The friction coefficient and diffusion of sub-micro particles straddling a monolayer

As the rheological measurement probe of bio-membrane and drug delivery carrier, it is of great scientific significance to study the fluid mechanics resistance and diffusion behavior of particles straddling a monolayer. Existing research focuses primarily on the friction of a disk-like cylinder embedded in a monolayer to simulate a singe lipid or protein molecule, which is a two-dimensional problem. Spherical particles protrude through the monolayer and reach the water subphase, resulting in more complex forces. According to resent research, when micro-sized particles diffuse on the air-water interface, the friction coefficient includes an extra component of the surface tension force induced by interface fluctuations resulting from the molecular thermal motion. This study discovered a similar phenomenon in the diffusion of sub-micro particles across the bio-monolayer interface. We modify the surface tension in the calculation of the friction coefficient by taking into account the different mechanical properties between the monolayer and the water interface, as well as the sub-micro scale. First, the surface tension includes a Maxwell term to account monolayer's viscoelasticity. Second, the surface tension includes the wave number term of thermal capillary waves to distinguish it from the macroscopic surface tension. It is discovered that the wave length fitted using the experimental friction coefficient is nearly equal to the average distance between the lipid molecules in the monolayer, confirming the theoretical descriptions of the interfacial thermal fluctuations. Furthermore, when the particles adhere to the condensed lipid domains within the monolayer, the resistance of the entire assembly is almost entirely derived from the condensed domains. The resistance force induced by water on the protruding particle or the force induced by the monolayer on the contact line are both negligible.