François Puel

Numerical simulation of mass transfer in a liquid–liquid membrane contactor for laminar flow conditions

Liquid-liquid phase membrane contactors are increasingly being used for mixing and reaction. The principle is the following: component A flows through the membrane device inlet to mix/react with component B which comes from the membrane pores. This study presents a numerical simulation using computational fluid dynamics (CFD) of momentum and mass transfer in a tubular membrane contactor for laminar flow conditions. The velocity and concentration profiles of components A-C are obtained by resolution of the Navier-Stokes and convection-diffusion equations. The numerical simulations show that mixing between A and B is obtained by diffusion along the streamlines separating both components. The mixing/reaction zone width is within the region of a few hundred of microns, and depends on the diffusion coefficients of A and B. Hollow fiber membrane devices are found to be of particular interest because their inner diameter is close to the mixing zone width.

3D kinematic and dynamic analysis of the front crawl tumble turn in elite male swimmers

The aim of this study was to identify kinematic and dynamic variables related to the best tumble turn times (3mRTT, the turn time from 3-m in to 3-m out, independent variable) in ten elite male swimmers using a three-dimensional (3D) underwater analysis protocol and the Lasso (least absolute shrinkage and selection operator) as statistical method. For each swimmer, the best-time turn was analyzed with five stationary and synchronized underwater cameras. The 3D reconstruction was performed using the Direct Linear Transformation algorithm. An underwater piezoelectric 3D force platform completed the set-up to compute dynamic variables. Data were smoothed by the Savitzky-Golay filtering method. Three variables were considered relevant in the best Lasso model (3mRTT=2.58-0.425 RD+0.204 VPe+0.0046 TD): the head-wall distance where rotation starts (RD), the horizontal speed at the force peak (VPe), and the 3D length of the path covered during the turn (TD). Furthermore, bivariate analysis showed that upper body (CUBei) and lower limb extension indexes at first contact (CLLei) were also linked to the turn time (r=-0.65 and p<0.05 for both variables). Thus the best turn times were associated with a long RD, slower VPe and reduced TD. By an early transverse rotation, male elite swimmers reach the wall with a slightly flexed posture that results in fast extension. These swimmers opt for a movement that is oriented forward and they focus on reducing the distance covered.

Explicit solutions of the three-dimensional inverse problem of dynamics, using the frenet reference frame

Given a two-parameter of three-dimensional orbits, we construct the unit tangent vector, the normal and the binormal which define the Frenet reference frame. In this frame, by writing that the force is conservative, we explicitly obtain the potential as a function of the energy along the trajectories and of its derivatives.

Formulation intrinseque de l'equation de Szebehely (intrinsic formulation of Szebehely's equation)

ResumeLéquation de Szébéhély caractérisant les potentiels qui donnent lieu à une famille dorbites planes donnée est formulée dune manière intrinsèque, puis généralisée à 3 ou n dimensions en coordonnées curvilignes et en notations tensorielles.AbstractThe equation of Szebehely for potentials generating a given family of planar orbits is given in an intrinsic way, then generalized to 3 or n dimensions in curvilinear coordinates and tensorial notations.

Separable and partially separable systems in the light of the inverse problem of dynamics

Using a generalization of Joukovskys formula, we determine three-dimensional families of curves that are orbits only in separable potentials and we note the importance of ‘iso-energetic’ families of orbits. We also obtain more general families that are orbits of partially separable systems and we examine from this point of view the classical curvilinear coordinate systems.

Numerical study of the rectilinear isosceles restricted problem

We study the orbit of a particle in the plane of symmetry of two equal mass primaries in rectilinear keplerian motion. Using the surfaces of section we look for periodic orbits, examine their stability and search for quasi-periodic orbits and regions of escape. For large values of the angular momentumC, we verify the validity of the approximation of two fixed centers. However, we also find irregular families of orbits and resonance zones.For small values ofC, the approximation is no longer valid, but we find invariant curves whose interpretation might be interesting.

Potentials having two orthogonal families of curves as trajectories

We study, using the tool of Joukovsky’s orthogonal coordinates, the determination of the potentials having two families of orthogonal trajectories. We show for compatible cases the existence and the uniqueness, up to a constant factor, of the solution. We note the importance of the ‘isothermal’ nets of curves. We study as an example the net of geometrically similar conic curves and orthogonal trajectories.

Equation de Szébéhély et principes variationnels

ResumeOn montre léquivalence entre léquation de Szebehely du ‘problème inverse’ et un problème variationnel déduit du principe de Maupertuis.AbstractWe show that the ‘inverse problem’ Szebehelys equations is equivalent to a multiple variation problem deduced from the principle of Maupertuis.

A Geometrical Interpretation of the Deflection of Almost Rectilinear Orbits in a Central Field

We give a geometrical interpretation for the deflection at the origin of rectilinear orbits in a central field. This interpretation is based on the correspondence between the plane orbits of a conservative force field and the geodesics of a certain surface. If the field is ‘hard’ near the origin, the surface is tangent to a cone. By considering the development of this cone, we obtain the deflection. We study also almost rectilinear orbits.

Three-dimensional kinematic and dynamic analysis of the crawl tumble turn performance: the expertise effect

1.66 ^ 0.05 1.76 ^ 0.04 ,0.0001 VOut (m/s) 1.68 ^ 0.12 2.01 ^ 0.19 ,0.001 A (years) 15.9 ^ 1.3 21.9 ^ 4.1 ,0.001 AT (s) 1.23 ^ 0.08 1.10 ^ 0.07 0.001 BM (kg) 55.2 ^ 5.6 63.5 ^ 5.9 0.004 VG (m/s) 2.31 ^ 0.22 2.55 ^ 0.15 0.011 V1mR (m/s) 21.57 ^ 0.13 21.73 ^ 0.13 0.013 UD (m) 2.29 ^ 0.33 2.62 ^ 0.35 0.046 Notes: Variables ranked by increasing p-value. Only variables for which p , 0.05 were reported.