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We study theoretically and experimentally how a thin layer of liquid flows along a flexible beam. The flow is modelled using lubrication theory and the substrate is modelled as an elastica which deforms according to the Euler-Bernoulli equation. A constant flux of liquid is supplied at one end of the beam, which is clamped horizontally, while the other end of the beam is free. As the liquid film spreads, its weight causes the beam deflection to increase, which in turn enhances the spreading rate of the liquid. This feedback mechanism causes the front position ${sigma}$(t) and the deflection angle at the front ${phi}$(t) to go through a number of different power-law behaviours. For early times, the liquid spreads like a horizontal gravity current, with ${sigma}$(t) = $t^{4/5}$ and ${phi}$(t) = $t^{13/5}$. For intermediate times, the deflection of the beam leads to rapid acceleration of the liquid layer, with ${sigma}$(t) = $t^4$ and ${phi}$(t) = $t^9$. Finally, when the beam has sagged to become almost vertical, the liquid film flows downward with ${sigma}$(t) = $t$ and ${phi}$(t) ~ ${pi}$/2. We demonstrate good agreement between these theoretical predictions and experimental results.
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We study the deformation and transport of elastic fibers in a viscous Hele-Shaw flow with curved streamlines. The variations of the global velocity and orientation of the fiber follow closely those of the local flow velocity. The ratios of the curvatures of the fibers by the corresponding curvatures of the streamlines reflect a balance between elastic and viscous forces: this ratio is shown experimentally to be determined by a dimensionless {it Sperm number} $Sp$ combining the characteristic parameters of the flow (transverse velocity gradient, viscosity, fiber diameter/cell gap ratio) and those of the fiber (diameter, effective length, Youngs modulus). For short fibers, the effective length is that of the fiber; for long ones, it is equal to the transverse characteristic length of the flow. For $S_p lesssim 250$, the ratio of the curvatures increases linearly with $Sp$; For $S_p gtrsim 250$, the fiber reaches the same curvature as the streamlines.
We address the flutter instability of a flexible plate immersed in an axial flow. This instability is similar to flag flutter and results from the competition between destabilising pressure forces and stabilising bending stiffness. In previous experimental studies, the plates have always appeared much more stable than the predictions of two-dimensional models. This discrepancy is discussed and clarified in this paper by examining experimentally and theoretically the effect of the plate aspect ratio on the instability threshold. We show that the two-dimensional limit cannot be achieved experimentally because hysteretical behaviour and three-dimensional effects appear for plates of large aspect ratio. The nature of the instability bifurcation (sub- or supercritical) is also discussed in the light of recent numerical results.
In this paper, the problem of compressible flow over a thin airfoil located near the ground is studied. A singular integral equation, also known as Possio equation, that relates the pressure jump along the airfoil to its downwash is derived. The derivation of the equation utilizes Laplace transform, Fourier transform, method of images, and theory of Mikhlin multipliers. The existence and uniqueness of solution to the Possio equation is verified for the steady state case and an approximate solution is obtained. The aerodynamic loads are then calculated based on the approximate solution. Moreover, the divergence speed of a continuum wing structure located near the ground is obtained based on the derived expressions for the aerodynamic loads.
Transforming a laser beam into a mass flow has been a challenge both scientifically and technologically. Here we report the discovery of a new optofluidics principle and demonstrate the generation of a steady-state water flow by a pulsed laser beam through a glass window. In order to generate a flow or stream in the same path as the refracted laser beam in pure water from an arbitrary spot on the window, we first fill a glass cuvette with an aqueous solution of Au nanoparticles. A flow will emerge from the focused laser spot on the window after the laser is turned on for a few to tens of minutes, the flow remains after the colloidal solution is completely replaced by pure water. Microscopically, this transformation is made possible by an underlying plasmonic nanoparticle-decorated cavity which is self-fabricated on the glass by nanoparticle-assisted laser etching and exhibits size and shape uniquely tailored to the incident beam profile. Hydrophone signals indicate that the flow is driven via acoustic streaming by a long-lasting ultrasound wave that is resonantly generated by the laser and the cavity through the photoacoustic effect. The principle of this light-driven flow via ultrasound, i.e. photoacoustic streaming by coupling photoacoustics to acoustic streaming, is general and can be applied to any liquids, opening up new research and applications in optofluidics as well as traditional photoacoustics and acoustic streaming.
We develop a framework for analyzing the momentum balance of laminar particle-laden flows based on immersed boundary methods, which solve the Navier-Stokes equations and resolve the particle surfaces. This framework differs from previous studies by explicitly accounting for the fluid inside the particles, which is a by-product of the immersed boundary method, allowing us to close the momentum balance for the flow around a single rolling sphere. We then compute a momentum balance of a laminar Poiseuille flow over a dense bed of particles, finding that the stresses remain in equilibrium even during unsteady flow conditions. While previous studies have focused on stresses for the streamwise momentum balance, the present approach also allows us to evaluate stress balances in the vertical direction, which are necessary to understand the role that collisions and hydrodynamic drag play during dilation and contraction of particle beds. While our analysis accounts for the fluid and particle phases separately, we attempt to establish a momentum balance for the fluid/particle mixture, but find that it does not completely close locally due to collision stresses not being resolved across the particle diameter. However, we find a correlation between the local shear rate and the gap in the mixture balance, which can potentially be used to close the balance for the mixture.
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