Interaction between parallel polymer fibers insonificated by ultrasound of low/mild intensity: An analytical theory and experiments

Abstract

The purpose of this article is to develop a simple mathematical model to address some bioeffects which may be caused by a static attractive force between two long neighboring parallel thin fibers (for example, a pair of collagen bundles of connective tissue) when they are insonificated by a continuous (CW) traveling plane ultrasound (US) under the condition that the fiber length ( L) ≫ the distance between them ( h) and h ≪ the wavelength of US ( λ). The theory predicts that there is an attractive force between these fibers when they are exposed to the CW US with an intensity of a magnitude of 100 mW/cm 2. The relationship between the relative approaching velocity of the fibers and the acoustic pressure amplitude can be calculated using the theory. An experiment was performed to verify the theoretical predictions. A plastic test chamber (diameter × height = 6 mm × 3.5 mm) with a cap made of a sound-absorbing material and filled full with distilled water was placed on a microscope stage. A polymer fiber pair of 100 μm diameter ( d) and 4 mm length ( L) were immersed in water and aligned parallel in a plane which is normal to the US propagation direction. They floated at the central area of the chamber and h ⩽ 10 d. A 25 mm diameter, 1 MHz quartz crystal was used as an ultrasound source as well as the bottom of the test chamber. The quartz crystal was gold-coated on both sides, but a 5 mm diameter center was left transparent (electrode free) to enable optical observation via a microscope. The maximum acoustic intensity, I max, of the CW wave generated by the source was set at 300 mW/cm 2; the corresponding acoustic pressure amplitude was 100 kPa. The magnitude of the average approaching velocity of the fiber pair due to the attractive force was found in agreement with that predicted by the theory.