Ordinary, transition, and Knudsen regime diffusion in random capillary structures

Respiratory droplets interception in fibrous porous media

We investigate, by means of pore-scale lattice Boltzmann simulations, the mechanisms of interception of respiratory droplets within fibrous porous media composing face masks. We simulate the dynamics, coalescence, and collection of droplets of the size comparable with the fiber and pore size in typical fluid-dynamic conditions that represent common expiratory events. We discern the fibrous microstructure into three categories of pores: small, large, and medium-sized pores, where we find that within the latter, the incoming droplets tend to be more likely intercepted. The size of the medium-sized pores relative to the fiber size is placed between the droplet-to-fiber size ratio and a porosity-dependent microstructural parameter L ϵ * = ϵ / ( 1 - ϵ ) , with ϵ being the porosity. In larger pores, droplets collection is instead inhibited by the small pore-throat-to-fiber size ratio that characterizes the pore perimeter, limiting their access. The efficiency of the fibrous media in intercepting droplets without compromising breathability, for a given droplet-to-fiber size ratio, can be estimated by knowing the parameter L ϵ * . We propose a simple model that predicts the average penetration of droplets into the fibrous media, showing a sublinear growth with L ϵ * . Permeability is shown also to scale well with L ϵ * but following a superlinear growth, which indicates the possibility of increasing the medium permeability at a little cost in terms of interception efficiency for high values of porosity. As a general design guideline, the results also suggest that a fibrous layer thickness relative to the fiber size should exceed the value L ϵ * in order to ensure effective droplets filtration.

Porous Membranes as Sacrificial Layers Enabling Conformal Chemical Vapor Deposition Involving Multiple Film-Forming Species

We propose a new, concise method for conformal chemical vapor deposition (CVD) using sacrificial layers (SLs) to fill three-dimensional features with microscopic pores. SLs are porous membranes (e.g., ceramic felts) that filter film-forming species having high sticking-probability (η). CVD processes with multiple film-forming species generally suffer from poor conformality due to preferential film deposition at the inlets of features by the high-η species, such as reactive intermediates. An SL traps such high-η species before they reach the target features and selectively supplies film-forming species with lower η (e.g., source precursors or stable intermediates) that enables conformal film deposition. Here the trapping efficiency of an SL was predicted and a procedure for designing an optimal SL was established. The procedure was demonstrated by CVD of silicon carbide (SiC) with multiple film-forming species of high-η species (η = 8.0 × 10^-3) and lower-η species (η = 5.9 × 10^-5 and 2.2 × 10^-7). The trapping of 99.2% of incident high-η species was achieved with an optimized SL, wherein the deposition rate (m/s) contribution by high-η species declined from 0.546 at the SL inlet to 0.014 at its outlet. Finally, using these optimized SLs, SiC-CVD filling of micron-scale trenches was demonstrated with an aspect-ratio of 16:1.

Elastic and transport properties of cellular solids derived from three-dimensional tomographic images

We describe a three-dimensional imaging and analysis study of eight industrial cellular foam morphologies. The foam morphologies were generated by differing industrial processing methods. Tomograms are acquired on an X-ray micro-computed tomography facility at scales of approximately equal to at resolutions down to 7 μm. The image quality is sufficient in all cases to measure local structure and connectivity of the foamed material, and the field of view large enough to calculate a range of material properties. Phase separation into solid and porous components is straightforward.

Three-dimensional structural characteristics are measured directly on the porous and solid phases of the images. A number of morphological parameters are obtained, including pore volume-to-surface-area ratio, connectivity, the pore and solid phase size distributions defined by maximal sphere openings and chord length measurements. We further calculate the pore size distribution associated with capillary pressure via simulating of mercury drainage on the digital images.

The binarized microstructures are used as a basis for calculations of transport properties (fluid permeability, diffusivity and thermal conductivity) and elastic moduli. From the data, we generate property–porosity relationships for the range of foam morphologies imaged and quantitatively analyse the effects of porosity and microstructure on the resultant properties of the foams.

We compare our numerical data to commonly used theoretical and empirical property–porosity relationships. For thermal conductivity, we find that the numerical results agree extremely well with an empirical expression based on experimental data of various foams. The upper Hashin–Shtrikman bound also provides an excellent prediction of the data across all densities. From simulation of the diffusivity, we can define the tortuosity of the pore space within the cellular solid. We find that different processing methods lead to strong variations in the tortuosity of the pore space of the foams. For elastic properties, our results show that for the Young modulus, E , both the differential effective medium theory and the classical correlation give a good correlation. Assuming a constant Poisson's ratio leads to reasonable agreement. The best correlation for is given by assuming a slight variation in as a linear function of porosity. The permeability of the foams varies over three orders of magnitude. Correlations for permeability based on the classical Kozeny–Carman equation lead to reasonable agreement, except at the lowest porosities. Permeability estimations based on mercury porosimetry give excellent agreement for all foams.