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Numerical simulations were carried out using the Finite Element Method (FEM) to determine the frequency characteristics of mechanical vibration of diatom silica frustules under the conditions and at frequencies that are not readily accessible to experimental measurement. The results revealed the influence of the frustule morphology on the natural frequency spectra. The effect of frustule density, stiffness, dimensions, pore size, and wall thickness on the eigenfrequencies and the corresponding modal shapes were studied in detail. Diatom frustules have natural frequencies in the range between several MHz and tens of MHz that make them a promising candidate for future MEMS applications. Eigenfrequencies depend linearly on the speed of sound in the frustule wall and decrease parabolically with the diameter and the pore size to diameter ratio. Dimensional analysis allowed obtaining functional correlations that encapsulate the various dependencies in compact analytical form. The satisfactory nature of our calculations and correlations derived from them is confirmed through an agreement with the analytical solutions from the literature.

Highlights • Photoacoustic and fluorescence lifetime imaging of diatoms was demonstrated for the first time. • The photoacoustic signal of diatom algae is proportional to their concentration. • Chlorophyll a and c and possibly fucoxanthin are the likely sources of photoacoustic signal. • Chlorophyll a in diatoms shows a strong fluorescence signal. • Fluorescence lifetime of the diatom chromophores is in the range 0.5–2 ns., Photoacoustic and fluorescent methods are used intensely in biology and medicine. These approaches can also be used to investigate unicellular diatom algae that are extremely important for Earth’s ecology. They are enveloped within silica frustules (exoskeletons), which can be used in drug delivery systems. Here, we report for the first time the successful application of photoacoustic (PA) and fluorescent visualization of diatoms. Chlorophyll a and c and fucoxanthin were found likely to be responsible for the photoacoustic effect in diatoms. The PA signal was obtained from gel drops containing diatoms and was found to increase with the diatom concentration. The fluorescence lifetime of the diatom chromophores ranged from 0.5 to 2 ns. The dynamic light scattering, absorbance, and SEM characterization techniques were also applied. The results were considered in combination to elucidate the nature of the photoacoustic signal. Possible biotechnological applications are proposed for the remote photoacoustic monitoring of algae.