Analysis of nano droplet dynamics with various sphericities using efficient computational techniques

Zolfagharian, Ali; Darzi, Milad; Ghasemi, S. E.

doi:10.1007/s11771-017-3647-x

Cited by 9 publications

(5 citation statements)

References 32 publications

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“…From the expression for u(t), the corresponding acceleration and fall distance are obtained by direct derivation and integration, respectively. In particular, in the case of non-spherical particles, the provided closed analytical functions are simple and generalize the approximate analytical solutions obtained by some authors [30][31][32][33] using different sound analytical techniques. It is to be remarked that such approximate expressions are written as a power series and that for obtaining an accurate estimation of particle settling velocity, many terms are needed, whose number cannot be established beforehand.…”

Section: Discussionsupporting

confidence: 69%

“…The functional form of Equation ( 5) is the same as Equation ( 4), where the parameter α is a function of particle sphericity. It has the advantage of not including additional nonlinearities in the drag coefficient, and it has been used in previous works dealing with non-spherical particles [30][31][32][33]; therefore, Equation (5) will be applied in this work to obtain closed analytical solutions of the particle motion equation, Equation (3). Now, plugging the expression of Equation ( 4) in Equation ( 3), it is obtained:…”

Section: Problem Statement and Development Of The Closed Analytical S...mentioning

confidence: 99%

“…Regarding non-spherical particles, the studies dealing with analytical approaches to solve the BBO (Basset-Boussinesq-Ossen) equation usually employ the Chien drag law [29], which depends on particle sphericity [30][31][32][33]. Sphericity is defined as the quotient of the superficial area of the spherical particle which has the same volume as the real particle and the surface area of that particle [34].…”

Section: Introductionmentioning

confidence: 99%

“…The resulting analytical expression, built using a different number of terms in the series, compared favorably with numerical solutions based on Runge-Kutta methods. In [33], HPM combined with Padé approximants was applied to investigate the falling motion of nano-droplets in quiescent viscous media with an initial velocity and compared their results with those obtained by VIM and numerical solutions, showing good agreement. All the mentioned methods provide analytical approximations to the solutions, which are either fairly complex or excessively extensive and not well suited to be implemented for design and control processes [25].…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solutions of the Riccati Differential Equation: Particle Deposition in a Viscous Stagnant Fluid

2023

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In this communication, the solution of the differential Riccati equation is shown to provide a closed analytical expression for the transient settling velocity of arbitrary non-spherical particles in a still, unbounded viscous fluid. Such a solution is verified against the numerical results of the integrated differential equation, establishing its accuracy, and validated against previous experimental, theoretical and numerical studies, illustrating the effect of particle sphericity. The developed closed analytical formulae are simple and applicable to general initial velocity conditions in the Stokes, transitional and Newtonian regimes, extending the range of application of former published analytical approximate solutions on this subject.

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Section: Discussionsupporting

confidence: 69%

Section: Problem Statement and Development Of The Closed Analytical S...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical Solutions of the Riccati Differential Equation: Particle Deposition in a Viscous Stagnant Fluid

2023

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“…As a result, modelling and analysis of pull-in characteristics in the micro-scale have found significant industrial applications. However, as the pull-in instability restricts the operational range of tiny devices, obtaining system characteristics becomes important in numerous micro/nano-structures [1][2][3][4][5][6][7][8][9][10][11] .…”

mentioning

confidence: 99%

Nonlinear dynamic stability of piezoelectric thermoelastic electromechanical resonators

SoltanRezaee

Bodaghi

2020

Sci Rep

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this research work deals with analyzing instability and nonlinear behaviors of piezoelectric thermal nano-bridges. An adjustable thermo-elastic model with the ability to control stability conditions is developed to examine the system behavior at different temperatures. To increase the performance range and improve system characteristics, a piezovoltage is applied and a spring is connected to the sliding end of the deformable beam as design parameters. The partial differential equations (PDEs) are derived using the extended Hamilton's principle and Galerkin decomposition is implemented to discretize the nonlinear equations, which are solved via a computational method called the step-bystep linearization method (SSLM). To improve the accuracy of the solution, the number of mode shapes and the size of voltage increments are analyzed and sufficient values are employed in the solution. The validity of the formulation and solution method is verified with experimental, analytical, and numerical data for several cases. finally, the vibration and eigenvalue problem of the actuated nanomanipulator subjected to electrostatic and casimir attractions are investigated. it is concluded that the fringing-fields correction changes the system frequency, static equilibrium, and pull-in characteristics significantly. The results are expected to be instrumental in the analysis, design, and operation of numerous adjustable advanced nano-systems.should be taken into account because this consideration improves the prediction of the critical voltage for the snap-through, and the overall behavior of arch nano-systems. Moreover, the experimental validation demonstrates that the fringing correction in nano-devices acts a key role that should be considered in the modelling.Thermal sensitive nano-electromechanical manipulators have numerous industrial applications. Rokni and Lu 26 studied the behavior of fully-clamped multi-layer nano-ribbons subjected to electric and Casimir forces at different temperatures without considering the size parameter. The stability of fully-clamped miniature beams under thermal, molecular and electromechanical effects was examined 27 without modelling the surface energy. The static pull-in instability of a thermal nano-cantilever piezowire under vdW attraction was examined by SoltanRezaee and Ghazavi 28 while the frequency analysis and investigation of different electric fringing-fields corrections were not carried out. Pradiptya and Ouakad 29 investigated the size-dependent dynamic response of fixed-fixed carbon nano-tubes subjected to DC and AC fields by considering thermal effects using SGT. The impacts of Poisson's ratio on structural behaviors of a nano-wire by considering high-temperature variations were studied using CST 30 . Recently, Tavakolian et al. 31 analyzed the dynamic stability of size-dependent nano-cantilevers under electro-thermal actuation without taking the surface layer effects into account. It is worth noting that the pull-in parameters of clamped-clamped smart MEMS were extensively studied...

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Effect of variable liquid properties on peristaltic transport of Rabinowitsch liquid in convectively heated complaint porous channel

Vaidya¹,

Rajashekhar

Manjunatha

et al. 2019

J. Cent. South Univ.

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Analysis of nano droplet dynamics with various sphericities using efficient computational techniques

Cited by 9 publications

References 32 publications

Analytical Solutions of the Riccati Differential Equation: Particle Deposition in a Viscous Stagnant Fluid

Analytical Solutions of the Riccati Differential Equation: Particle Deposition in a Viscous Stagnant Fluid

Nonlinear dynamic stability of piezoelectric thermoelastic electromechanical resonators

Effect of variable liquid properties on peristaltic transport of Rabinowitsch liquid in convectively heated complaint porous channel

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