M. A. Manna, A. Neveu
From a columnar approximation of the Euler equations of an incompressible fluid with surface tension, we derive in the short-wave approximation a new integrable classical 1+1 dimensional field theory for the motion of the surface. Together with a Lorentz invariance,this system has the novel feature of solutions which become multiple valued in finite time.
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We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume a constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero we recover the well known integrable three-wave system.
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…
Understanding the dynamical transition from capillary-driven to pure inertial focusing is important to revealing the mechanism underlying the most singular micro-jetting produced from drop-impact craters. Herein we study dimple dynamics from the collapse of these craters when the drop is of a different immiscible liquid than the pool. The parameter space is considerably more complex than for identical liquids, revealing intricate compound-dimple shapes. In contrast to the universal capillary-inertial drop pinch-off regime, where the neck radius scales as $R\sim t^{2/3}$, a purely inertial coll…
The flow through a capillary tube with non-constant radius and where bubbles of yield stress fluid are injected is strongly non-linear. In particular below a finite yield pressure drop, $P_y$, flow is absent, while a singular behaviour is expected above it. In this paper we compute the yield pressure drop statistics and the mean flow rate in two cases: (i) when a single bubble is injected, (ii) when many bubbles are randomly injected in the fluid.
We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity $c_\text{min} = 23 {\rm cm/s}$. At higher velocities the emission of capillary-gravity waves creates an additional drag force. The behavior of this force near the critical velocity is still poorly understood. A linear response theory where the object is replaced by an effective pressure source predicts a singular behavior for the wave drag. Ho…
Capillary levelling of thin liquid films of power-law rheology
本研究针对受表面张力作用的非牛顿幂律流体薄液膜流平问题，分别推导了周期性和局域化初始条件下的相似特解，发现其在压力梯度为零处存在弱奇异性，并通过数值模拟验证了解的正确性。
We consider the phase equilibria of a fluid confined in a deep capillary groove of width $L$ with identical side walls and a bottom made of a different material. All walls are completely wet by the liquid. Using density functional theory and interfacial models, we show that the meniscus separating liquid and gas phases at two phase capillary-coexistence meets the bottom capped end of the groove at a capillary contact angle $θ^{\rm cap}(L)$ which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then $θ^{\rm cap}>…
We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent root-bracketing techniques or Chebyshev interpolation to locate bifurcation points. Only positive singular values have to be computed, though the method relies on the existence of an analytic or smooth singular value decomposition (SVD). The sign of the determinant of the Jacobian, computed as part of the bidiagonal reduction in the SVD algorithm, eliminates slope discontinuities at the zeros of the smallest singula…
In this paper we develop an asymptotic theory for steadily travelling gravity-capillary waves under the small-surface tension limit. In an accompanying work [Shelton et al. (2021), J. Fluid Mech., vol 922] it was demonstrated that solutions associated with a perturbation about a leading-order gravity wave (a Stokes wave) contain surface-tension-driven parasitic ripples with an exponentially-small amplitude. Thus a naive Poincaré expansion is insufficient for their description. Here, we shall develop specialised methodologies in exponential asymptotics for derivation of the parasitic ripples on…
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…
In this paper we re-examine the flow produced by the normal impact of a laminar liquid jet onto an infinite plane when the flow is dominated by surface tension. It is observed experimentally that after impact the liquid spreads radially over the plane away from the point of impact in a thin film. It is also observed that, at a finite radius, there is an abrupt increase in thickness of the film which has been identified as a hydraulic jump,and that this radius is independent of the orientation of the surface showing that gravity is unimportant (Bhagat et al. 2018). We show that the application …
Singular jets during droplet impact on superhydrophobic surfaces
研究发现超疏水表面液滴撞击过程中存在由水平惯性引发的新型奇异喷射现象，揭示了其形成机制与状态图谱。
Capillary-gravity wave resistance of a translating, pulsating source
针对平移脉动源的毛细重力波阻力问题，推导了线源平均波阻力的闭式表达式，发现脉动会消除稳态源的无阻力亚阈值区域，且表面张力对该阻力至关重要。
End-pinching and inertial-capillary reopening in viscoplastic ligaments at low Ohnesorge number
研究粘弹性丝线在低Ohnesorge数下的端部捏缩与惯性-毛细重开机制，通过轴对称模拟揭示粘弹性对丝线断裂路径的影响，发现两种不同重开机制。
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear nature of the obstruction, asymptotic expansions in the low-Froude or low-Bond number limits can be derived, but here, the solutions are waveless to every order. This is because the waves are in fact, exponentially small, and thus beyond-all-orders of regular asymptotics; their formation is a consequence of the divergence of the asymptotic series and the associa…
Bubbles at a free surface surface usually burst in ejecting myriads of droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we propose a simple scaling for the jet velocity and we unravel experimentally the intricate roles of bubble shape, capillary waves, gravity and liquid properties. We demonstrate that droplets ejection unexpectedly changes with liquid properties. In particular, using damping action of viscosity, self-similar collapse can be sheltered from capillary ripples and continue closer to the singular limit, therefore producing faster and smaller droplets.Thes…
The role of wetting on the flow of two immiscible fluids in porous media
通过混合相场-浸入边界方法模拟多孔介质中两相流体界面动力学，揭示了毛细数和润湿性对毛细指进与稳定穿透模式的影响，并提出基于穿透长度和速度识别界面模式的新方法。
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