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Numerical analysis of common assumptions in acoustofluidics
In the theoretical framework of acoustofluidics we find an extensive use of assumptions. The aim of the project is to estimate the range of validity for some common assumptions, using the numerical analysis.
Keywords: Acoustofluidics, assumptions, numerical analysis, FEM
In the theoretical framework of acoustofluidics we find an extensive use of assumptions. These often lead to elegant solutions and are a valuable tool for theoreticians, as well as for those who apply the theory to practical problems.
One of the most common assumptions is an inviscid fluid, which simplifies the Navier-Stokes equations to the Euler equations [1]. The problems are then usually treated as adiabatic and isothermal, which leads to the dismissal of the energy equation [2]. Another common assumption is the incompressibility of the fluid flow, which simplifies the equation of continuity [2]. Very often, the perturbation technique is applied in derivations, implying conditions that are usually not discussed. Friend and Yeo [3] give further common assumptions and the history behind.
References:
[1] Landau, L. D., & Lifsic, E. M. (1987). 6: Fluid Mechanics. Butterworth-Heinemann.
[2] Blackstock, D. T. (2001). Fundamentals of physical acoustics.
[3] Friend, J., & Yeo, L. Y. (2011). Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics. Reviews of Modern Physics, 83(2), 647.
[4] Rednikov, A. Y., & Sadhal, S. S. (2011). Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples. Journal of fluid mechanics, 667, 426-462.
In the theoretical framework of acoustofluidics we find an extensive use of assumptions. These often lead to elegant solutions and are a valuable tool for theoreticians, as well as for those who apply the theory to practical problems. One of the most common assumptions is an inviscid fluid, which simplifies the Navier-Stokes equations to the Euler equations [1]. The problems are then usually treated as adiabatic and isothermal, which leads to the dismissal of the energy equation [2]. Another common assumption is the incompressibility of the fluid flow, which simplifies the equation of continuity [2]. Very often, the perturbation technique is applied in derivations, implying conditions that are usually not discussed. Friend and Yeo [3] give further common assumptions and the history behind.
References: [1] Landau, L. D., & Lifsic, E. M. (1987). 6: Fluid Mechanics. Butterworth-Heinemann. [2] Blackstock, D. T. (2001). Fundamentals of physical acoustics. [3] Friend, J., & Yeo, L. Y. (2011). Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics. Reviews of Modern Physics, 83(2), 647. [4] Rednikov, A. Y., & Sadhal, S. S. (2011). Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples. Journal of fluid mechanics, 667, 426-462.
Many assumptions are of very general nature, and their validity is not established explicitly, even when the theory is applied to a practical case. In the course of this project, some of the common assumptions will be analysed, together with the range of their applicability and validity. The main tool for the investigation will be the finite element method framework COMSOL. The study could serve as a tangible guideline for researchers in the field of acoustofluidics, and improve the understanding of limitations of theoretical solutions appearing in the field.
Many assumptions are of very general nature, and their validity is not established explicitly, even when the theory is applied to a practical case. In the course of this project, some of the common assumptions will be analysed, together with the range of their applicability and validity. The main tool for the investigation will be the finite element method framework COMSOL. The study could serve as a tangible guideline for researchers in the field of acoustofluidics, and improve the understanding of limitations of theoretical solutions appearing in the field.