This study was undertaken to determine the effectiveness of acetic acid iontophoresis in the treatment of heel pain. Thirty-five patients with chronic heel pain were treated with acetic acid iontophoresis over a 4-year period. Ninety-four percent of patients had complete or substantial relief of heel pain after an average of 5.7 sessions of acetic acid iontophoresis over an average period of 2.8 weeks. Heel pain levels were rated from 0 to 10, with 10 representing the most severe pain. Heel pain prior to iontophoresis treatment received an average rating of 7.5; by the end of therapy, the average rating had decreased to 1.8. At an average follow-up time of 27 months, heel pain levels averaged 0.64, indicating continued reduction in heel pain. Ninety-four percent of participants said that they would recommend acetic acid iontophoresis to someone with similar heel pain.
Purpose
The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure.
Design/methodology/approach
A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV).
Findings
The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model.
Originality/value
Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.
The present investigation is concerned with one dimensional problem in a homogeneous, isotropic thermoelastic medium with double porosity structure in the presence of Hall currents subjected to thermomechanical sources. A state space approach has been applied to investigate the problem. As an application of the approach, normal force and thermal source have been taken to illustrate the utility of the approach. The expressions for the components of normal stress, equilibrated stress and the temperature change are obtained in the frequency domain and computed numerically. A numerical simulation is prepared for these quantities. The effect of the Hartmann number is depicted graphically on the resulting quantities for a specific model. Some particular cases of interest are also deduced from the present investigation.
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