Abstract
Additive manufacturing, especially in the form of 3D printing, offers the exciting possibility of generating heterogeneous articles with precisely controlled internal microstructure. One area in which this feature can be of significant advantage is in diffusion control, specifically in the design and fabrication of microstructures which optimize the rate of transport of a solute to and from a contained fluid. In this work we focus on the use of flakes as diffusion-control agents and study computationally and theoretically the effect of orientation on the barrier properties of flake-filled composites. We conducted over 1500 simulations in two-dimensional, doubly-periodic unit cells each containing up to 3000 individual flake cross-sections which are randomly placed and with their axes forming an angle () with the direction of macroscopic diffusion. We consider long-flake systems of aspect ratio () 100 and 1000, from the dilute () and into the concentrated () regime. Based on the rotation properties of the diffusivity tensor, we derive a model which is capable of accurately reproducing all computational results ( and ). The model requires as inputs the two principal diffusivities of the composite, normal and parallel to the flake axis. In this respect, we find the models of Lape et al. [1] and Nielsen [2] form an excellent combination. Both our model and our computational data predict that at the quadratic dependence of the Barrier Improvement Factor (BIF) on () is lost, with the BIF approaching a plateau at higher values of (). This plateau is lower as () increases. We derive analytical estimates of this maximum achievable BIF at each level of misalignment; these are also shown to be in excellent agreement with the computational results. Finally we show that our computational results and model are in agreement with experimental evidence at small values of ().
Highlights
Additive manufacturing, especially in the form of 3D printing, offers the exciting possibility of generating articles with precisely controlled internal microstructure
We derive analytical estimates of this maximum achievable Barrier Improvement Factor (BIF) at each level of misalignment; these are shown to be in excellent agreement with the computational results
Given the capability afforded by 3D printing to fully control flake orientation as well as generate articles with flake loadings approaching those at maximum packing, it is desirable to predict the effective diffusion coefficient as an explicit function of the flake orientation angle and for very high, previously untenable, concentrations
Summary
Especially in the form of 3D printing, offers the exciting possibility of generating articles with precisely controlled internal microstructure. One notable disadvantage of traditional processing methods vis-à-vis flakefilled composites is the fact that flake orientation cannot be precisely controlled. In such operations (extrusion, compression or injection molding, thermoforming and others) flake orientation is achieved due to the propensity of the flakes to orient in accordance to the prevailing flow field—either in the main direction of flow when the flow is shear or transverse to it when the flow is extensional [17]. Given the capability afforded by 3D printing to fully control flake orientation as well as generate articles with flake loadings approaching those at maximum packing, it is desirable to predict the effective diffusion coefficient (or its inverse, the barrier improvement factor, BIF) as an explicit function of the flake orientation angle and for very high, previously untenable, concentrations. We show that the implications of our theoretical model are fully supported by extensive computational results
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