Adiabatic theorem | EPFL Graph Search

The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: :A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged. Diabatic vs. adiabatic processes At some initial time t_0 a quantum-mechanical system has an energy given by the Hamiltonian \hat{H}(t_0); the system is in an eigenstate of \hat{H}(t_0) labelled \psi(x,t_0). Changing conditions modify the Hamiltonian in a continuous manner, resulting in a final Ha

Steric Effects in the Chemisorption of Vibrationally Excited Methane on Nickel

Bruce Yoder

In this thesis, steric effects in the dissociative chemisorption of quantum state-prepared methane on single crystal surfaces of nickel (Ni(100) and Ni(110)) are detected and quantified for the first time. Exploiting a new, continuous-wave, high-power, single-mode infrared optical parametric oscillator, I produced an intense, quantum state-prepared molecular beam by rapid adiabatic passage. During the infrared excitation of the antisymmetric (ν3) stretch of CH4 or the C-H (ν1) stretch of CD3H by linearly polarized radiation, the angular momentum and vibrational transition dipole moment of methane is aligned in the laboratory frame. The excited, aligned molecular beam is used to probe the stereodynamics of the chemisorption reaction of vibrationally excited methane. For the reaction on Ni(100), an increase in state-prepared methane reactivity of nearly 60% is observed when the laser polarization direction is changed from normal to parallel to the surface. The dependence of the alignment effect on the rotational branch used for excitation (P-, Q-, or R-branch) indicates that alignment of the vibrational dipole moment rather than the angular momentum is responsible for the alignment dependent reactivity. Dephasing of the initially prepared alignment due to hyperfine coupling is observed to be on the timescale of 5-15 microseconds which does not preclude the study of alignment dependent reactivity in our experimental setup. Reactivity decreased monotonically from parallel to perpendicular alignment for both methane isotopologues studied. The alignment effect is shown to be independent of incident velocity for CH4(ν3) and decreases with increasing velocity of CD3H(ν1). For the Ni(110) surface, which consists of parallel rows of closely spaced Ni atoms separated by one-layer deep troughs, I probed if the reactivity depends on the methane alignment relative to the direction of the surface rows. The CH4(ν3) reactivity increases a factor of two when the laser polarization direction is changed from normal to parallel to the surface. Alignment of the vibration perpendicular to the surface rows produced a ∼10% higher reactivity than alignment parallel to the surface rows. Steric effects in a chemical reaction reveal detailed information about the reactive potential energy surface, which makes experimental studies of stereochemistry a powerful probe of microscopic chemical dynamics. The results in this thesis demonstrate and quantify specific steric requirements for this benchmark gas-surface reaction and will serve as a stringent test of multi-dimensional dynamics calculations.

EPFL2010

Ammonia two-phase flow in a horizontal smooth tube: Flow pattern observations, diabatic and adiabatic frictional pressure drops and assessment of prediction methods

Ricardo Lima, Jesus Moreno Quiben, John Richard Thome

The present study illustrates new experimental two-phase flow pattern observations together with diabatic boiling and adiabatic two-phase frictional pressure drop results for ammonia (R7117) flowing inside a 14-mm internal diameter, smooth horizontal stainless steel tube. The flow pattern observations were made for mass velocities of 50, 100 and 160 kg s(-1) m(-2) and saturation temperatures of -14, -2 and 12 degrees C for vapor qualities ranging from 0.05 to 0.6. The flow patterns observed during the study included: stratified-wavy, slug-stratified-wavy, slug, intermittent and annular. For all the experimental conditions, the flow structure observations were compared against the predictions of the flow pattern map model of Wojtan et al. [L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes: part I - a new diabatic two-phase How pattern map, Int. J. Heat Mass Transfer 48 (2005) 2955-2969] and showed very good correspondence. The frictional pressure drop measurements were obtained for vapor qualities from 0.05 to 0.6, saturation temperatures from -14 to 14 degrees C, mass velocities from 50 to 160 kg s(-1) m(-2) and heat fluxes from 12 to 25 kW m(-2). The experimental results show the traditional pressure drop trends: the frictional pressure drop increases with vapor quality and mass velocity. Moreover, the results also show that both diabatic and adiabatic frictional pressure drop values are similar, that is, the boiling process in itself does not affect the frictional pressure drop. The correlations of Friedel [L. Friedel, Improved friction drop correlations for horizontal and vertical two-phase pipe flow, in: European Two-Phase Flow Group Meeting, paper E2, Ispra, Italy, 1979], Lockhart and Martinelli [R.W. Lockhart, R.C. Martinelli, Proposed correlation of data for isothermal two-phase two-component in pipes, Chem. Eng. Process 45 (1949) 39-48] and Muller-Steinhagen and Heck [H. Muller-Steinhagen, K. Heck, A simple friction pressure correlation for two-phase flow in pipes, Chem. Eng. Process 20 (1986) 297-308] predicted only 54%, 52% and 60% of the experimental data within +/- 30%, respectively. The correlation of Gronnerud [R. Gronnerud, Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type of evaporators, part iv: two-phase flow resistance in boiling refrigerans, in: Annexe 1972-1, Bull. de I'Inst. Froid, 1979] predicted 93% of the data and the flow pattern based method of Moreno Quiben and Thome [J. Moreno Quiben, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part II: new phenomenological model, Int.J. Heat Fluid Flow 28 (2007) 1060-1072] predicted more than 97% of the experimental data within the same error band, while the latter method captures almost 89% of the data within +/- 20%. (C) 2008 Elsevier Ltd. All rights reserved.

2009

Experimental and analytical study of two-phase pressure drops during evaporation in horizontal tubes

Jesus Moreno Quiben

Two-phase flow of gases and liquids or vapors and liquids in pipes, channels, equipment, etc. is frequently encountered in industry and has been studied intensively for many years. The reliable prediction of pressure drop in two-phase flow is thereby an important aim. Because of the complexity of these types of flow, empirical or semiempirical relationships are only of limited reliability and pressure drops predicted using leading methods may differ by up to 100%. In order to improve prediction methods, this work presents an experimental and analytical investigation of two-phase pressure drops during evaporation in horizontal tubes. The goal of the experimental part was to obtain accurate two-phase pressure drop values over a wide range of experimental conditions. The existing LTCM intube refrigerant test loop has been modified and adapted to the new test conditions and measurement methods. Two new test sections have been also implemented into the modified test rig. The new test section consists of two zones: diabatic and adiabatic. This configuration allows tests to be run that obtain experimental two-phase pressure drop values under diabatic and adiabatic conditions simultaneously. The experimental campaign acquired 2543 experimental two-phase pressure drop values. Based on a comprehensive state-of-the-art review and comparison with two-phase frictional pressure drop prediction methods, it is proven that none of these methods were able to accurately, reliably predict the present experimental values. In the second part of this work, an analytical study was undertaken in order to develop a new two-phase frictional prediction method. It has been shown in the literature that the so called "phenomenological approach" tends to provide more accurate and realistic predictions as the interfacial structure between the phases is taken into account. Based on that, a phenomenological flow pattern approach was chosen in the present study. The recent Wojtan-Ursenbacher-Thome [155] map was chosen to provide the corresponding interfacial structure. The new model treats each flow regime (i.e. interfacial structure) separately and then ensures a smooth transition in between, being in agreement with the experimental observations. Another important feature of the proposed model is that it matches the correct limits at x = 0 (single-phase liquid flow) and x = 1 (single-phase gas flow). Based on a statistically comparison, it is concluded that the new two-phase frictional pressure drop model based on flow pattern map successfully predicts the new experimental data. The present work completes the fourth basic step in LTCM's flow pattern based work on two-phase flow and heat transfer inside horizontal round tubes: (i) generalized flow pattern map, (ii) flow boiling heat transfer model, (iii) convective condensation model and (iv) two-phase frictional pressure drop model.

EPFL2005