scholarly journals Two-dimensional numerical simulations of nonlinear acoustic streaming in standing waves

Wave Motion ◽  
2013 ◽  
Vol 50 (5) ◽  
pp. 955-963 ◽  
Author(s):  
Virginie Daru ◽  
Diana Baltean-Carlès ◽  
Catherine Weisman ◽  
Philippe Debesse ◽  
Gurunath Gandikota
Keyword(s):  
Numerical Simulations ◽  
Acoustic Streaming ◽  
Standing Waves ◽  
Two Dimensional ◽  
Nonlinear Acoustic

Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary width

2003 ◽  
Vol 113 (1) ◽  
pp. 153-160 ◽  
Author(s):  
Mark F. Hamilton ◽  
Yurii A. Ilinskii ◽  
Evgenia A. Zabolotskaya
Keyword(s):  
Acoustic Streaming ◽  
Standing Waves ◽  
Two Dimensional

Acoustic streaming in Maxwell fluids generated by standing waves in two-dimensional microchannels

2022 ◽  
Vol 933 ◽  
Author(s):  
C. Vargas ◽  
I. Campos-Silva ◽  
F. Méndez ◽  
J. Arcos ◽  
O. Bautista
Keyword(s):  
Acoustic Streaming ◽  
Oscillation Amplitude ◽  
Standing Waves ◽  
Deborah Number ◽  
Two Dimensional ◽  
Regular Perturbation ◽  
Viscous Boundary Layer ◽  
Hydrodynamic Behaviour ◽  
High Dependency ◽  
Maxwell Fluids

In this work, a semianalytic solution for the acoustic streaming phenomenon, generated by standing waves in Maxwell fluids through a two-dimensional microchannel (resonator), is derived. The mathematical model is non-dimensionalized and several dimensionless parameters that characterize the phenomenon arise: the ratio between the oscillation amplitude of the resonator and the half-wavelength ( $\eta =2A/\lambda _{a}$ ); the product of the fluid relaxation time times the angular frequency known as the Deborah number ( $De=\lambda _{1}\omega$ ); the aspect ratio between the microchannel height and the wavelength ( $\epsilon =2 H_{0}/\lambda _{a}$ ); and the ratio between half the height of the microchannel and the thickness of the viscous boundary layer ( $\alpha =H_{0}/\delta _{\nu }$ ). In the limit when $\eta \ll 1$ , we obtain the hydrodynamic behaviour of the system using a regular perturbation method. In the present work, we show that the acoustic streaming speed is proportional to $\alpha ^{2.65}De^{1.9}$ , and the acoustic pressure varies as $\alpha ^{6/5}De^{1/2}$ . Also, we have found that the growth of inner vortex is due to convective terms in the Maxwell rheological equation. Furthermore, the velocity antinodes show a high dependency on the Deborah number, highlighting the fluid's viscoelastic properties and the appearance of resonance points. Due to the limitations of perturbation methods, we will only analyse narrow microchannels.

scholarly journals Towards explicit regulating-ion-transport: nanochannels with only function-elements at outer-surface

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qun Ma ◽  
Yu Li ◽  
Rongsheng Wang ◽  
Hongquan Xu ◽  
Qiujiao Du ◽  
...  
Keyword(s):  
Ion Transport ◽  
Numerical Simulations ◽  
Power Density ◽  
Outer Surface ◽  
Internal Resistance ◽  
Porous Membranes ◽  
Two Dimensional ◽  
Ionic Selectivity ◽  
Key Features ◽  
Energy Conversion Devices

AbstractFunction elements (FE) are vital components of nanochannel-systems for artificially regulating ion transport. Conventionally, the FE at inner wall (FEIW) of nanochannel−systems are of concern owing to their recognized effect on the compression of ionic passageways. However, their properties are inexplicit or generally presumed from the properties of the FE at outer surface (FEOS), which will bring potential errors. Here, we show that the FEOS independently regulate ion transport in a nanochannel−system without FEIW. The numerical simulations, assigned the measured parameters of FEOS to the Poisson and Nernst-Planck (PNP) equations, are well fitted with the experiments, indicating the generally explicit regulating-ion-transport accomplished by FEOS without FEIW. Meanwhile, the FEOS fulfill the key features of the pervious nanochannel systems on regulating-ion-transport in osmotic energy conversion devices and biosensors, and show advantages to (1) promote power density through concentrating FE at outer surface, bringing increase of ionic selectivity but no obvious change in internal resistance; (2) accommodate probes or targets with size beyond the diameter of nanochannels. Nanochannel-systems with only FEOS of explicit properties provide a quantitative platform for studying substrate transport phenomena through nanoconfined space, including nanopores, nanochannels, nanopipettes, porous membranes and two-dimensional channels.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

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