arXiv subjects

Amir D. Gat

Publications and source records attributed to Amir D. Gat.

29 records · Page 2Linked to original sources

arXiv2018

Dynamics and instabilities of an arbitrarily clamped elastic sheet in potential flow with application to shape-morphing airfoils

The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions, such as canceling of deflection due to aerodynamic forces and transition between two predefined cambers via continuous actuation of the airfoil. The steady results are validated by numerical calculations based on commercially available software. We then examine stability and transient dynamics by assuming small deflections and applying multiple-scale analysis to obtain a stability condition. The condition is attained via the compatibility equations of the orthogonal spatial modes of the first-order correction. The results yield the maximal stable speed as a function of elastic damping, fluid density and location of clamping. The results show that the interaction between the front and rear segments is the dominant mechanism for instability for various discrete locations of clamping. Instabilities due to interaction dynamics between the front and rear segments become more significant as the location of clamping approaches the leading edge. Several transient dynamics are presented for stable and unstable configurations, as well as instability dynamics initiated by cyclic actuation at the natural frequency of the airfoil.

physics.flu-dyn↗

arXiv2017

Gaseous viscous peeling of linearly elastic substrates

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the flow-field is governed by the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the governing evolution equation and enable solution by self-similarity. These limits correspond to different time-scales and physical regimes which include compressiblity-elasticity-viscosity, compressiblity-viscosity and elasticity-viscosity dominant balances. For a prewetting layer thickness which is similar to the elastic deformation generated by the background pressure, a symmetry between compressibility and elasticity allows to obtain a self-similar solution which includes weak rarefaction effects. The results are validated by numerical solutions of the evolution equation

physics.flu-dyn↗

arXiv2017

Transient Dynamics of Elastic Hele-Shaw Cell Due to External Forces with Application to Impulse Mitigation

We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the flow-field via the lubrication approximation, and the plate deformation by the Kirchhoff-Love plate theory. We obtain a self-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed form expressions. We examine a uniform external pressure acting on the elastic plate over a finite region and during a finite time period, similar to the viscous-elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure, thus suggesting such configurations may be used for impact mitigation.

physics.flu-dyn↗

arXiv2017

Frequency Response and Resonance of Elastic Hele-Shaw Cells with Application to Mechanical Filters

We study steady-state oscillations of an elastic Hele-Shaw cell excited by traveling pressure waves over its upper surface. The fluid within the cell is bounded by two asymmetric elastic sheets which are connected to a rigid surface via distributed springs and modeled by the linearized plate theory. Modal analysis yields the frequency response of the configuration as a function of three parameters: the fluidic Womersley number and two ratios of elastic stress to viscous pressure for each of the sheets. These ratios, analogous to the Capillary number, combine the effects of fluid viscosity and the sheets inertia, bending and tension. The resonance frequencies of the configuration include the resonance frequency of the upper sheet, and the resonance frequency of both sheets with a constraint of constant gap. Near the resonance frequency of the upper sheet, the fluid pressure is identical in amplitude and phase to the external excitation. For configurations where both sheets are near resonance, small changes in frequency yield significant modification of the fluidic pressure. In addition, a new resonance frequency is observed, related to the interaction between motion of fluid parallel to the elastic sheets and relative elastic displacements of the sheets. The ratio of the amplitude of the fluidic pressure to the external pressure is presented vs. frequency for several characteristic solid and fluid properties, yielding a bandpass filter behaviour. For configurations with a rigid lower surface the pressure ratio is unity at the passband, while for two elastic sheets pressure amplification or reduction occurs near the resonance frequencies. The results presented here may allow to utilize elastic Hele-Shaw configurations as protective surfaces and mechanical filters.

physics.flu-dyn↗

arXiv2016

Interaction Between Two Closely-Spaced Waving Slender Elastic Cylinders Immersed in a Viscous Fluid

We study the hydrodynamic interaction between two closely-spaced waving elastic cylinders immersed within a viscous liquid, at the creeping flow regime. The cylinders are actuated by a forced oscillation of the slope at their clamped end and are free at the opposite end. We obtain an expression for the interaction force and apply an asymptotic expansion based on a small parameter representing the ratio between the elastic deflections and the distance between the cylinders. The leading-order solution is an asymmetric oscillation pattern at the two frequencies ($ω_1,ω_2$) in which the cylinders are actuated. Higher orders oscillate at frequencies which are combinations of the actuation frequencies, where the first-order includes the $2ω_1,2ω_2,ω_1+ω_2$, and $ω_1-ω_2$ harmonics. For in-phase actuation with $ω_1= ω_2$, the deflection dynamics are identical to an isolated cylinder with a modified Sperm number. For configurations with $ω_1\approx ω_2$, the $ω_1-ω_2$ mode represents the dominant first-order interaction effect due to significantly smaller effective Sperm number. Experiments are conducted to verify and illustrate the theoretical predictions.

physics.flu-dyn↗

arXiv2016

Flow of Power-Law Liquids in a Hele-Shaw Cell Driven by Non-Uniform Electroosmotic Slip in the Case of Strong Depletion

We analyze flow of non-Newtonian fluids in a Hele-Shaw cell, subjected to spatially non-uniform electroosmotic slip. Motivated by their potential use for increasing the characteristic pressure fields, we specifically focus on power-law fluids with wall depletion properties. We derive a p-Poisson equation governing the pressure field, as well as a set of linearized equations representing its asymptotic approximation for weakly non-Newtonian behavior. To investigate the effect of non-Newtonian properties on the resulting fluidic pressure and velocity, we consider several configurations in one- and two-dimensions, and calculate both exact and approximate solutions. We show that the asymptotic approximation is in good agreement with exact solutions even for fluids with significant non-Newtonian behavior, allowing its use in the analysis and design of microfluidic systems involving electro-kinetic transport of such fluids.

physics.flu-dyn↗

arXiv2015

Deformation of an Elastic Beam due to Viscous Flow in an Embedded Parallel Channel Network

Elastic deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotic applications. In this work, we analyze interaction between the elastic deflection of a slender beam and viscous flow within a long serpentine channel, embedded in the elastic beam. The channel is positioned asymmetrically with regard to the midplane of the beam, and thus pressure within the channel creates a local moment deforming the beam. We focus on creeping flows and small deflections of the elastic beam and obtain, in leading order, a fourth-order partial integro-differential equation governing the time-dependent deflection field. This relation enables the design of complex time-dependent deformation patterns of beams with embedded channel networks, including inertia-like standing and moving wave solutions in configurations with negligible inertia.

physics.flu-dyn↗

arXiv2015

Interaction Forces Between Microfluidic Droplets in a Hele-Shaw Cell

Various microfluidic systems, such as chemical and biological lab-on-a-chip devices, involve motion of multiple droplets within an immersing fluid in shallow micro-channels. Modeling the dynamics of such systems requires calculation of the forces of interaction between the moving droplets. These forces are commonly approximated by superposition of dipoles solutions, which requires an assumption of sufficiently large distance between the droplets. In this work we obtain exact solutions (in the Hele-Shaw limit) for two moving droplets, and a droplet within a droplet, located within a moving immersing fluid, without limitation on the distance between the droplets. This is achieved by solution of the pressure field in a bi-polar coordinate system and calculation of the force in a Cartesian coordinate system. Our results are compared with numerical computations, experimental data and the existing dipole-based models. We utilize the results to calculate the dynamics of a droplet within a droplet, and of two close droplets, located within an immersing fluid with oscillating speed. The obtained results may be used to study the dynamics of dense droplet lattices, common to many microfluidic systems.

physics.flu-dyn↗

arXiv2015

Electroosmotic flow in Hele-Shaw configurations with non-uniform surface charge

We present an analytical study, validated by numerical simulations, of electroosmotic flow in a Hele-Shaw cell with non-uniform surface charge patterning. Applying the lubrication approximation and assuming thin electric double layer, we obtain a pair of uncoupled Poisson equations which relate the pressure and the stream function, respectively, to gradients in the zeta potential distribution parallel and perpendicular to the applied electric field. We solve the governing equations for the fundamental case of a disk with uniform zeta potential and show that the flow-field in the outer region takes the form of a pure dipole. We illustrate the ability to generate complex flow-fields around smooth convex regions by superposition of such disks with uniform zeta potential and a uniform pressure driven flow. This method may be useful for future on-chip devices, allowing flow control without the need for mechanical components.

physics.flu-dyn↗

arXiv2015

Axial Creeping Flow in the Gap between a Rigid Cylinder and a Concentric Elastic Tube

We examine transient axial creeping flow in the annular gap between a rigid cylinder and a concentric elastic tube. The gap is initially filled with a thin fluid layer. The study focuses on viscous-elastic time-scales for which the rate of solid deformation is of the same order-of-magnitude as the velocity of the fluid. We employ an elastic shell model and the lubrication approximation to obtain a forced nonlinear diffusion equation governing the viscous-elastic interaction. In the case of an advancing liquid front into a configuration with a negligible film layer (compared with the radial deformation of the elastic tube), the governing equation degenerates into a forced porous medium equation, for which several closed-form solutions are presented. In the case where the initial film layer is non-negligible, self-similarity is used to devise propagation laws for a pressure driven liquid front. When advancing external forces are applied on the tube, the formation of dipole structures is shown to dominate the initial stages of the induced flow and deformation regimes. These are variants of the dipole solution of the porous medium equation. Finally, since the rate of pressure propagation decreases with the height of the liquid film, we show that isolated moving deformation patterns can be created and superimposed to generate a moving wave-like deformation field. The presented interaction between viscosity and elasticity may be applied to fields such as soft-robotics and micro-scale or larger swimmers by allowing for the time-dependent control of an axisymmetric compliant boundary.

physics.flu-dyn↗

arXiv2015

Preventing Buckling of Slender Cylindrical Structures by Internal Viscous Flows

Viscous flows within an elastic structure apply stress on the solid-liquid interface. The stress-field created by the viscous flow can be utilized to counter stress created by external forces and thus may be applied as a tool for delaying the onset of structural failure. To illustrate this concept we study viscous flow within an elastic cylinder under compressive axial force. We obtain a closed-form expression showing an approximately linear relation between the critical buckling load and the liquid inlet pressure. Our results are validated by numerical computations. We discuss future research directions of fluid-solid composite materials which create flow under external stress, yielding enhanced resistance to structural failure.

cond-mat.soft↗