WJ
W. Jin
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Self-limiting gas-surface reactions lead to reaction fronts that penetrate nanoporous materials with a finite speed. We present a closed form theoretical model, validated against molecular simulations, that shows the influence of the fractal scaling law on the time needed to fully penetrate fractal agglomerates of nanoparticles. For very large agglomerate sizes, this penetration time scales with the number of particles N in the agglomerate as [Fourmula presented]. The penetration time for agglomerates with fractal dimensions Df<3 may therefore be orders of magnitude smaller than for non-fractal porous materials.
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Self-limiting gas-surface reactions lead to reaction fronts that penetrate nanoporous materials with a finite speed. We present a closed form theoretical model, validated against molecular simulations, that shows the influence of the fractal scaling law on the time needed to fully penetrate fractal agglomerates of nanoparticles. For very large agglomerate sizes, this penetration time scales with the number of particles N in the agglomerate as [Fourmula presented]. The penetration time for agglomerates with fractal dimensions Df<3 may therefore be orders of magnitude smaller than for non-fractal porous materials.
Nanoparticles are increasingly applied in a range of fields, such as electronics, catalysis, energy and medicine, due to their small sizes and consequent high surface-volume ratio. In many applications, it is attractive to coat the nanoparticles with a layer of different materials in order to gain new functionalities. For instance, a coated layer can modify the chemical properties of the nanoparticles, protect the core material resulting in increased stability, facilitate the biofunctionalization, etc. Atomic layer deposition (ALD) is a gas-phase technique that can form an ultrathin solid film on a range of substrates. It utilizes two self-limiting surface reactions applied in an alternating sequence. By controlling the number of applied cycles, the thickness of the coated layer can be controlled with nanometer precision. Several experimental reports in literature have shown that applying ALD to nanoparticles using a fluidized bed is a promising way of producing large quantities of coated nanoparticles. Fluidization is a gas-phase technique that can process large quantities of particles by suspending them in an upward gas stream. It provides good gas-solid mixing, scale-up potential, and allows continuous processing. However, due to the strong cohesive forces between particles, nanoparticles cluster into large agglomerates when fluidized. These agglomerates have a complex, hierarchical structure, which has been commonly described as fractal for their self-similarity under different length scales. During the ALD process, the precursors have to diffuse into such structures to reach the surface of inner particles.
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Nanoparticles are increasingly applied in a range of fields, such as electronics, catalysis, energy and medicine, due to their small sizes and consequent high surface-volume ratio. In many applications, it is attractive to coat the nanoparticles with a layer of different materials in order to gain new functionalities. For instance, a coated layer can modify the chemical properties of the nanoparticles, protect the core material resulting in increased stability, facilitate the biofunctionalization, etc. Atomic layer deposition (ALD) is a gas-phase technique that can form an ultrathin solid film on a range of substrates. It utilizes two self-limiting surface reactions applied in an alternating sequence. By controlling the number of applied cycles, the thickness of the coated layer can be controlled with nanometer precision. Several experimental reports in literature have shown that applying ALD to nanoparticles using a fluidized bed is a promising way of producing large quantities of coated nanoparticles. Fluidization is a gas-phase technique that can process large quantities of particles by suspending them in an upward gas stream. It provides good gas-solid mixing, scale-up potential, and allows continuous processing. However, due to the strong cohesive forces between particles, nanoparticles cluster into large agglomerates when fluidized. These agglomerates have a complex, hierarchical structure, which has been commonly described as fractal for their self-similarity under different length scales. During the ALD process, the precursors have to diffuse into such structures to reach the surface of inner particles.
For simulating rarefied gas flows around a moving body, an immersed boundary method is presented here in conjunction with the Direct Simulation Monte Carlo (DSMC) method in order to allow the movement of a three dimensional immersed body on top of a fixed background grid. The simulated DSMC particles are reflected exactly at the landing points on the surface of the moving immersed body, while the effective cell volumes are taken into account for calculating the collisions between molecules. The effective cell volumes are computed by utilizing the Lagrangian intersecting points between the immersed boundary and the fixed background grid with a simple polyhedra regeneration algorithm. This method has been implemented in OpenFOAM and validated by computing the drag forces exerted on steady and moving spheres and comparing the results to that from conventional body-fitted mesh DSMC simulations and to analytical approximations.
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For simulating rarefied gas flows around a moving body, an immersed boundary method is presented here in conjunction with the Direct Simulation Monte Carlo (DSMC) method in order to allow the movement of a three dimensional immersed body on top of a fixed background grid. The simulated DSMC particles are reflected exactly at the landing points on the surface of the moving immersed body, while the effective cell volumes are taken into account for calculating the collisions between molecules. The effective cell volumes are computed by utilizing the Lagrangian intersecting points between the immersed boundary and the fixed background grid with a simple polyhedra regeneration algorithm. This method has been implemented in OpenFOAM and validated by computing the drag forces exerted on steady and moving spheres and comparing the results to that from conventional body-fitted mesh DSMC simulations and to analytical approximations.
Coated nanoparticles have many potential applications; production of large quantities is feasible by atomic layer deposition (ALD) on nanoparticles in a fluidized bed reactor. However, due to the cohesive interparticle forces, nanoparticles form large agglomerates, which influences the coating process. In order to study this influence, the authors have developed a novel computational modeling approach which incorporates (1) fully resolved agglomerates; (2) a self-limiting ALD half cycle reaction; and (3) gas diffusion in the rarefied regime modeled by direct simulation Monte Carlo. In the computational model, a preconstructed fractal agglomerate of up to 2048 spherical particles is exposed to precursor molecules that are introduced from the boundaries of the computational domain and react with the particle surfaces until these are fully saturated. With the computational model, the overall coating time for the nanoparticle agglomerate has been studied as a function of pressure, fractal dimension, and agglomerate size. Starting from the Gordon model for ALD coating within a cylindrical hole or trench [Gordon et al., Chem. Vap. Deposition 9, 73 (2003)], the authors also developed an analytic model for ALD coating of nanoparticles in fractal agglomerates. The predicted coating times from this analytic model agree well with the results from the computational model for Df = 2.5. The analytic model predicts that realistic agglomerates of O(10⁹) nanoparticles require coating times that are 3–4 orders of magnitude larger than for a single particle.
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Coated nanoparticles have many potential applications; production of large quantities is feasible by atomic layer deposition (ALD) on nanoparticles in a fluidized bed reactor. However, due to the cohesive interparticle forces, nanoparticles form large agglomerates, which influences the coating process. In order to study this influence, the authors have developed a novel computational modeling approach which incorporates (1) fully resolved agglomerates; (2) a self-limiting ALD half cycle reaction; and (3) gas diffusion in the rarefied regime modeled by direct simulation Monte Carlo. In the computational model, a preconstructed fractal agglomerate of up to 2048 spherical particles is exposed to precursor molecules that are introduced from the boundaries of the computational domain and react with the particle surfaces until these are fully saturated. With the computational model, the overall coating time for the nanoparticle agglomerate has been studied as a function of pressure, fractal dimension, and agglomerate size. Starting from the Gordon model for ALD coating within a cylindrical hole or trench [Gordon et al., Chem. Vap. Deposition 9, 73 (2003)], the authors also developed an analytic model for ALD coating of nanoparticles in fractal agglomerates. The predicted coating times from this analytic model agree well with the results from the computational model for Df = 2.5. The analytic model predicts that realistic agglomerates of O(10⁹) nanoparticles require coating times that are 3–4 orders of magnitude larger than for a single particle.
Direct Simulation Monte Carlo (DSMC) is a widely applied numerical technique to simulate rarefied gas flows. For flows around immersed moving objects, the use of body fitted meshes is inefficient, whereas published methods using cut-cells in a fixed background mesh have important limitations. We present a novel cut-cell algorithm, which allows for accurate DSMC simulations around arbitrarily shaped moving objects. The molecule–surface interaction occurs exactly at the instantaneous collision point on the moving body surface, and accounts for its instantaneous velocity, thus precisely imposing the desired boundary conditions. A simple algorithm to calculate the effective volume of cut cells is presented and
shown to converge linearly with grid refinement. The potential and efficiency of method is demonstrated by calculating rarefied gas flow drag forces on steady and moving immersed spheres. The obtained results are in excellent agreement with results obtained with a body-fitted mesh, and with analytical approximations for high-Knudsen number flows. ...
shown to converge linearly with grid refinement. The potential and efficiency of method is demonstrated by calculating rarefied gas flow drag forces on steady and moving immersed spheres. The obtained results are in excellent agreement with results obtained with a body-fitted mesh, and with analytical approximations for high-Knudsen number flows. ...
Direct Simulation Monte Carlo (DSMC) is a widely applied numerical technique to simulate rarefied gas flows. For flows around immersed moving objects, the use of body fitted meshes is inefficient, whereas published methods using cut-cells in a fixed background mesh have important limitations. We present a novel cut-cell algorithm, which allows for accurate DSMC simulations around arbitrarily shaped moving objects. The molecule–surface interaction occurs exactly at the instantaneous collision point on the moving body surface, and accounts for its instantaneous velocity, thus precisely imposing the desired boundary conditions. A simple algorithm to calculate the effective volume of cut cells is presented and
shown to converge linearly with grid refinement. The potential and efficiency of method is demonstrated by calculating rarefied gas flow drag forces on steady and moving immersed spheres. The obtained results are in excellent agreement with results obtained with a body-fitted mesh, and with analytical approximations for high-Knudsen number flows.
shown to converge linearly with grid refinement. The potential and efficiency of method is demonstrated by calculating rarefied gas flow drag forces on steady and moving immersed spheres. The obtained results are in excellent agreement with results obtained with a body-fitted mesh, and with analytical approximations for high-Knudsen number flows.