The propagation of water waves is altered when interacting with curved surfaces. Here, we consider the problem of capillary waves interacting with a 3D cylindrical meniscus. We show that when capillary waves scatter off an object surrounded by a meniscus, the resulting wavefield can be drastically altered by refraction to increase wave presence in the otherwise shadowed region behind a cylinder. This indicates that a meniscus acts as an effective coating around an object, slowing down the wave's propagation speed in its region of influence. Our results are not only an important step in surface tension dominated wave interactions, but may have implications in the biological communication of surface dwelling animals.
A computational fluid dynamics (CFD) model is developed to simulate the dynamics of meniscus formation and capillary flow between vertical parallel plates. The arbitrary Lagrangian-Eulerian (ALE) approach was employed to predict and reconstruct the exact shape of the meniscus. The model was used to simulate the rise of water and the evolution of the meniscus in vertical channels with various spacing values of 0.5 mm, 0.7 mm, and 1 mm. The validity of the model was established by comparing the steady-state capillary height and the meniscus profile with analytical solutions. The developed model …
Surface waves called meniscus waves often appear in the systems that are close to the capillary length scale. Since the meniscus shape determines the form of the meniscus waves, the resulting streaming circulation has a structure distinct from that caused by other capillary-gravity waves recently reported in the literature. In the present study, we produce symmetric and antisymmetric meniscus shapes by controlling boundary wettability and excite meniscus waves by oscillating the meniscus vertically. The symmetric and antisymmetric configurations produce different surface capillary-gravity wave…
It is usually expected that surface tension driven flow dominates at small scales. Evaporation from the meniscus of ethanol/methanol confined in a capillary induces Marangoni convection at the meniscus which has been investigated by previous researchers. However, Marangoni convection is unexpectedly absent at an evaporating water meniscus confined inside a small micro-channel which is reported in this work. The velocity near the water meniscus is studied using confocal micro-PIV. The water meniscus is formed at the end of a micro-channel filled with water keeping the meniscus exposed to atmosp…
Small water droplets or particles located at an oil meniscus typically climb the meniscus due to unbalanced capillary forces. Here, we introduce a size-dependent reversal of this meniscus-climbing behavior, where upon cooling of the underlying substrate, droplets of different sizes concurrently ascend and descend the meniscus. We show that microscopic Marangoni convection cells within the oil meniscus are responsible for this phenomenon. While dynamics of relatively larger water microdroplets are still dominated by unbalanced capillary forces and hence ascend the meniscus, smaller droplets are…
A liquid surface touching a solid usually deforms in a near-wall meniscus region. In this work, we replace part of the free surface with a soft polymer and examine the shape of this elasto-capillary meniscus, result of the interplay between elasticity, capillarity and hydrostatic pressure. We focus particularly on the extraction threshold for the soft object. Indeed, we demonstrate both experimentally and theoretically the existence of a limit height of liquid tenable before breakdown of the compound, and extraction of the object. Such an extraction force is known since Laplace and Gay-Lussac,…
In this article, we construct a novel 1D-model of microfluidic laminar flows in tapered circular and rectangular channels assuming the flow in channels fully developed. In the model, we take into account the inertance and dynamic pressure terms. The model can be used for a wide range of flows: from the pure capillary flow regime, where the capillary forces are the main driver of the liquid in the channel, to the external pressure flow regime where the external pressure applied to the liquid at the entrance to the channel is much larger than the capillary pressure in the channel, so that the ca…
We study numerically the hydrodynamics of dip coating from a suspension and report a mechanism for colloidal assembly and pattern formation on smooth and uniform substrates. Below a critical withdrawal speed of the substrate, capillary forces required to deform the meniscus prevent colloidal particles from entering the coating film. Capillary forces are overcome by hydrodynamic drag only after a minimum number of particles organize in a close-packed formation within the meniscus. Once within the film, the formed assembly moves at nearly the withdrawal speed and rapidly separates from the next …
We study the meniscus on the outside of a small spherical particle with radius $R$ at a liquid-vapor interface. The liquid is confined in a cylindrical container with a finite radius $L$ and has a contact angle $π/2$ at the container surface. The center of the particle is placed at various heights along the central axis of the container. By varying $L$, we are able to systematically study the crossover of the meniscus from nanometer to macroscopic scales. The meniscus rise or depression on the particle is found to grow as $\ln (2L/R)$ when $R\ll L\ll κ^{-1}$ with $κ^{-1}$ being the capillary l…
Capillary driven flow is a famous problem in fluid dynamics which dates back to Leonardo da Vinci. In this paper, we apply an analytic approximation method for highly nonlinear problem, namely the homotopy analysis method (HAM), to a model of the meniscus movement in a uniform vertical circular tube. Convergent explicit series solution is successfully obtained. Our results agree well with the numerical results given by the symbolic computing software Mathematica using six-order Runge-Kutta methods. More importantly, our analytic solution is valid in the whole region of physical parameters, and…
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier--Stokes problem. Generalizing previous work by Tomotika (N=2), Stone & Brenner (N=3, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalized eigenproblem in the Stokes case. Furthermore, we demonstrate by…
Bundle-of-tubes model was previously used to understand the flow behaviour in a porous medium. The interacting nature of the pores within a porous medium can be well depicted by an interacting capillary model. However, the arrangement of pores is crucial in understanding the flow behaviour in an interacting capillary system, which also leads to different governing equations of spontaneous imbibition. To this end, in the present work, we first develop a generalized one-dimensional lubrication approximation model to predict the imbibition behaviour in an interacting multi-capillary system. Using…
We propose a numerical approach to regularize the contact line singularity appearing in the computation of viscous capillary-gravity waves with moving contact line in cylindrical containers. The linearized Navier-Stokes equations are complemented by a macroscopic Navier-like slip condition on the container side wall, with a depth-varying slip-length bridging a free-slip condition at the contact line to a no-slip condition further away from the meniscus. In accordance with suggestions from the literature, this characteristic penetration depth is chosen as the typical Stokes layer thickness pert…
The capillary levelling of cylindrical holes in viscous polystyrene films was studied using atomic force microscopy as well as quantitative analytical scaling arguments based on thin film theory and self-similarity. The relaxation of the holes was shown to consist of two different time regimes: an early regime where opposing sides of the hole do not interact, and a late regime where the hole is filling up. For the latter, the self-similar asymptotic profile was derived analytically and shown to be in excellent agreement with experimental data. Finally, a binary system of two holes in close pro…
The dynamics of individual liquid plugs pushed at constant pressure head inside prewetted cylindrical capillary tubes is investigated experimentally and theoretically. It is shown that, depending on the thickness of the prewetting film and the magnitude of the pressure head, the plugs can either experience a continuous acceleration leading to a dramatic decrease of their size and eventually their rupture or conversely, a progressive deceleration associated with their growth and an exacerbation of the airway obstruction. These behaviors are quantitatively reproduced with a simple nonlinear mode…
Lubricant-infused surfaces in an outer liquid flow generally reduce viscous drag. However, owing to the meniscus deformation, the infused state could collapse. Here we discuss the transition between infused and collapsed states of transverse shallow grooves, considering the capillary number, liquid/lubricant viscosity ratio and aspect ratio of the groove as parameters for inducing this transition. It is found that depending on the depth of the grooves, two different scenarios occur. A collapse of lubricant-infused surfaces could happen due to a depinning of the meniscus from the front groove e…
We report on an experimental investigation of the propagation of gravity-capillary waves in a narrow channel with a pinned contact line. By using Fourier Transform Profilometry (FTP) we measure the static curved meniscus as well as the surface perturbation. By varying the channel width, between 7 and 15 times the capillary length, we show how edge constraints modify the surface curvature and therefore the dispersion relation. From the space-time resolved field, we obtain a decomposition of the linear mode onto transverse modes satisfying the condition of pinned contact line. This approach, in …
We report the observation of a transition in the dynamical properties of water nano-menicus which dramatically change when probed at different time scales. Using a AFM mode that we name Force Feedback Microscopy, we observe this change in the simultaneous measurements, at different frequencies, of the stiffness G'(N/m), the dissipative coefficient G''(kg/sec) together with the static force. At low frequency we observe a negative stiffness as expected for capillary forces. As the measuring time approaches the microsecond, the dynamic response exhibits a transition toward a very large positive s…
We investigated the flow profile of a polymer solution in a thinning capillary bridge. Fluorescent tracer particles with a diameter of 3$μ$m were used to visualize the flow. The cylindrical shape of the filament introduced strong optical abberations that could be corrected for, and we were able to characterize the flow in filaments with a thickness ranging from 150 to 30 $μ$m. In the first regime when the filament was still sufficiently large, we used a PIV algorithm to deduce the flow field. At later stages when the number of particles in the observation plane decreased a PTV algorithm was us…
We study the microscale propulsion of a rotating helical filament confined by a cylindrical tube, using a boundary-element method for Stokes flow that accounts for helical symmetry. We determine the effect of confinement on swimming speed and power consumption. Except for a small range of tube radii at the tightest confinements, the swimming speed at fixed rotation rate increases monotonically as the confinement becomes tighter. At fixed torque, the swimming speed and power consumption depend only on the geometry of the filament centerline, except at the smallest pitch angles for which the fil…
Capillary filling dynamics of liquid n-tetracosane (n-C24H50) in a network of cylindrical pores with 7 and 10 nm mean diameter in monolithic silica glass (Vycor) exhibit an abrupt temperature-slope change at Ts=54 deg C, ~4 deg C above bulk and ~16 deg C, 8 deg C, respectively, above pore freezing. It can be traced to a sudden inversion of the surface tension's T slope, and thus to a decrease in surface entropy at the advancing pore menisci, characteristic of the formation of a single solid monolayer of rectified molecules, known as surface freezing from macroscopic, quiescent tetracosane melt…
Recent experimental observations have demonstrated interesting instability phenomenon during thermal drawing of microstructured glass/polymer fibers, and these observations motivate us to examine surface-tension-driven instabilities in concentric cylindrical shells of viscous fluids. In this paper, we focus on a single instability mechanism: classical capillary instabilities in the form of radial fluctuations, solving the full Navier--Stokes equations numerically. In equal-viscosity cases where an analytical linear theory is available, we compare to the full numerical solution and delineate th…
The well-known thermal capillary wave theory, which describes the capillary spectrum of the free surface of a liquid film, does not reveal the transient dynamics of surface waves, e.g., the process through which a smooth surface becomes rough. Here, a Langevin model is proposed that can capture these dynamics, goes beyond the long-wave paradigm which can be inaccurate at the nanoscale, and is validated using molecular dynamics simulations for nanoscale films on both planar and cylindrical substrates. We show that a scaling relation exists for surface roughening of a planar film and the scaling…
Floating of bodies heavier than the supporting liquid is discussed. Floating of cylindrical, ellipsoidal bodies and rectangular plates possessing lateral dimensions smaller than the capillary length is treated. It is demonstrated that more elongated bodies of a fixed volume are better supported by capillary forces, due to the increase in the perimeter of the triple line. Thus, floating of metallic needles obtains reasonable explanation.
One mechanism for airway closure in the lung is the surface-tension-driven instability of the mucus layer which lines the airway wall. We study the instability of an axisymmetric layer of viscoplastic Bingham liquid coating the interior of a rigid tube, which is a simple model for an airway that takes into account the yield stress of mucus. An evolution equation for the thickness of the liquid layer is derived using long-wave theory, from which we also derive a simpler thin-film evolution equation. In the thin-film case, we show that two branches of marginally-yielded static solutions of the e…
A recent experiment showed that cylindrical segments of water filling a hydrophilic stripe on an otherwise hydrophobic surface display a capillary instability when their volume is increased beyond the critical volume at which their apparent contact angle on the surface reaches ninety degrees (Gau et al., Science, 283, 1999). Surprisingly, the fluid segments did not break up into droplets -- as would be expected for a classical Rayleigh-Plateau instability -- but instead displayed a long-wavelength instability where all excess fluid gathered in a single bulge along each stripe. We consider here…
We account for the presence of surface charges towards describing variations in the dynamic contact angle of an advancing liquid-gas meniscus. Starting from the thin-film based formalism, we present closed-form analytical expressions relating the dynamic contact-angle with the capillary number (essentially normalized contact-line speed) and other interfacial parameters. Specifically, our analysis presents, within the realm of hydrodynamic paradigm, a connection between the micro- and macro-scale physics at the vicinity of the contact-line region, taking the combined confluence of viscous and c…
This work explores the dynamics of capillary effects in pure H2O excited by hydrodynamic cavitation, which has been reported to introduce a non-equilibrium state of para- and ortho- isomers of water. Differential measurements are conducted with 0.3mm and 0.5mm capillary tubes and precision digital vernier height gauges. Water samples are degassed at -0.09 MPa, their temperature is equalized. Since the non-equilibrium state of isomers is expected to exist in ice-like building blocks near the water interfaces, the immersion depth of capillary tubes was set to 10mm, 2mm and about 0.1mm below the …
We study the capillary retraction of a Newtonian semi-infinite liquid filament through analytical methods. We derive a long-time asymptotic-state expansion for the filament profile using a one-dimensional free-surface slender cylindrical flow model based on the three-dimensional axisymmetric Navier-Stokes equations. The analysis identifies three distinct length and time scale regions in the retraction domain: a steady filament section, a growing spherical blob, and an intermediate matching zone. We show that liquid filaments naturally develop travelling capillary waves along their surface and …
We analyse the effect of surface viscoelasticity on the temporal stability of a free cylindrical liquid jet coated with insoluble surfactant, extending the results of Timmermans & Lister (J. Fluid Mech., vol. 459, 2002, pp. 289-306). Our development requires, in particular, deriving the correct expressions for the normal and tangential stress boundary conditions at a general axisymmetric interface when surface viscosity is modelled with the Boussinesq-Scriven constitutive equation. These stress conditions are applied to obtain a new dispersion relation for the liquid thread, which is solved to…
A long cylindrical cavity through a soft solid forms a soft microfluidic channel, or models a vascular capillary. We observe experimentally that, when such a channel bears a pressurized fluid, it first dilates homogeneously, but then becomes unstable to a peristaltic elastic instability. We combine theory and numerics to fully characterize the instability in a channel through a bulk neo-Hookean solid, showing that instability occurs supercritically with wavelength $2π/k=12.278....a$ when the pressure exceeds $2.052....μ$. In finite solids, the threshold pressure is reduced, and peristalsis is …
The theoretical and numerical models for gravity driven coating flow on upper cylinder and sphere are formulated. Using a perturbation method, the governing equations which depend on one Bond number $Bo$ are derived for a liquid film flow down the outside of a horizontal cylinder and a sphere. They can be simplified to one-dimensional form due to the symmetries. The general structure of the two-dimensional and axisymmetric capillary waves under high $Bo$ condition is focused on. An asymptotic theory is used to solve for the free-surface profiles in the outer and inner region, respectively. Eve…
We deploy linear stability analysis to find the threshold wavelength ($λ$) and surface tension ($γ$) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius $R_0$. First we consider a solid cylinder, and recover the well-known, infinite wavelength instability for $γ\ge6 μR_0$, where $μ$ is the solid's shear modulus. Second, we consider a volume-conserving (e.g.\ fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite wavelength instability for $γ\ge 2 μR_0$. Third, we cons…
We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of axisymmetric linear waves propagating on the cylindrical ferrofluid layer that are found in good agreem…
To find the regularities of formed fingers in gravity driven coating flows on upper cylinder and sphere, the mathematical formulation to model the fingering instability on cylindrical or spherical surface which consists of a capillary wave equation and a linear perturbation equation is constructed, based on the leading order governing equation in standard cylindrical or spherical coordinate system. A disjoining pressure model is introduced to simulate the partial wetting process near moving contact line. The fingering number in high $Bo$ coating flow is focused on from a linear perspective. Us…
