Biomedical subjects
Publications and source records attributed to Mark F Hamilton.
The dynamic response of an acoustically driven spherical bubble between parallel plates is investigated in the linear approximation. For the case of rigid plates, explicit expressions are provided for the resonance frequency and damping, and the importance of including compressibility of the liquid is discussed. For wide channels, approximate results are presented that account for finite acoustic impedance of the plates.
A model equation for the oscillation of a pressurized gas bubble in a nonlinear incompressible elastic medium [Emelianov et al., J. Acoust. Soc. Am. 115, 581 (2004)] is extended to include effects of surface tension, viscosity, weak compressibility, and confinement by an elastic shell. The significance of this work is that starting from first principles, the full nonlinearity of the incompressible elastic medium surrounding the bubble and forming its shell is taken into account. Measurements of equilibrium radius as a function of external pressure for a gas bubble in a tissue-like gel are also presented. A general approach to including hysteresis is also discussed.
A nonlinear model in the form of the Rayleigh-Plesset equation is developed for a gas bubble in an essentially incompressible elastic medium such as a tissue or rubberlike medium. Two constitutive laws for the elastic medium are considered: the Mooney potential, and Landau's expansion of the strain energy density. These two constitutive laws are compared at quadratic order to obtain a relation between their respective elastic constants. Attention is devoted to the relative importance of shear stress on the bubble dynamics, allowing for the equilibrium gas pressure in the bubble to differ substantially from the pressure at infinity. The model for the bubble motion is approximated to quadratic order to assess the importance of shear stress in the surrounding medium relative to that of the gas pressure in the bubble. Relations are derived for the value of the shear wave speed at which the two contributions are comparable, which provide an assessment of when shear stress in the surrounding medium must be taken into account when modeling bubble dynamics.
An analytic solution is derived for acoustic streaming generated by a standing wave in a viscous fluid that occupies a two-dimensional channel of arbitrary width. The main restriction is that the boundary layer thickness is a small fraction of the acoustic wavelength. Both the outer, Rayleigh streaming vortices and the inner, boundary layer vortices are accurately described. For wide channels and outside the boundary layer, the solution is in agreement with results obtained by others for Rayleigh streaming. As channel width is reduced, the inner vortices increase in size relative to the Rayleigh vortices. For channel widths less than about 10 times the boundary layer thickness, the Rayleigh vortices disappear and only the inner vortices exist. The obtained solution is compared with those derived by Rayleigh, Westervelt, Nyborg, and Zarembo.
Acoustic streaming generated by standing waves in channels of arbitrary width is investigated analytically. In a previous paper by the authors [J. Acoust. Soc. Am. 113, 153-160 (2003)], a purely viscous fluid in a two-dimensional channel was considered. That analysis is extended here to a gas in which heat conduction and dependence of the viscosity on temperature are taken into account. Calculations are presented for typical working gases used in thermoacoustic engines at standard temperature and pressure. In channels that are very wide in comparison with the viscous penetration depth, which is the Rayleigh streaming regime, the influence of the two thermal effects is comparable but small. The same is true in very narrow channels, having widths on the order of the viscous penetration depth. In channels having intermediate widths, 10-20 times the viscous penetration depth, the effect of heat conduction can be substantial. The analysis is performed for cylindrical tubes as well as two-dimensional channels, and the results are found to be qualitatively the same.
Sonic boom propagation can be affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. Turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometrical acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results from numerical experiments that simulate the propagation of spark-produced N waves through turbulence are presented. It is observed that turbulence decreases, on average, the peak pressure of the N waves and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The effects of random vector fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wave front are also presented. These observations confirm the results from the model experiment in which spark-produced N waves are used to simulate sonic boom propagation through a turbulent atmosphere.
A two-dimensional model and efficient solution algorithm are developed for studying nonlinear effects in thermoacoustic engines. There is no restriction on the length or location of the stack, and the cross-sectional area of the resonator may vary with position along its axis. Reduced model equations are obtained by ordering spatial derivatives in terms of rapid variations across the pores in the stack, versus slow variations along the resonator axis. High efficiency is achieved with the solution algorithm because the stability condition for numerical integration of the model equations is connected with resonator length rather than pore diameter. Computation time is reduced accordingly, by several orders of magnitude, without sacrificing spatial resolution. The solution algorithm is described in detail, and the results are verified by comparison with established linear theory. Two examples of nonlinear effects are investigated briefly, the onset of instability through to saturation and steady state, and nonlinear waveform distortion as a function of resonator shape.