. At the highest surface activity, the bottom rivulet transforms rapidly into an annular liquid film. The surfactant influence on the behavior of the rivulets in minitubes is incomparably stronger than the classic example of the known surfactant stabilizing influence on a free jet. The evolution of a rivulet in the downstream flow inside a long minitube includes the following sequence of hydrodynamic modes/patterns: i) single rivulet; ii) rivulet and sub-rivulets; and iii) rivulet, sub-rivulets, sub-rivulet fragments, cornered droplets, linear droplet arrays, linear arrays of sub-rivulet fragments and annular film. The formation of these many different hydrodynamic patterns downstream is in drastic contrast with the known characteristics of two-phase flow, which demonstrates one mode for the entire tube length. Recent achievements in fluid mechanics regarding the stability of sliding thin films and in wetting dynamics have allowed us to interpret many of our findings. However, the most important phenomenon of the surfactant influence on sub-rivulet formation remains poorly understood. To achieve further progress in this new area, an interdisciplinary approach based on the use of methods of two-phase flow, wetting dynamics and interfacial rheology will be necessary.

A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate

“…Rivulet flow of a viscous fluid is a problem of enduring theoretical and experimental interest, not least because it occurs in a wide range of practical and industrial situations, including condensers and heat exchangers, 1 geophysical flows of ice, lava, and mud, 2 rain-wind-induced vibrations of cable-stayed bridges, 3,4 two-phase flow in narrow capillaries, 5 and even rivulets of rain water draining down a window pane.…”

Pinning, de-pinning and re-pinning of a slowly varying rivulet

“…The gravity-driven draining of a rivulet of fluid down an inclined substrate is a fundamental fluid mechanics problem of enduring interest, not least because of the wide range of industrial devices and processes to which it is relevant, including heat exchangers (see, for example, Vlasogiannis et al [1]), trickle-bed reactors (see, for example, Maiti, Khanna and Nigam [2]), various coating processes (see, for example, Kistler and Schweizer [3]), and even the cleaning of the long and narrow tubes found in endoscopes (see, for example, Labib et al [4]). In particular, the pioneering studies by Towell and Rothfeld [5], Allen and Biggin [6], Bentwich et al [7], and Davis and co-workers [8]- [10] have led to a substantial body of subsequent work on unidirectional (i.e.…”

Rivulet flow of generalized Newtonian fluids

“…In summary, when μ = μ(q) is prescribed, h and p are given by (16), u is given parametrically (with parameter q)by (17) and (23), and Q is given by (27). In Sec.…”

“…If the viscosity function is of the form μ = μ(τ ) then the solution analogous to (23) and (27) takes the explicit form…”

“…(27) cannot, in general, be evaluated in closed form, and so Q must, in general, be evaluated numerically. In the limit λ →∞, corresponding to a Newtonian fluid with viscosity μ = μ ∞ , we obtain…”