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The dynamics of a self-rewetting film falling along a vertical fiber under the influence of gravity are considered. The evolution equation of the interface of the self-rewetting film is established in the framework of a long-wave approximation theory. The effect of thermocapillarity (Marangoni effect) on the absolute/convective instability (AI/CI)...
Citations
... Recent studies conducted by Liu and Ding (2021) have demonstrated the efficacy of the domain mapping technique in solving the Navier-Stokes equations, with results that align closely with experimental observations across all three flow regimes. The impact of external physical fields on the dynamics of coating flows has garnered significant attention, notably the effects within radial electric fields (Li et al. 2009;Ding et al. 2014;Liu et al. 2018;Ding and Willis 2019), along heated fibers Dong et al. 2020), and around rotating fibers (Liu et al. 2017;Liu and Ding 2020;Ding and Liu 2011). These external influences are known to augment the absolute instability of the flows, predisposing the liquid film towards fragmentation into smaller droplets. ...
The present paper investigated the dynamics of coating flow on array of cylindrical fibres. In the experiments, it is observed that there exist three distinct flow regimes when the fiber array is fully coated by liquid film, namely, regime ‘a’, ‘b’ and ‘c’. The flow regime ‘a’ is characterized by the formation of a streamwise uniform film; The flow regime ‘b’ and ‘c’ are in the form of traveling waves consisting of asymmetrical wavy structures and symmetrical beads, respectively. We conducted a comprehensive parametric study on the dynamics of the coating flow on fiber array, including the flow rate, fiber spacing and droplet amplitude, all of which serve as reliable indicators of different flow regimes.
... 27, 28 Kliakhandler et al. 29 observed three typical flow regimes that increase with velocity: the isolated droplet regime, the Rayley-Plateau regime, and the convective regime. Additionally, many authors have worked on the coating flow of vertical cylindrical fibers in more complex situations, such as radial electric fields, 30 conductive liquid films, 31 applying external oscillations, 32 heating fibers, 33 and rotating fibers. 34 Pan et al. 35 found that the volume of retained droplets on curved fibers is three times larger than that on horizontal fibers, and the optimal angle is about 36 . ...
Cross fibers at different angles are essential for enhancing the separation of emulsions as the basic structure in fiber fillers. In this article, the retention and detachment process of droplets on fiber intersection were investigated using high‐speed camera technology to explore the critical volume, slip path and droplet oscillation. The results indicate that the critical volume retained on the intersection is significantly affected by the fiber slope, cross angle between fibers, and liquid viscosity. A droplet‐fiber interfacial force balance model is established to predict the critical volume and the tilt angle corresponding to maximum critical volume. The switching behaviors of selected fiber slippage depend on the slope, diameter, and affinity of the fiber. Compared with the lipophobic fiber woven mesh, the droplets on the lipophilic fiber mesh slip upward with a larger oscillate deformation and obvious periodicity. The mean deformation of droplets is 1.16 times that on lipophobic fiber.
... The coating flow down a vertical fiber exhibits rich interesting dynamical phenomena, including the travelling waves of droplets or beads, due to the Plateau-Rayleigh mechanism (Rayleigh 1892) and the gravity. Recently, many authors have devoted to studying the coating flow on a vertical cylindrical fiber in more complicated situations, e.g. in a radial electric field (Li et al. 2009;Wray et al. 2013;Ding et al. 2014;Liu et al. 2018), a heated fiber Dávalos 2017;Dávalos 2019;Dong et al. 2020), and a rotating fiber (Liu and Ding 2020). These flows are driven by a Plateau-Rayleigh mechanism modified by the existence of gravity and different destabilizing body force which play roles in the formation of bead-like structures and a series of stable or oscillatory travelling waves (De Ryck and Quéré 1996;Zuccher 2008;Duprat et al. 2009). ...
The dynamics of coating flows down a vertical fiber is investigated experimentally. An oscillatory flow has been observed in experiments, which corresponds to a relative periodic orbit (RPO) in nonlinear dynamics. This type of RPO manifests as a periodic process in which a large droplet swallows small droplets, and then the film behind the large droplet evolves into new small droplets. In order to understand the physical mechanisms of RPOs, we studied the transition from travelling waves (TWs) to RPOs for different physical parameters, including the dynamic viscosities, fiber diameters and flow rates. The experimental results show that such a process is periodic, and there exists a critical flow rate at which the RPOs appear. It is interesting that a small-scale RPO has been observed in experiments when the flow rate is much smaller than the critical flow rate at which the normal-scale RPO appears. As the flow rate is decreased further, the relative periodic orbits transformed into an irregular state. This indicates that the appearance of multi-scale RPOs is a transition from an ordered state to a disordered state.
... Their work focused on the Marangoni effects that originate from the linear dependence of the variation of surface tension with temperature. The works of Liu, Chen & Wang (2019) and Dong, Li & Liu (2020) extended this result by considering a self-rewetting fluid (Batson, Agnon & Oron 2017) with the surface tension modelled as a quadratic function of temperature. Ding et al. (2019) also investigated the influence of thermally induced Marangoni effects and van der Waals attractions on the break-up of ultra-thin liquid films (Ji & Witelski 2017). ...
... Their study demonstrated that the interfacial tension nonmonotonically depending on temperature had a crucial influence on drop spreading. Liu et al. 33 found that thermocapillarity played adverse roles while the interfacial temperature crossed the critical temperature T 0 , and on the basis of Liu's study, the effect of thermocapillarity (Marangoni effect) on the absolute/convective instability (AI/CI) was further investigated by Dong et al. 34 In the analysis of bubbles in self-rewetting fluid, a role transfer in the instability was also discovered. 35,36 Besides the long-wave disturbance, Sarma and Mondal 37 focused on the short-wave disturbance as well and concluded that the oscillatory mode was more critical as the short-wave disturbance increased the range of the dimensionless parameters. ...
... This property has a very large potential application in evaporative cooling, especially in heat transfer and microgravity boiling in spacecraft modules. 25,34 At the end of the section, we give the linear stability results for different Bi. The growth rate of the perturbation for different ...
This paper examines the evolution patterns and essential mechanisms of flow instability of a self-rewetting fluid (SRF) coating on an inclined plane. Considering that the self-rewetting liquid has an anomalous surface tension with temperature change, some interesting phenomenon will be found and should be explained. Using the thin-film model, the evolution equation of the air-liquid interface is derived, and the thickness of the liquid film is determined by a Fourth-order partial differential equation. Taking $T_0$ (temperature corresponding to the minimum of surface tension) as a cutoff point, two representative cases of the nonlinear flow are comprehensively discussed. One is the case of $T_i > T_0$, and the other is $T_i < T_0$ (interfacial temperature $T_i$ ). Based on traveling wave solutions, linear stability analysis (LSA) of the small perturbation applied to the initial condition is given, and the results of LSA are confirmed and explained by the numerical simulations. Results show that the inclined angle and the Weber number always stabilize the free surface, while the Marangoni effect and the Biot number play different roles for the two cases. As $T_i - T_0$ varies from a negative value to a positive value, the Marangoni effect switches to the reverse Marangoni effect, With $T_i - T_0 < 0$, the Marangoni effect enhance the fingering instability, while the Marangoni effect make the flow more stable if $T_i - T_0 >0$. The Biot number $Bi=1$ corresponds to the most unstable state for $T_i < T_0$ and to the most stable state for $T_i > T_0$.
In this paper, we investigate the quadratic Marangoni instability along with inertia in a self-rewetting fluid film that has a nonmonotonic variation of surface tension with temperature. The dynamics of such a thin self-rewetting fluid film flowing along an inclined heated substrate is examined by deriving an evolution equation for the film thickness using long-wave theory and asymptotic expansions. By adopting the derived long-wave model that includes the inertial and thermocapillary effects, we perform a linear stability analysis of the flat film solution. Two cases of the nonlinear flow are explored in depth using Tm (temperature corresponding to the minimum of surface tension) as the cutoff point. One is the case of (Ti,s−Tm)<0, and the other is (Ti,s−Tm)>0, where Ti,s is the interface temperature corresponding to the flat film. The Marangoni effect switches to the anomalous Marangoni effect as (Ti,s−Tm) shifts from a negative value to a positive value. Our calculations reveal that the Marangoni effect augments the flat film instability when (Ti,s−Tm)<0, whereas the stability of the flat film is promoted for (Ti,s−Tm)>0. Our further analysis demonstrates that the destabilizing inertial forces can be entirely compensated by the stabilizing anomalous thermocapillary forces. We verify the linear stability predictions of the long-wave Benney-type model with the solution to the Orr–Sommerfeld problem in the long-wave limit. Our time-dependent computations of the long-wave model establish the modulation of interface deformation in the presence of inertia and temperature gradients in the conventional Marangoni regime, whereas such deformations are suppressed in the anomalous Marangoni regime. A comparison of the numerical computations with the linear theory shows good agreement.
We study the enhanced spreading and internal diffusion of a cold, self-rewetting droplet laden with both surfactant and medicine that is placed over a hot liquid film. Spreading is induced by solutocapillary and thermocapillary effects simultaneously. A numerical simulation based on Stokes flow is performed, and the internal velocity map is obtained. The horizontal velocity flux and total medicine absorption are calculated to examine the internal diffusion and transport behaviors for a low-viscosity case and a high-viscosity mucus case. The results show that solutocapillary and thermocapillary effects contribute to droplet spreading positively and negatively, respectively. Self-rewetting fluids enhance spreading by increasing the surface tension gradient and prolonging the time required for spreading to reach a steady regime. For the self-rewetting fluid case at the final calculation time, the thermo-Marangoni number Σ T = 0.03, and the soluto-Marangoni number Σ S = 0.9, the internal diffusion and medicine absorption are enhanced by 9.1% and 8.3% relative to the ordinary fluid, respectively. When a droplet spreads on a high-viscosity mucus at the same Marangoni numbers, both spreading and diffusion are hindered. The spreading enhancement provided by self-rewetting fluids is much smaller than in low-viscosity cases. However, medicine absorption still increases by 11%.
The flow dynamics of a thin viscous film down on a fiber is associated with a variety of industrial applications. In this paper, we experimentally investigate the flow behaviors of a thin film falling on differently shaped fibers. For a spiral fiber, flow behaviors show three typical flow regimes as the cylindrical fiber, which indicates the isolated regime, Rayleigh–Plateau regime, and convective regime. However, the transition process of various fiber shapes is distinctively different. Unlike the cylindrical fiber, flow on a spiral fiber exhibits a wider range of flow rate in the Rayleigh–Plateau regime, which is helpful for the precise control of flow patterns in a relatively stable regime. We further quantitatively investigate three important characteristic parameters of flow dynamics of a spiral fiber, i.e., bead velocity, thickness, and spacing. Results reveal that a thin film on a spiral fiber has a higher bead velocity, larger bead thickness, and larger bead spacing. Our findings provide important insights for understanding flow dynamics of a thin viscous film down on shaped fibers, which may also inspire coating flow control methods in various applications.
Nonlinear dynamic analysis of a self-rewetting fluid (SRWF) film flowing
down the surface of a vertical cylinder is performed in this paper. The effect of the Biot number, Marangoni number and the substrate curvature on
the interfacial evolution patterns and flow stabilities are discussed by linear
stability analysis and numerical simulations of the evolution equation of the
film thickness. Starting from the characteristic temperature T0 relating to
the minimum surface tension and the interfacial temperature Ti, the nonlinear dynamics of the liquid film is investigated numerically in the cases of
either Ti > T0 or Ti < T0. Good agreement of linear stability analysis with
numerical simulations proves that the LSA could predict the development
of thin liquid film flows in the early-time evolution. Through the analysis,
we demonstrate that the Marangoni number Ma and the Biot number Bi
play contrary roles for the two cases. For Ti < T0, the fingering instability
is enhanced by the Marangoni effect while the inverse Marangoni effect stabilizes the interface for Ti > T0. The growth rate changes linearly with the
increase of Marangoni number while it changes in forms of arched shapes versus lg(Bi). The growth rate reaches a maximum/minimum value at Bi = 1,
corresponding to the most/least unstable state. The radius of the cylinder R
plays a significant role in the long wavelength modes, showing a stabilizing
effect. For perturbations of short waves, increment of R expands the instability region. Nonlinear oscillatory waves (Rayleigh{Plateau instability) appears when the radius is smaller than 1 and fingering pattern tends to
occur if the cylinder has a large radius (R ≥ 1)
The surface tension of a self-rewetting fluid (SRF) has a non-monotonic variation with the increase of temperature, implying potential applications in many industrial fields. In this paper, flow patterns and stability analysis are numerically performed for a gravity-driven self-rewetting fluid film flowing down a heated vertical plane with wall slip. Using the thin film theory, the evolution equation for the interfacial thickness is derived. The discussion is given considering two cases in the review of the temperature difference between the interfacial temperature and the temperature corresponding to the minimum surface tension. The base state of the two-dimensional flow is firstly obtained and the influence of the Marangoni effect and slippery effect is analyzed. Then linear stability analysis
and related numerical verification are displayed, showing good consistency with each other. For a low interfacial temperature, the Marangoni promotes the fingering instability and for a high interfacial temperature, the inverse Marangoni impedes the surface instability. The wall slip is found to influence the free surface in a complex way
because it can either destabilize or stabilize the flow of the free surface.
