Porodynamics

Wave propagation in porous materials has many applications in geophysics, the energy industry, mining engineering, acoustics, military engineering, and even medical technology. Seismic waves have long been used to map geological formations, for geo-prospecting, and for other geophysical purposes. Historically, the concept of seismicity has been based on elastic wave propagation and jointed rock masses with interfacial frictions. The hydrodynamics of the fluid in the pores was typically ignored. Of late, the focus on the mechanical interaction of solid and fluid has not only refined the science, but also allowed new applications such as the real-time monitoring of oil and gas recovery, geothermal reservoir operations, $\mathrm{C}{\mathrm{O}}_2$ sequestration, and secure deposition of chemical and nuclear wastes.

The founding of the dynamic theory of fluid infiltrated porous materials has been attributed to Maurice A. Biot in his pair of seminal papers in 1956 in the J. Acoust. Soc. Am.. In these papers, he theoretically predicted the presence of a second type of compressional wave, also called the Biot slow wave. (Laboratory confirmation of such a wave came much later; see Smeulders in this issue.) He also provided the hydrodynamic theory that predicted the wave dispersion and attenuation, and the relaxation phenomenon.

A less-known fact, however, is that the second wave was first theoretically predicted by the Russian physicist Yacov Il’ich Frenkel (also known as Jacob Frenkel) in his 1944 article “On the theory of seismic and seismoelectric phenomena in a moist soil” (republished in this issue). Indeed, Biot cited this paper in his articles and it appeared to be what motivated Biot to embark on his own, but more thorough, construction of the theory.

Frenkel predicted not only the second type of wave, but also the seismoelectric phenomenon (see Pride and Garambois, this issue). The presence of electrolytes in the fluid and the relative movement between the solid and fluid phases induced by seismic motion can generate small local electrical currents, which in turn emit electromagnetic waves. One can imagine an acoustic wave sent through the human body saturated with fluid that is rich in electrolytes. While the acoustic waves tell of the mechanical properties of the tissue for medial imaging purposes, the emitted electromagnetic waves can be associated with abnormal chemical activities.

Frenkel was a great Russian physicist who spent a large portion of his professional life in the troubled times of war and revolution in Russia (see the biography by Lopatnikov and Cheng, this issue), during which times he made amazing contributions to science, including electrodynamics, theory of liquid, the drop model of the atom, the exciton, Frenkel defects in crystalline structure, and quantum theory of electroconductivity of metals. As early as 1929, he envisioned the quantum tunneling effect. Geophysics was his side interest, but he also made indelible contributions.

While to the Western world Frenkel’s work on porous media remains largely unknown, in Russia, he was honored as the founder of the mechanics of porous materials. The Biot theory known to the West has been the Biot–Frenkel theory in Russia (see the review article by Nikolaevskiy, this issue).

In this issue, we have assembled a panel of international experts to contribute review as well as cutting-edge research articles on dynamics of porous materials (porodynamics) to honor Ya. Frenkel, who would have been 111 years old in February of 2005.