{'fraction_non_alphanumeric': 0.01833460656990069, 'fraction_numerical': 0.0, 'mean_word_length': 4.954545454545454, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Viscous drag effect in the flexural rigidity and cantilever stiffness of bio- and nano-filaments measured with the shooting-bead method.

The so-called shooting-bead method is a fast and easy experimental technique for evaluating cantilever stiffness and flexural rigidity of semiflexible to semirigid rodlike biological and nano-filaments based on the measurement of just two distances. In this paper we have derived the shooting-bead formula for cantilever stiffness and flexural rigidity taking into account the effects of the viscous drag force exerted on the filament itself. To this end, we have defined a key variable, called the filament energy-loss factor (or filament drag factor), which accounts for all the energy-loss effects. It has been shown that due to the logarithmic dependence of the filament energy-loss factor on the radius and the length of the filament, inclusion of this factor in the formula for the flexural rigidity has a very noticeable effect on the result even for very thin or long filaments. It has also been shown that the effect due to the consideration of filament energy-loss factor on calculation of the flexural rigidity increases with increasing the flexibility of the filament. We have also considered various sources of experimental error and estimated their effects.