Effect of Surface Waves and Mucus Viscoelasticity in the Modelling of Shear-Induced Aerosol Generation in the Human Respiratory System
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Respiratory aerosol is generated in the airways among others by shear induced stripping of particles from the mucus. One approach to model the number and size distribution of stripped particles is a combination of a Eulerian Wall Film (EWF) to model the generation of particles with a Discrete Phase Model (DPM) to compute the trajectory of the stripped particles. However, the EWF model lacks two main aspects which are necessary for representing shear-induced aerosol generation. Firstly, the local thickness of the film is only modelled as a property of the surface with no impact on the flow. Thus, the formation of surface waves and their effect on the local wall shear stress is neglected. However, as we found in experimental analyses, surface waves occur in mucus mimetics exposed to shear flow, which induced wall shear stresses in an equivalent range to those occurring in the human body during breathing. In first computational analyses we represented these wave structures with generic surfaces with superimposed symmetrical, sinusoidal waves. These generic waves caused differences between the minimum and maximum wall shear stress of up to 81 % of the peak wall shear stress. Thus, because the main criterion for the occurrence of particle stripping in the EWF is the local wall shear stress, the thickness of the film and the formation of surface waves are not negligible. Secondly, the parameters, which govern particle stripping in the current implementation of the EWF, neglect the highly complex viscoelastic behavior of the mucus. Especially the limited range of the linear viscoelastic region (LVR) likely affects the occurrence of particle stripping, as strain loads exceeding the LVR disrupt internal structures in the mucus. Resulting weaker internal bonds within the fluid might decrease its resistance to particle stripping and affect the size of generated particles. Thus, constant parameters for the critical stress for particle stripping, and the mass and diameter of the particles are likely not applicable. In this work, we measure the geometry and propagation of surface waves in the mucus in simplified flow experiments using laser light techniques. Further, we measure the number and size distribution of generated particles using an aerosol spectrometer to analyze the effect of the mucus viscoelasticity. Based on the experimental study, we formulate a model, which includes both the effects of surface waves and of the mucus viscoelasticity.