Thermal wave decay depth

The thermal wave decay depth, and hence the extent of saturation, may be reduced by increasing the modulation frequency, which is done by increasing the optical velocity of the interferometer. As the scan speed is increased, the situation changes from the condition where L > pp to one where L < pp and the relative intensities of the absorption bands becomes closer to their tme values. 

The second microscale heat transfer issue considered in this paper deals with short time scales and their influence on the dimensions required for good heat transfer. Many cryocoolers use oscillating flows and pressures with frequencies as high as about 70 Hz. Heat flow at such high frequencies can penetrate a medium only short distances, known as the thermal penetration depth temperature amplitude of a thermal wave decays as it travels within a medium. The distance at which the amplitude is 1/e of that at the surface is the thermal penetration depth, which is given by... 

The infrared absorption coefficient and thermal wave decay coefficients, a(v) and flj, respectively, determine the magnitude of the photoacoustic signal. The term ot( exp —[a( +fls]x in the expression for temperature oscillation leads to a linear PA signal dependence on infrared absorption when a( thermal wave decay length, L, although it is sometimes referred to as the sampling depth, penetration depth, or thermal diflusion depth. The sample layer extending a distance L beneath the surface contributes... 

The difference between the viscous depth and the thermal depth provides an answer to the observed differences between emulsions and solid particle dispersions. These parameters characterize the penetra tion of the shear wave and thermal wave, respectively, into the liquid. Particles oscillating in the sound wave generate these waves which damp in the particle vicinity. The characteristic distance for the shear wave amplitude to decay is the viscous depth 5y. The corresponding distance for the thermal wave is the thermal depth 5. The following expressions give these parameter values in dilute systems ... 

The photothermal signal is proportional to the sample s thermal expansion, to the absorbed energy per unit area t/abs> for short laser pulses to the duration of the thermal excitation in the sample. The sample s thermal expansion is proportional to its thickness z while is approximately proportional to z. Thus, the photothermal signal S should be proportional to the product of and z. The absorption by the sample will depend on the exponentially decaying evanescent electric field intensity. For thicknesses less than the depth of penetration of the evanescent wave d, the AFM-IR signal increases with an increase in sample thickness z. For nonabsorbing samples, the value of is given by the well-known equation ... 

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