Publisher Summary This chapter discusses the fluid dynamics and science of magnetic liquids. Fluid media composed of solid magnetic particles of subdomain size colloidally dispersed in a liquid carrier are the basis for the highly stable, strongly magnetizable liquids known as magnetic fluids or ferrofluids. The number density of particles in suspension is in the order of lO23/m3. It is the existence of these synthetic materials that makes the study of magnetic liquid fluid dynamics (ferrohydrodynamics) possible. There are two broad ways to make a magnetic fluid: size reduction of coarse material and chemical precipitation of small particles. Size reduction has been done by spark evaporation–condensation, electrolysis, and grinding. Chemical routes include decomposition of metal carbonyls and precipitation from salt solutions. The fluid dynamics of magnetic fluids differ from that of ordinary fluids in that stresses of magnetic origin appear and, unlike in magnetohydrodynamics, there need not be electrical currents. Magnetic fluid pushes the nonmagnetic fluid in the presence of tangential applied field. The fluid motion is normal to the interfacial boundary between the two fluids.

Fluid Dynamics and Science of Magnetic Liquids

Reversible, field induced agglomeration in magnetic colloids☆

Power Limitations of Sonic Transducers

Research on the rheological properties of a perfluoropolyether based ferrofluid

When a high-speed railway train enters a tunnel, a compression wave is generated ahead of the train and propagates along the tunnel. The attenuation and distortion of the compression wave were measured in three Shinkansen tunnels and the results were compared with the numerical values calculated using a second-order TVD scheme. The strength of a compression wave is exponentically attenuated with distance as it propagates along the tunnel in both slab and ballast track tunnels, and the attenuation in the ballast track tunnel is considerably larger than that in the slab track tunnel. In the slab track tunnel, the compression wave is steepened as it propagates, while it spreads in the ballast track tunnel. The criterion for judgment whether the compression wave is steepend or spreads is expressed by the value of acoustic Reynolds number of about 10∼15.

Attenuation and Distortion of a Compression Wave Propagating in a High-Speed Railway Tunnel.

A new technique recently used for solution of the plane‐wave Burgers' equation in a lossless medium has led to the development of an approximate analytical solution to Burgers' equation with dissipation for plane, cylindrical, and spherical sinusoidal waves. The solution is valid for the initial propagation zone prior to sawtooth formation for Gol'dberg numbers larger than 5 as indicated by comparison with a previous numerical solution of Burgers' equation for a plane wave. The approximate solution is expressed as a series that converges rapidly enough to permit calculations of harmonic levels by hand. For more viscous cases, where the approximate solution fails, the above technique leads easily to a numerical solution of Burgers' equation. By comparing the harmonic levels predicted by the numerical solution with empirical data taken on distorting spherical waves, it is concluded that numerical results tend to be below the measured values. It is felt that the numerical method can be of use in predicting distortion levels for practical underwater systems that exploit finite‐amplitude effects.

Prediction of Finite-Amplitude Waveform Distortion with Dissipation and Spreading Loss

An assessment of the suitability of ferrofluids for acoustic transducer and receiver applications has led to the following conclusions: First, the magnetostrictive mode of operation is not efficient enough to offer an alternative to conventional solid materials in use. Second, the piston motion of the ferrofluid induced by an applied field gradient does provide a real alternative to conventional magnetostrictive transducers. For an applied static field of 4000 Oe and a field gradient of 1000 Oe/cm, it is possible to achieve an overall efficiency that is greater than that for the ferromagnetic solids. Third, ferrofluids appear to provide a desirable alternative for pressure‐sensing applications in severe environments (e.g., detonations) where piezoelectric and pyroelectric materials suffer fatigue and failure. Fourth, ferrofluids offer the prospect of obtaining broadband frequency response when radiating or receiving in liquid media.

On the Utilization of Ferrofluids for Transducer Applications

Burgers' equation is a nonlinear acoustical wave equation which approximately governs the propagation of finite‐amplitude waves with dissipation and spreading losses. A new solution is derived for a spherically diverging sinusoidal waveform. By means of this solution, the amplitudes of the harmonic levels above the third can be more readily estimated than by successive approximation.

Modification of the Bessel‐Fubini Solution That Includes Attenuation

From Naugol'nykh's spherical sawtooth‐wave solution, curves are constructed which predict the nonlinear induced extra loss in fundamental amplitude. As in the plane wave case, the propagation path can be split into three zones. In the first zone, nonlinear effects dominate over attenuation. In the second zone, a stable distorted waveform is propagated. In the third zone, attenuation reduces the amplitude so that nonlinear effects are no longer important. Although the predicted losses are smaller than in the plane wave case, they are not negligible. A criterion for cavitation is used in order to define depths in the ocean where cavitation will be the limiting factor on sound power level and not extra losses. By considering a specific example, it is concluded that cavitation will indeed be the limiting factor down to a depth of about 2000 ft. At depths below 2000 ft, extra losses can become significant for propagation from steady‐state spherical sources operating below the cavitation threshold.

Boyd B. Cary

Papers

Prediction of Finite-Amplitude Waveform Distortion with Dissipation and Spreading Loss

On the Utilization of Ferrofluids for Transducer Applications

Modification of the Bessel‐Fubini Solution That Includes Attenuation

Nonlinear Losses Induced in Spherical Waves

Errata: “Modification of the Bessel‐Fubini Solution Which Includes Attenuation” [B. Cary, J. Acoust. Soc. Amer. 49, 1687–1688 (L) (1971)]