We develop a mathematical model of nanoparticles depositing onto and penetrating into a biofilm grown in a parallel-plate flow cell. We carry out deposition experiments in a flow cell to support the modeling. The modeling and the experiments are motivated by the potential use of polymer nanoparticles as part of a treatment strategy for killing biofilms infecting the deep passages in the lungs. In the experiments and model, a fluid carrying polymer nanoparticles is injected into a parallel-plate flow cell in which a biofilm has grown over the bottom plate. The model consists of a system of transport equations describing the deposition and diffusion of nanoparticles. Standard asymptotic techniques that exploit the aspect ratio of the flow cell are applied to reduce the model to two coupled partial differential equations. We perform numerical simulations using the reduced model. We compare the experimental observations with the simulation results to estimate the nanoparticle sticking coefficient and the diffusion coefficient of the nanoparticles in the biofilm. The distributions of nanoparticles through the thickness of the biofilm are consistent with diffusive transport, and uniform distributions through the thickness are achieved in about four hours. Nanoparticle deposition does not appear to be strongly influenced by the flow rate in the cell for the low flow rates considered.
In the context of one-dimensional linear wave propagation, a gradient-type interface is a point at which the velocity profile of a scattering medium suffers a jump in first derivative. In this paper, a time domain approach to scattering from such an interface leads to an integrodifferential equation involving the kernel of the reflection operator (impulse response), which can be solved exactly if the velocity profile is piecewise parabolic. This special case provides the basis for an approximate numerical scheme to solve the inverse scattering problem (recover the velocity profile from reflection data) for a general velocity profile. The algorithm is fast and affords good results if the velocity profile is nearly parabolic or the interest is in short time only. A detailed error estimate for the approximation is provided.
This work is a modeling and simulation extension of an integrated experimental/modeling investigation of a procedure to coat nanofibers and core-clad nanostructures with thin film materials using plasma enhanced physical vapor deposition. In the experimental effort, electrospun polymer nanofibers are coated with metallic materials under different operating conditions to observe changes in the coating morphology. The modeling effort focuses on linking simple models at the reactor level, nanofiber level, and atomic level to form a comprehensive model. The comprehensive model leads to the definition of an evolution equation for the coating free surface. This equation was previously derived and solved under a single-valued assumption in a polar geometry to determine the coating morphology as a function of operating conditions. The present work considers the axisymmetric geometry and solves the evolution equation without the single-valued assumption and under less restrictive assumptions on the concentration field than the previous work.
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