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.