Accurate measurement of the gas diffusion coefficient through porous media is of significant interest to science and engineering applications including mass transfer through soils, building materials, and fuel cells to name a few. Accurate measurements are necessary for simulation and optimization of complex systems involving gas transport. The Loschmidt cell, or closed tube method has been extensively used to measuring the binary gas diffusion coefficient of gas pairs. Recent studies have used a modified Loschmidt cell with an additional porous sample to measure the effective diffusion coefficient through the porous sample. The method employs what is called the resistance network method for calculating the effective diffusion coefficient through the porous sample. In this study, a one-dimensional simulation was developed to evaluate the accuracy of the resistance network method with a modified Loschmidt cell. Dimensionless parameters are shown to be applicable for both the conventional Loschmidt cell as well as the modified Loschmidt cell with the porous sample. A parametric simulation study was performed to show that the error relates closely to the ratio of diffusive resistances of the sample and bulk gas denoted as the resistance ratio, Ω*. With a simulated experimental duration of 250s, which is typical of experiments in literature, the error was found to be negligible when Ω* < 0.1 but increased dramatically for Ω* > 0.1 up to a maximum of approximately 20% error. The equivalent Fourier number, Fo_eq, based on the equivalent diffusivity, D_eq, was proposed as an approximate expression for the degree to which the concentration gradient in the test cell has evolved. It was found that the error has nearly a linear relationship with Fo_eq. Since a lower Fo_eq means a less decayed profile with significant transience remaining, as Fo_eq drops, the the error increases. By controlling the simulation test length for different thickness and diffusivity samples such that Fo_eq = 12.5, the error was reduced to less than 1% over most of the range of parameters and less than 6% over the full range of parameters spanning two orders of magnitude for both thickness and diffusivity. The resistance network method requires the measurement of the sample thickness, a diffusion length, and two diffusion coefficients using with the modified Loschmidt cell (one with the porous sample and one without). Analysis found that the equation used for calculating the effective diffusion coefficient, D_eff, through the porous sample inherently magnifies the relative uncertainty of the measured values in the final calculated value for D_eff. When Ω* < 1, the percentage uncertainty in both diffusion coefficient measurements could potentially be magnified by one or more orders of magnitude. To mitigate uncertainty in D_eff, Ω* must be greater than 1 to ensure that the uncertainty is magnified by no more than a factor of 2. This study recommends that modified Loschmidt experiments aim for Ω* = 1 and Fo_eq = 12.5 to greatly reduce the error and uncertainty in the measurement of D_eff.

Accurate measurement of the gas diffusion coefficient through porous media is of significant interest to science and engineering applications including mass transfer through soils, building materials, and fuel cells to name a few. Accurate measurements are necessary for simulation and optimization of complex systems involving gas transport. The Loschmidt cell, or closed tube method has been extensively used to measuring the binary gas diffusion coefficient of gas pairs. Recent studies have used a modified Loschmidt cell with an additional porous sample to measure the effective diffusion coefficient through the porous sample. The method employs what is called the resistance network method for calculating the effective diffusion coefficient through the porous sample. In this study, a one-dimensional simulation was developed to evaluate the accuracy of the resistance network method with a modified Loschmidt cell. Dimensionless parameters are shown to be applicable for both the conventional Loschmidt cell as well as the modified Loschmidt cell with the porous sample. A parametric simulation study was performed to show that the error relates closely to the ratio of diffusive resistances of the sample and bulk gas denoted as the resistance ratio, Ω*. With a simulated experimental duration of 250s, which is typical of experiments in literature, the error was found to be negligible when Ω* < 0.1 but increased dramatically for Ω* > 0.1 up to a maximum of approximately 20% error. The equivalent Fourier number, Fo_eq, based on the equivalent diffusivity, D_eq, was proposed as an approximate expression for the degree to which the concentration gradient in the test cell has evolved. It was found that the error has nearly a linear relationship with Fo_eq. Since a lower Fo_eq means a less decayed profile with significant transience remaining, as Fo_eq drops, the the error increases. By controlling the simulation test length for different thickness and diffusivity samples such that Fo_eq = 12.5, the error was reduced to less than 1% over most of the range of parameters and less than 6% over the full range of parameters spanning two orders of magnitude for both thickness and diffusivity. The resistance network method requires the measurement of the sample thickness, a diffusion length, and two diffusion coefficients using with the modified Loschmidt cell (one with the porous sample and one without). Analysis found that the equation used for calculating the effective diffusion coefficient, D_eff, through the porous sample inherently magnifies the relative uncertainty of the measured values in the final calculated value for D_eff. When Ω* < 1, the percentage uncertainty in both diffusion coefficient measurements could potentially be magnified by one or more orders of magnitude. To mitigate uncertainty in D_eff, Ω* must be greater than 1 to ensure that the uncertainty is magnified by no more than a factor of 2. This study recommends that modified Loschmidt experiments aim for Ω* = 1 and Fo_eq = 12.5 to greatly reduce the error and uncertainty in the measurement of D_eff.

A single polymer electrolyte membrane fuel cell (PEMFC) is comprised of several sub-millimetre thick layers of varying porosity sandwiched together. The thickness of each layer, which typically ranges from 10 to 200μm, is kept small in order to minimize the transport resistance of heat, mass, electrons, and protons, that limit reaction rate. However, the thickness of these materials presents a significant challenge to engineers characterizing the transport properties through them, which is of considerable importance to the development and optimization of fuel cells. The objective of this research is to address the challenges associated with measuring the heat conduction and gas diffusion transport properties of thin porous media used in PEMFCs. An improvement in the accuracy of the guarded heat flow technique for measuring thermal conductivity and the modified Loschmidt Cell technique for measuring gas diffusivity are presented for porous media with a sub-millimetre thickness. The improvement in accuracy is achieved by analyzing parameters in each apparatus that are sensitive to measurement error and have the largest contribution to measurement uncertainty, and then developing ways to minimize the error. The experimental apparatuses are used to investigate the transport properties of the gas diffusion layer (GDL) and the microporous layer (MPL), while the methods would also be useful in the study of the catalyst layer (CL). Gas diffusion through porous media is critical for the high current density operation of a PEMFC, where the electrochemical reaction becomes rate-limited by the diffusive flux of reactants reaching reaction sites. However, geometric models that predict diffusivity of the GDL have been identified as inaccurate in current literature. Experimental results give a better estimate of diffusivity, but published works to date have been limited by high measurement uncertainty. In this thesis, the effective diffusivity of various GDLs are measured using a modified Loschmidt cell and the relative differences between GDLs are explained using scanning electron microscopy and the method of standard porosimetry. The experimental results from this study and others in current literature are used to develop a generalized correlation for predicting diffusivity as a function of porosity in the through-plane direction of a GDL. The thermal conductivity and contact resistance of porous media are important for accurate thermal analysis of a fuel cell, especially at high current densities where the heat flux becomes large. In this thesis, the effective through-plane thermal conductivity and contact resistance of the GDL and MPL are measured. GDL samples with and without a MPL and coated with 30%-wt. PTFE are measured using the guarded steady-state heat flow technique described in the ASTM standard E 1225-04. Thermal contact resistance of the MPL with the iron clamping surface was found to be negligible, owing to the high surface contact area. Thermal conductivity and thickness of the MPL remained constant for compression pressures up to 15bar at 0.30W/m°K and 55μm, respectively. The thermal conductivity of the GDL substrate containing 30%−wt. PTFE varied from 0.30 to 0.56W/m°K as compression was increased from 4 to 15bar. As a result, the GDL contain- ing MPL had a lower effective thermal conductivity at high compression than the GDL without MPL. At low compression, differences were negligible. The constant thickness of the MPL suggests that the porosity, as well as heat and mass transport properties, remain independent of the inhomogeneous compression by the bipolar plate. Despite the low effective thermal conductivity of the MPL, thermal performance of the GDL can be improved by exploiting the excellent surface contact resistance of the MPL while minimizing its thickness.

A single polymer electrolyte membrane fuel cell (PEMFC) is comprised of several sub-millimetre thick layers of varying porosity sandwiched together. The thickness of each layer, which typically ranges from 10 to 200μm, is kept small in order to minimize the transport resistance of heat, mass, electrons, and protons, that limit reaction rate. However, the thickness of these materials presents a significant challenge to engineers characterizing the transport properties through them, which is of considerable importance to the development and optimization of fuel cells. The objective of this research is to address the challenges associated with measuring the heat conduction and gas diffusion transport properties of thin porous media used in PEMFCs. An improvement in the accuracy of the guarded heat flow technique for measuring thermal conductivity and the modified Loschmidt Cell technique for measuring gas diffusivity are presented for porous media with a sub-millimetre thickness. The improvement in accuracy is achieved by analyzing parameters in each apparatus that are sensitive to measurement error and have the largest contribution to measurement uncertainty, and then developing ways to minimize the error. The experimental apparatuses are used to investigate the transport properties of the gas diffusion layer (GDL) and the microporous layer (MPL), while the methods would also be useful in the study of the catalyst layer (CL). Gas diffusion through porous media is critical for the high current density operation of a PEMFC, where the electrochemical reaction becomes rate-limited by the diffusive flux of reactants reaching reaction sites. However, geometric models that predict diffusivity of the GDL have been identified as inaccurate in current literature. Experimental results give a better estimate of diffusivity, but published works to date have been limited by high measurement uncertainty. In this thesis, the effective diffusivity of various GDLs are measured using a modified Loschmidt cell and the relative differences between GDLs are explained using scanning electron microscopy and the method of standard porosimetry. The experimental results from this study and others in current literature are used to develop a generalized correlation for predicting diffusivity as a function of porosity in the through-plane direction of a GDL. The thermal conductivity and contact resistance of porous media are important for accurate thermal analysis of a fuel cell, especially at high current densities where the heat flux becomes large. In this thesis, the effective through-plane thermal conductivity and contact resistance of the GDL and MPL are measured. GDL samples with and without a MPL and coated with 30%-wt. PTFE are measured using the guarded steady-state heat flow technique described in the ASTM standard E 1225-04. Thermal contact resistance of the MPL with the iron clamping surface was found to be negligible, owing to the high surface contact area. Thermal conductivity and thickness of the MPL remained constant for compression pressures up to 15bar at 0.30W/m°K and 55μm, respectively. The thermal conductivity of the GDL substrate containing 30%−wt. PTFE varied from 0.30 to 0.56W/m°K as compression was increased from 4 to 15bar. As a result, the GDL contain- ing MPL had a lower effective thermal conductivity at high compression than the GDL without MPL. At low compression, differences were negligible. The constant thickness of the MPL suggests that the porosity, as well as heat and mass transport properties, remain independent of the inhomogeneous compression by the bipolar plate. Despite the low effective thermal conductivity of the MPL, thermal performance of the GDL can be improved by exploiting the excellent surface contact resistance of the MPL while minimizing its thickness.

Accuracy in the effective diffusion coefficient of the gas diffusion layer (GDL)/microporous layer (MPL) is important to accurately predict the mass transport limitations for high current density operation of polymer electrolyte membrane (PEM) fuel cells. All the previous studies regarding mass transport limitations were limited to pure GDLs, and experimental analysis of the impact of the MPL on the overall diffusion in the porous GDL is still lacking. The MPL is known to provide beneficial water management properties at high current operating conditions of PEM fuel cells but its small pore sizes become a resistance in the diffusion path for mass transport to the catalyst layer. A modified Loschmidt cell with an oxygen-nitrogen mixture is used in this work to determine the effect of MPL on the effective diffusion coefficients. It is found that Knudsen effects play a dominant role in the diffusion through the MPL where pore diameters are less than 1 μm. Experimental results show that the effective diffusion coefficient of the MPL is only about 21% that of its GDL substrate and Knudsen diffusion accounts for 80% of the effective diffusion coefficient of the GDL with MPL measured in this study. No existing correlations can correlate the effective diffusion coefficient with significant Knudsen contribution.

Accuracy in the effective diffusion coefficient of the gas diffusion layer (GDL)/microporous layer (MPL) is important to accurately predict the mass transport limitations for high current density operation of polymer electrolyte membrane (PEM) fuel cells. All the previous studies regarding mass transport limitations were limited to pure GDLs, and experimental analysis of the impact of the MPL on the overall diffusion in the porous GDL is still lacking. The MPL is known to provide beneficial water management properties at high current operating conditions of PEM fuel cells but its small pore sizes become a resistance in the diffusion path for mass transport to the catalyst layer. A modified Loschmidt cell with an oxygen-nitrogen mixture is used in this work to determine the effect of MPL on the effective diffusion coefficients. It is found that Knudsen effects play a dominant role in the diffusion through the MPL where pore diameters are less than 1 μm. Experimental results show that the effective diffusion coefficient of the MPL is only about 21% that of its GDL substrate and Knudsen diffusion accounts for 80% of the effective diffusion coefficient of the GDL with MPL measured in this study. No existing correlations can correlate the effective diffusion coefficient with significant Knudsen contribution.

<p>The development of ultracold atom physics enables people to study fundamental questions in quantum mechanics within this highly-tunable platform. This dissertation focuses on several topics of the dynamical evolution of quantum systems.</p><p>Chapter 2 and 3 talk about Loschmidt echo, a simple quantity that reveals many hidden properties of a system’s time evolution. Chapter 2 looks for vanishing Loschmidt echo in the complex plane of time and the corresponding dynamical quantum phase transitions (DQPT) in the thermodynamic limit. For a two-site Bose-Hubbard model consisting of weakly interacting particles, DQPTs reside at the time scale inversely proportional to the interaction, where highly entangled pair condensates also show up. Chapter 3 discusses the revival of Loschmidt echo in a discrete time crystal, a Floquet system whose discrete temporal transition symmetry is spontaneously broken. We propose a new design and demonstrate its robustness against the fluctuations in the driving field. It can also be used in precision measurement to go beyond the Heisenberg limit. Experimental schemes are presented.</p><p>Out-of-time-order correlator (OTOC) is a more complicated variant of Loschmidt echo. Experimentally it requires reversing the time evolution. In Chapter 4, by exploiting the SU(1,1) symmetry of a weakly interacting BEC and connecting its quantum dynamics to a hyperbolic space, we obtain a geometric framework that enables experimentalists to manipulate the evolution with great freedom. Backward evolution is then realized effectively to measure OTOC of such SU(1,1) systems.</p><p>Chapter 5 discusses the decoherence of a spin impurity immersed in a spinor BEC. Our calculations show that by looking at the dynamics of the impurity’s reduced density matrix, the phase of the spinor BEC can be detected.</p>