ALBERT

Description: The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude number/Reynolds number plane for different fuel jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

Description: The planar laminar flow resulting from the impingement of two gaseous jets of different density issuing into an open space from aligned steadily fed slot nozzles of semi-width separated by a distance is investigated by numerical and analytical methods. Specific consideration is given to the high Reynolds and low Mach number conditions typically present in counterflow-flame experiments, for which the flow is nearly inviscid and incompressible. It is shown that introduction of a density-weighted vorticity-streamfunction formulation effectively reduces the problem to one involving two jets of equal density, thereby removing the vortex-sheet character of the interface separating the two jet streams. Besides the geometric parameter , the solution depends only on the shape of the velocity profiles in the feed streams and on the jet momentum-flux ratio. While conformal mapping can be used to determine the potential solution corresponding to uniform velocity profiles, numerical integration is required in general to compute rotational flows, including those arising with Poiseuille velocity profiles, with simplified solutions found in the limits and . The results are used to quantify the near-stagnation-point region, of interest in counterflow-flame studies, including the local value of the strain rate as well as the curvature of the separating interface and the variations of the strain rate away from the stagnation point. © 2017 Cambridge University Press.

Description: Radionuclide scanning images published in Nature by Di Chiro in 1964 showed a downward migration along the spinal canal of particle tracers injected in the brain ventricles while also showing an upward flow of tracers injected in the lumbar region of the canal. These observations, since then corroborated by many radiological measurements, have been the basis for the hypothesis that there must be an active circulation mechanism associated with the transport of cerebrospinal fluid (CSF) deep down into the spinal canal and subsequently returning a portion back to the cranial vault. However, to date, there has been no physical explanation for the mechanism responsible for the establishment of such a bulk recirculating motion. To investigate the origin and characteristics of this recirculating flow, we have analyzed the motion of the CSF in the subarachnoid space of the spinal canal. Our analysis accounts for the slender geometry of the spinal canal, the small compliance of the dura membrane enclosing the CSF in the canal, and the fact that the CSF is confined to a thin annular subarachnoid space surrounding the spinal cord. We apply this general formulation to study the characteristics of the flow generated in a simplified model of the spinal canal consisting of a slender compliant cylindrical pipe with a coaxial cylindrical inclusion, closed at its distal end, and subjected to small periodic pressure pulsations at its open entrance. We show that the balance between the local acceleration and viscous forces produces a leading-order flow consisting of pure oscillatory motion with axial velocities on the order of a few centimetres per second and amplitudes monotonically decreasing along the length of the canal. We then demonstrate that the nonlinear term associated with the convective acceleration contributes to a second-order correction consisting of a steady streaming that generates a bulk recirculating motion of the CSF along the length of the canal with characteristic velocities two orders of magnitude smaller than the leading-order oscillatory flow. The results of the analysis of this idealized geometry of the spinal canal are shown to be in good agreement not only with experimental measurements in an in-vitro model but also with radiological measurements conducted in human adults. © 2018 Cambridge University Press.

Description: This paper investigates the transport of a solute carried by the cerebrospinal fluid (CSF) in the spinal canal. The analysis is motivated by the need for a better understanding of drug dispersion in connection with intrathecal drug delivery (ITDD), a medical procedure used for treatment of some cancers, infections and pain, involving the delivery of the drug to the central nervous system by direct injection into the CSF via the lumbar route. The description accounts for the CSF motion in the spinal canal, described in our recent publication (Sánchez et al., J. Fluid Mech., vol. 841, 2018, pp. 203-227). The Eulerian velocity field includes an oscillatory component with angular frequency , equal to that of the cardiac cycle, and associated tidal volumes that are a factor smaller than the total CSF volume in the spinal canal, with the small velocity corrections resulting from convective acceleration providing a steady-streaming component with characteristic residence times of order . An asymptotic analysis for accounting for the two time scales and is used to investigate the prevailing drug-dispersion mechanisms and their dependence on the solute diffusivity, measured by the Schmidt number . Convective transport driven by the time-averaged Lagrangian velocity, obtained as the sum of the Eulerian steady-streaming velocity and the Stokes-drift velocity associated with the non-uniform pulsating flow, is found to be important for all values of . By way of contrast, shear-enhanced Taylor dispersion, which is important for values of of order unity, is shown to be negligibly small for the large values corresponding to the molecular diffusivities of all ITDD drugs. Results for a model geometry indicate that a simplified equation derived in the intermediate limit provides sufficient accuracy under most conditions, and therefore could constitute an attractive reduced model for future quantitative analyses of drug dispersion in the spinal canal. The results can be used to quantify dependences of the drug-dispersion rate on the frequency and amplitude of the pulsation of the intracranial pressure, the compliance and specific geometry of the spinal canal and the molecular diffusivity of the drug. © 2018 Cambridge University Press.