Florian J. Blonigen

Stabilization of electrically conducting capillary bridges using feedback control of radial electrostatic stresses and the shapes of extended bridges

Electrically conducting, cylindrical liquid bridges in a density-matched, electrically insulating bath were stabilized beyond the Rayleigh–Plateau (RP) limit using electrostatic stresses applied by concentric ring electrodes. A circular liquid cylinder of length L and radius R in real or simulated zero gravity becomes unstable when the slenderness S=L/2R exceeds π. The initial instability involves the growth of the so-called (2, 0) mode of the bridge in which one side becomes thin and the other side rotund. A mode-sensing optical system detects the growth of the (2, 0) mode and an analog feedback system applies the appropriate voltages to a pair of concentric ring electrodes positioned near the ends of the bridge in order to counter the growth of the (2, 0) mode and prevent breakup of the bridge. The conducting bridge is formed between metal disks which are grounded. Three feedback algorithms were tested and each found capable of stabilizing a bridge well beyond the RP limit. All three algorithms stabiliz...

Leaky helical flexural wave backscattering contributions from tilted cylindrical shells in water: Observations and modeling

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)], flexural helical waves on cylindrical shells can significantly enhance the backscattering. These contributions are compared and modeled here for an empty cylinder. Experiments using tone bursts were performed on a tilted stainless steel shell to investigate the contributions caused by flexural leaky Lamb waves above the coincidence frequency of the shell. In some of the measurements the tone bursts were of sufficient duration to superpose helical wave contributions of successive circumnavigations, along with the meridional contribution near the critical tilt, to arrive at a quasi-steady-state backscattering amplitude for the cylinder. These measurements are compared with an approximate numerical partial-wave series solution and a ray theory as a function of the tilt angle. The data for ka = 20 follow the basic shape of the ray theory and the relevant features of the partial-wave model. They illustrate the importance of the interference of successive helical wave contributions. Measurements (also as a function of the tilt angle) using tone bursts that were sufficiently short to separate the earliest helical wave contribution from later contributions also support the ray theory.

Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: Observations and theory

Bulk shear and longitudinal waves give rise to important contributions to the scattering of ultrasound by tilted finite plastic and rubber cylinders in water. This occurs in situations where either the shear or longitudinal speed is less than the speed of sound in the surrounding water. At a certain critical tilt angle, large backscattering enhancements are observed for finite cylinders, where the wave vector can reverse direction upon reflection from the cylinder truncation. The scattering process is analogous to the enhancement produced by the merging of rainbow caustics of primary rainbow rays in the scattering of light by long dielectric cylinders, also known as the caustic merging transition [C. M. Mount, D. B. Thiessen, and P. L. Marston, Appl. Opt. 37, 1534-1539 (1998)]. A ray theory was developed to model the backscattering mechanism at the critical tilt angle. It employs the idea of the Bravais effective refractive index, convenient for constructing ray diagrams for the projections of rays in the base plane of the cylinder. There is general agreement between the theory and the experiment down to relatively low ultrasonic frequencies (ka as small as 10). The enhancement is the most significant backscattering contribution for a wide range of tilt angles.

Leaky helical flexural wave scattering contributions from tilted cylindrical shells: Ray theory and wave-vector anisotropy

At sufficiently high frequencies, cylindrical shells support a wave whose properties are analogous to those of the lowest antisymmetric Lamb wave on plates. When the shell is in water and the frequency exceeds the coincidence frequency, the flexural wave is a leaky wave that can be a major contributor to the scattering by tilted shells [G. Kaduchak, C. M. Wassmuth, and C. M. Loeffler, J. Acoust. Soc. Am. 100, 64-71 (1996)]. While the meridional ray-scattering contributions for such leaky flexural waves were previously modeled, the helical contribution can also be significant. A ray theory for those contributions is compared with the exact partial wave series (PWS) solution for infinitely long empty shells. The agreement between the ray theory and the PWS is only possible when a weak anisotropy of the flexural wave parameters is included in the evaluation of the ray theory. The anisotropy is determined numerically from the roots of a denominator in the PWS because approximations for the anisotropy from thin-shell mechanics are not applicable significantly above the coincidence frequency.

Leaky helical flexural wave backscattering contributions from tilted water-filled cylindrical shells.

Helical flexural waves on a bluntly truncated tilted water-filled cylindrical steel shell in water are found to give large contributions to the backscattering above the coincidence frequency. The presence of the water inside the shell increases the damping of the leaky wave when short tone bursts are used. The magnitude of the scattering is found by modifying a ray analysis developed for empty shells. When longer bursts are used, some of the internally radiated energy (corresponding to the case of one internal chord) is superposed on the ordinary helical ray backscattering. This occurs as a consequence of the internal excitation of helical rays.

Ultrasonic Backscattering Enhancements for Truncated Objects in Water: Quantitative Models, Tests and Special Cases

This survey is concerned with the scattering of sound in water by objects whose size significantly exceeds the acoustic wavelength. Diffraction from the edges of the object can be important for regions where reflected contributions are weak. Elastic contributions to the scattering, however, can be much larger in magnitude for certain viewing angles than simple edge diffraction. Such elastic contributions can greatly enhance the visibility of truncated cylinders imaged with a sonar [1]. For situations where the dominant elastic contributions are the result of leaky waves excited on truncated objects, an approximation method has been developed [2, 3]. Leaky waves have phase velocities that exceed the speed of sound in water. Examples include Rayleigh waves on metallic objects, the symmetric generalization of Lamb waves on plates and shells, and (at sufficiently high frequencies) the lowest antisymmetric generalization of a Lamb wave. This type of scattering enhancement has been measured by us for metallic tilted bluntly truncated cylinders [4, 5, 6] and cubes [7] and glass disks. For most of these examples, the leaky wave is significantly attenuated upon traveling the length of the scatterer. As a consequence of that damping, the quality factor Q is small for the global modes associated with the reverberations of the leaky waves between truncations on the object.

Backscattering from empty and water‐filled tilted cylindrical shells due to leaky helical flexural waves: Comparison and ray theory

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785–794 (1998)], helical rays on empty and water‐filled steel shells can significantly enhance the backscattering. These contributions are compared and modeled in the present work. Such contributions in the water‐filled case are found to be weaker in amplitude, which is to be expected since additional energy is lost through radiation leaked to the inner fluid. A modified ray theory taking into account the increased radiation damping was compared with experimental results for the earliest helical wave arrival, yielding satisfactory agreement. However, the energy lost to the interior of the shell may be at least partially recovered, as internal rays can excite additional leaky waves on the shell. Contributions from rays with one internal chord inside the cylinder were superposed with those of the first helical wave, and the resulting backscattering amplitude was nearly tha...

Scattering by tilted cylindrical shells in water above the coincidence frequency

Experimental, theoretical, and computational results indicate that flexural waves on bluntly truncated tilted cylindrical steel shells are a major contributor to the backscattering of sound at high frequencies over a wide range of tilt angles. Important contributions are associated with meridional rays and with helical rays [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785–794 (1998); S. F. Morse and P. L. Marston, J. Acoust. Soc. Am. 106, 2595–2600 (1999); S. F. Morse and P. L. Marston, IEEE J. Ocean. Eng. 26, 152–155 (2001)]. Successful development of a ray model for helical ray scattering contributions required the computation (at high frequencies) of the anisotropy of the flexural‐wave velocity and radiation‐damping parameters [F. J. Blonigen and P. L. Marston, J. Acoust. Soc. Am. (accepted for publication)]. In backscattering experiments with short and long tone bursts, the associated meridional and helical ray contributions are typically much larger than the scattering estimated for diffraction by a...

Backscattering by tilted cylindrical shells above the coincidence frequency caused by helical flexural waves

Generalized leaky Lamb waves excited by ultrasound incident on cylindrical shells in water produce important backscattering effects. At a certain critical tilt angle, leaky waves launched along the meridian of the cylinder have been shown to lead to large backscattering enhancements [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785–794 (1998)]. At angles less than the critical tilt, these leaky waves follow helical paths and also make significant contributions. In the present work, experiments using tone bursts were performed on a stainless steel shell to investigate the contributions of a0 leaky Lamb modes. The tone bursts were of sufficient duration to superpose helical wave bursts of successive circumnavigations, along with the meridional contribution near the critical tilt, to arrive at a steady state backscattering amplitude for the cylinder. This was compared against an approximate numerical partial wave series solution and a ray theory solution as a function of the tilt angle. The data follow the b...

Backscattering enhancements of ultrasound by tilted solid plastic cylinders in water due to the caustic merging transition: High angular resolution scans

Bulk shear and longitudinal waves can make important contributions to the scattering of ultrasound by tilted finite plastic and rubber cylinders in water when the phase velocity of the wave is less than the speed of sound of the surrounding fluid. At a certain critical tilt angle, a backscattering enhancement is observed as a result of merging rainbow caustics associated with bulk transmitted rays internally reflected off the cylinder truncation [F. J. Blonigen and P. L. Marston, J. Acoust. Soc. Am. 107 (2000)]. The backscattering away from this angle is otherwise weak. The critical angle is calculated using the Bravais effective refractive index for the projections of rays on the base plane of the cylinder. New ultrasonic observations are reported for a polystyrene cylinder over a wide range of tilt angles at high angular resolution. The backscattering amplitude angle scan takes on the shape of a Pearcey function with the peak amplitude offset from the critical angle. Backscattering amplitudes at the cri...