Experimental study of zeolitic diffusion by use of a concentration-dependent surface diffusion model

Surface diffusivity in adsorption and ion exchange processes is probably the most important property studied expensively in the literature but some aspects, especially its dependence on solid phase concentration, is still an open subject to discussion. In this study a new concentration-dependent surface diffusion model, equipped with a flexible double selectivity equilibrium relationship is applied on the removal of Pb2+, Cr3+, Fe3+ and Cu2+ from aqueous solutions using a natural zeolite. The model incorporates the Chen-Yang surface diffusivity correlation able to deal with positive and negative dependence with surface coverage. The double selectivity equilibrium relationship successfully represents the experimental equilibrium data, which follow Langmurian isotherm type for Pb2+, sigmoidal for Cr3+ and Fe3+ and linear for Cu2+. The concentration-dependent surface diffusion model was compared with the constant diffusivity surface diffusion model and found to be moderately more accurate but considerably more useful as it provides more insights into the diffusion mechanism. The application of the model resulted in an average deviation of 8.56 ± 6.74% from the experimental data and an average solid phase diffusion coefficients between 10−9 and 10−10 cm2/s. The results showed that the diffusion of metal ions in the zeolite structure is unhindered following the surface diffusion mass transfer mechanism

Critical Biot Number of a Periodic Array of Rectangular Fins

We consider the heat transfer problem associated with a periodic array of rectangular fins subjected to convection heat transfer with a uniform heat transfer coefficient. Our analysis differs from the classical approach as (i) we consider two-dimensional (2D) heat conduction and (ii) the wall, to which the fins are attached, is included in the analysis

Variable diffusivity homogeneous surface diffusion model and analysis of merits and fallacies of simplified adsorption kinetics equations

Adsorption and ion exchange phenomena are encountered in several separation processes, which in turn, are of vital importance across various industries. Although the literature on adsorption kinetics modeling is rich, the majority of the models employed are empirical, based on chemical reaction kinetics or oversimplified versions of diffusion models. In this paper, the fifteen most popular simplified adsorption kinetics equations are presented and discussed. A new versatile variable-diffusivity two-phase homogeneous diffusion model is presented and used to evaluate the analytical adsorption models. Aspects of ion exchange kinetics are also addressed

Optimal Design of Helical Springs of Power Law Materials

In this paper the geometric dimensions of a compressive helical spring made of power law materials are optimized to reduce the amount of material. The mechanical constraints are derived to form the geometric programming problem. Both the prime and the dual problem are examined and solved semi-analytically for a range of spring index. A numerical example is provided to validate the solution

Optimal Design of Helical Springs of Power Law Materials

In this paper the geometric dimensions of a compressive helical spring made of power law materials are optimized to reduce the amount of material. The mechanical constraints are derived to form the geometric programming problem. Both the prime and the dual problem are examined and solved semi-analytically for a range of spring index. A numerical example is provided to validate the solution

Heat transfer enhancement of a periodic array of isothermal pipes

We address the problem of two-dimensional heat conduction in a solid slab whose upper and lower surfaces are subjected to uniform convection. In the midsection of the slab there is a periodic array of isothermal pipes of general cross section. The main objective of this work is to find the optimum shapes of the pipes that maximize the Shape Factor (heat transport rate). The Shape Factor is obtained by transforming the periodic array of pipes into a periodic array of strips, using the generalized Schwarz- Christoffel transformation, and applying the collocation boundary element method on the transformed domain. Subsequently we pose the inverse problem, i.e. finding the shape that maximizes the Shape factor given the perimeter of the pipes. For large Biot number the optimum shapes are in agreement with the isothermal case, i.e. circular for sufficiently small perimeters/heat transfer, and elongated towards the surfaces of the slab for larger perimeters/heat transfer. Furthermore, for the isothermal case, we were able to discover a new family of optimum shapes for large thickness of the slab and large perimeters, which do not have their maximum width on the horizontal axis of symmetry. For small Biot number the optimum pipes are flatter than the isothermal ones for a given perimeter. The flatness becomes more apparent for larger perimeters. Most important, for large perimeters there exists a critical thickness which is characterized by maximum heat transfer rate. This is further investigated using the finite element method to obtain the critical thickness of a slab and the critical depth of the periodic array of circular pipe

Optimum shapes of a periodic array of isothermal pipes embedded in a slab subjected to uniform convection

The project's main objective is to obtain optimum shapes of a periodic array of isothermal pipes that maximize heat transfer. The pipes are embedded in a two-dimensional slab whose surfaces are subjected to uniform convection

Two-phase homogeneous diffusion model for the fixed bed sorption of heavy metals on natural zeolites

In this work, the fixed bed removal kinetics of Pb2+, Zn2+, Mn2+, Cr3+, Fe3+ and Cu2+ from aqueous solutions on natural zeolites was studied. For this aim, a non-dimensional two-phase homogeneous solid diffusion model including axial dispersion and equipped with a universal double-selectivity equilibrium model is developed and applied. In total 9 isotherms, representing 128 experimental points and 25 breakthrough curves, representing 764 experimental points are used in modeling. The application of the model is satisfactory resulted in an average deviation from the experimental data of 11.19 ± 5.53%. The solid phase diffusion coefficients are between 10−7 and 10−9 cm2/s depending on the metal, flow rate and particle size in the decreasing order of Cu > Fe, Cr > Zn, Pb > Mn. The study is supplemented by an extended literature review on fixed bed models and experimentally derived solid phase diffusion coefficients in zeolites

Scalable machine learning-assisted clear-box characterization for optimally controlled photonic circuits

Photonic integrated circuits offer a compact and stable platform for generating, manipulating, and detecting light. They are instrumental for classical and quantum applications. Imperfections stemming from fabrication constraints, tolerances and operation wavelength impose limitations on the accuracy and thus utility of current photonic integrated devices. Mitigating these imperfections typically necessitates a model of the underlying physical structure and the estimation of parameters that are challenging to access. Direct solutions are currently lacking for mesh configurations extending beyond trivial cases. We introduce a scalable and innovative method to characterize photonic chips through an iterative machine learning-assisted procedure. Our method is based on a clear-box approach that harnesses a fully modeled virtual replica of the photonic chip to characterize. The process is sample-efficient and can be carried out with a continuous-wave laser and powermeters. The model estimates individual passive phases, crosstalk, beamsplitter reflectivity values and relative input/output losses. Building upon the accurate characterization results, we mitigate imperfections to enable enhanced control over the device. We validate our characterization and imperfection mitigation methods on a 12-mode Clements-interferometer equipped with 126 phase shifters, achieving beyond state-of-the-art chip control with an average 99.77 % amplitude fidelity on 100 implemented Haar-random unitary matrices

Experimental study of zeolitic diffusion by use of a concentration-dependent surface diffusion model

https://www.sciencedirect.com/science/article/pii/S2405844019358037Surface diffusivity in adsorption and ion exchange processes is probably the most important property studied expensively in the literature but some aspects, especially its dependence on solid phase concentration, is still an open subject to discussion. In this study a new concentration-dependent surface diffusion model, equipped with a flexible double selectivity equilibrium relationship is applied on the removal of Pb2+, Cr3+, Fe3+ and Cu2+ from aqueous solutions using a natural zeolite. The model incorporates the Chen-Yang surface diffusivity correlation able to deal with positive and negative dependence with surface coverage. The double selectivity equilibrium relationship successfully represents the experimental equilibrium data, which follow Langmurian isotherm type for Pb2+, sigmoidal for Cr3+ and Fe3+ and linear for Cu2+. The concentration-dependent surface diffusion model was compared with the constant diffusivity surface diffusion model and found to be moderately more accurate but considerably more useful as it provides more insights into the diffusion mechanism. The application of the model resulted in an average deviation of 8.56 ± 6.74% from the experimental data and an average solid phase diffusion coefficients between 10−9 and 10−10 cm2/s. The results showed that the diffusion of metal ions in the zeolite structure is unhindered following the surface diffusion mass transfer mechanism