scholarly journals Oscillations of a soft viscoelastic drop

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Saiful I. Tamim ◽  
Joshua B. Bostwick
Keyword(s):  
Surface Tension ◽  
Frequency Response ◽  
Maxwell Model ◽  
Forced Oscillations ◽  
Microgravity Environment ◽  
Free Oscillations ◽  
Polymer Fluids ◽  
Theoretical Predictions ◽  
Deposition Processes ◽  
Soft Gels

AbstractA soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin–Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a “drop vibration rheometer”, suggesting future experiments using either ultrasonic levitation or a microgravity environment.

scholarly journals A curved multi-component aerosol hygroscopicity model framework: 1 – Inorganics

2004 ◽  
Vol 4 (6) ◽  
pp. 8627-8676 ◽  
Author(s):  
D. O. Topping ◽  
G. B. McFiggans ◽  
H. Coe
Keyword(s):  
Surface Tension ◽  
Companion Paper ◽  
Dry Density ◽  
Model Framework ◽  
Aerosol Model ◽  
Modelling Framework ◽  
Systematic Uncertainties ◽  
Model Aerosol ◽  
Theoretical Predictions ◽  
Models Comparison

Abstract. A thermodynamic modelling framework to predict the equilibrium behaviour of mixed inorganic salt aerosols is developed, and then coupled with a technique for finding a solution to the Köhler equation in order to create a diameter dependent hygroscopic aerosol model (Aerosol Diameter Dependent Equilibrium Model – ADDEM). The model described here provides a robust and accurate inorganic basis using a mole fraction based activity coefficient model and adjusted energies of formation for treating solid precipitation. The model framework can accommodate organic components, though this added complexity is considered in a companion paper, whereas this paper describes the development of the modelling architecture to be used and predictions of an inorganic model alone. The modelling framework has been developed to flexibly use a combination of mixing rules and other potentially more accurate techniques where available to calculate the water content. Comparisons with other state-of-the-art general equilibrium models and experimental data are presented and show excellent agreement. The Kelvin effect can be considered in this scheme using a variety of surface tension models. Comparison of predicted diameter dependent phenomena, such as the increased relative humidity for onset of deliquescence with decreasing diameter, with another diameter dependent model is very good despite the different approach used. The model is subject to various sensitivities. For the inorganic systems studied here, the model is sensitive to choice of surface tension scheme used, which decreases for larger aerosol. Large sensitivities are found for the value of dry density used. It is thus likely that the history of the aerosol studied in a hygroscopic tandem differential mobility analyser (HTDMA), specifically the nature of the drying process that will influence the final crystalline form, will create systematic uncertainties upon comparisons with theoretical predictions. However, the magnitudes of all of the above sensitivities are potentially less than those introduced when using a semi ideal growth factor analogue for certain conditions.

The liquid blister test

2008 ◽  
Vol 464 (2099) ◽  
pp. 2887-2906 ◽  
Author(s):  
Julien Chopin ◽  
Dominic Vella ◽  
Arezki Boudaoud
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Vertical Displacement ◽  
Quantitative Agreement ◽  
Elastic Plates ◽  
Blister Test ◽  
Thin Liquid Layer ◽  
Theoretical Predictions ◽  
Thin Elastic Plates ◽  
Adhesive Forces

We consider a thin elastic sheet adhering to a stiff substrate by means of the surface tension of a thin liquid layer. Debonding is initiated by imposing a vertical displacement at the centre of the sheet and leads to the formation of a delaminated region or ‘blister’. This experiment reveals that the perimeter of the blister takes one of three different forms depending on the vertical displacement imposed. As this displacement is increased, we observe first circular, then undulating and finally triangular blisters. We obtain theoretical predictions for the observed features of each of these three families of blisters. The theory is built upon the Föppl–von Kármán equations for thin elastic plates and accounts for the surface energy of the liquid. We find good quantitative agreement between our theoretical predictions and experimental results, demonstrating that all three families are governed by different balances between elastic and capillary forces. Our results may bear on micrometric tapered devices and other systems, where elastic and adhesive forces are in competition.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

Small oscillations of systems with several degrees of freedom

2020 ◽  
pp. 29-40
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Free Oscillations ◽  
Small Oscillations ◽  
Symmetry Properties ◽  
Gyroscopic Forces ◽  
Simple Molecules ◽  
Simple Systems ◽  
Three Degrees Of Freedom

This chapter addresses the free and forced oscillations of simple systems (with two or three degrees of freedom), the free oscillations of systems with the degenerate frequencies, and the eigen-oscillations of the electromechanical systems. This chapter also studies the oscillations of more complex systems using orthogonality of eigenoscillations and the symmetry properties of the system, the free oscillations of an anisotropic charged oscillator moving in a uniform constant magnetic field, and the perturbation theory adapted for the small oscillations. Finally, the chapter addresses oscillations of systems in which gyroscopic forces act and the eigen-oscillations of the simple molecules.

A Quantitative Evaluation of the Frequency-Response Characteristics of Active Human Skeletal Muscle In Vivo

1979 ◽  
Vol 101 (1) ◽  
pp. 28-37 ◽  
Author(s):  
G. I. Zahalak ◽  
S. J. Heyman
Keyword(s):  
Skeletal Muscle ◽  
Frequency Response ◽  
Human Skeletal Muscle ◽  
Muscle Stiffness ◽  
Forced Oscillations ◽  
Muscle Stretch ◽  
Gain Parameter ◽  
Response Characteristics ◽  
Frequency Response Characteristics

This paper describes an investigation of the frequency-response characteristics of active human skeletal muscle in vivo over the frequency range 1 Hz to 15 Hz. The applied force, forearm position, and surface electromyograms (from biceps, triceps, and brachioradialis) were recorded simultaneously in four normal adult male subjects for small oscillations of the forearm about a mean position of 90 deg flexion. Two modes of oscillatory behavior are discussed: externally forced oscillations under constant muscle force and voluntary oscillations against an elastic resistance. The observed amplitude and phase relations are presented herein and are compared to the response predicted by a simple model for neuromuscular dynamics. It appears that the small amplitude frequency response of normal skeletal muscle in vivo can be represented by a second order model. The main muscle parameters of this model are a muscular stiffness K, two time constants τ1 and τ2 associated with contraction dynamics, and a time delay τ: typical values of these parameters at moderate contraction levels (approximately 20 percent of maximum voluntary effort) are K = 100 N · m/rad, τ1 and τ2 = 50 ms, and τ = 10 ms. Reflex feedback under forced-oscillation conditions was also examined and may be characterized by a gain parameter (ΔE/Δθ), the ratio of the surface EMG amplitude to the angular displacement of the forearm, and the phase by which the EMG leads muscle stretch. The reflex EMG is observed to lead muscle stretch at all frequencies between 1 Hz and 15 Hz. The muscle stiffness K and the reflex gain parameter (ΔE/Δθ) are approximately proportional to the average force of contraction.

scholarly journals Fabrication of Beltlike Fibers by Electrospinning

Polymers ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 1087 ◽  
Author(s):  
Yan-Qing Liu ◽  
Chun-Hui He ◽  
Xiao-Xia Li ◽  
Ji-Huan He
Keyword(s):  
Surface Tension ◽  
Polyethylene Glycol ◽  
Theoretical Analysis ◽  
Minimal Surface ◽  
Crystallite Size ◽  
Zro2 Nanoparticles ◽  
One Dimensional ◽  
Theoretical Predictions ◽  
Spinning Process ◽  
Moving Jet

Electrospinning is always used to fabricate one-dimensional nanofibers. Cylindrical fibers are formed during the spinning process due to the minimal-surface principle. However, when the moving jet has high rigidity, which can counteract the surface tension for a minimal surface, beltlike fibers can be obtained. Using the Hall–Petch effect, the rigidity of the moving jet can be greatly enhanced by adding nanoparticles. Polyethylene glycol with a nanometric crystallite size of 4 nm and ZrO2 nanoparticles are used as additives in the experiment, a theoretical analysis is carried out, and the theoretical predictions are verified experimentally.

Oscillations of a rigid sphere embedded in an infinite elastic solid

1967 ◽  
Vol 63 (4) ◽  
pp. 1189-1205 ◽  
Author(s):  
P. Chadwick ◽  
E. A. Trowbridge
Keyword(s):  
Elastic Solid ◽  
Forced Oscillations ◽  
Graphical Form ◽  
Rigid Sphere ◽  
Free Oscillations ◽  
Modes Of Vibration ◽  
Fixed Axis ◽  
Steady Oscillations ◽  
Angular Oscillations ◽  
Elastic Shear

AbstractA detailed study is made of angular oscillations of small amplitude about a fixed axis of a rigid sphere embedded in an infinite elastic solid. Three modes of vibration of the sphere are considered: steady oscillations arising from the application of a periodic torque; forced oscillations produced by an arbitrary time-dependent torque; and free oscillations excited by an impulsive torque. Due to the transfer of energy to the surrounding material by the radiation of an elastic shear wave, free oscillations of the sphere are damped, the principal parameter affecting the damping being the density contrast between the sphere and its surroundings. Illustrative numerical results, referring to steady and free oscillations of the sphere, are presented in graphical form.

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