Flows of granular material in two-dimensional channels

Secondary cone-type crushing machines are an important part of the aggregate production process. These devices process roughly crushed material into aggregate of greater consistency and homogeneity. We apply a continuum model for granular materials (`A Constitutive Law For Dense Granular Flows', Nature 441, p727-730, 2006) to flows of granular material in representative two-dimensional channels, applying a cyclic applied crushing stress in lieu of a moving boundary. Using finite element methods we solve a sequence of quasi-steady fluid problems within the framework of a pressure dependent particle size problem in time. Upon approximating output quantity and particle size we adjust the frequency and strength of the crushing stroke to assess their impact on the output

Energy considerations in accelerating rapid shear granular flows

We present a complete expression for the total energy associated with a rapid frictional granular shear flow down an inclined surface. This expression reduces to the often used energy for a non-accelerating flow of an isotropic, ideal fluid in a horizontal channel, or to the energy for a vertically falling mass. We utilize thickness-averaged mass and momentum conservation laws written in a slope-defined coordinate system. Both the enhanced gravity and friction are taken into account in addition to the bulk motion and deformation. The total energy of the flow at a given spatial position and time is defined as the sum of four energy components: the kinetic energy, gravity, pressure and the friction energy. Total energy is conserved for stationary flow, but for non-stationary flow the non-conservative force induced by the free-surface gradient means that energy is not conserved. Simulations and experimental results are used to sketch the total energy of non-stationary flows. Comparison between the total energy and the sum of the kinetic and pressure energy shows that the contribution due to gravity acceleration and frictional resistance can be of the same order of magnitude, and that the geometric deformation plays an important role in the total energy budget of the cascading mass. Relative importance of the different constituents in the total energy expression is explored. We also introduce an extended Froude number that takes into account the apparent potential energy induced by gravity and pressure

Beyond Spirometry: Linking Wasted Ventilation to Exertional Dyspnea in the Initial Stages of COPD

AbstractExertional dyspnea, a key complaint of patients with chronic obstructive pulmonary disease (COPD), ultimately reflects an increased inspiratory neural drive to breathe. In non-hypoxemic patients with largely preserved lung mechanics – as those in the initial stages of the disease – the heightened inspiratory neural drive is strongly associated with an exaggerated ventilatory response to metabolic demand. Several lines of evidence indicate that the so-called excess ventilation (high ventilation-CO2 output relationship) primarily reflects poor gas exchange efficiency, namely increased physiological dead space. Pulmonary function tests estimating the extension of the wasted ventilation and selected cardiopulmonary exercise testing variables can, therefore, shed unique light on the genesis of patients’ out-of-proportion dyspnea. After a succinct overview of the basis of gas exchange efficiency in health and inefficiency in COPD, we discuss how wasted ventilation translates into exertional dyspnea in individual patients. We then outline what is currently known about the structural basis of wasted ventilation in “minor/trivial” COPD vis-à-vis the contribution of emphysema versus a potential impairment in lung perfusion across non-emphysematous lung. After summarizing some unanswered questions on the field, we propose that functional imaging be amalgamated with pulmonary function tests beyond spirometry to improve our understanding of this deeply neglected cause of exertional dyspnea. Advances in the field will depend on our ability to develop robust platforms for deeply phenotyping (structurally and functionally), the dyspneic patients showing unordinary high wasted ventilation despite relatively preserved FEV1