Papers by Aline Lefebvre-Lepot
We consider here a discrete system of spheres interacting through a lubrication force. This force... more We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation.
Computing optimal Strokes for Low Reynolds Number Swimmers
The IMA Volumes in Mathematics and its Applications, 2012
We discuss connections between low-Reynolds-number swimming and geometric control theory, and pre... more We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.
Confluentes Mathematici, 2010
We are interested in existence results for second order differential inclusions, involving finite... more We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal normal cone to a time-dependent set. In order to prove these existence results, we study an extension of the numerical scheme introduced in [8] and prove a convergence result for this scheme.
We present a way to handle contacts between rigid particles in shear flow. The influence of such ... more We present a way to handle contacts between rigid particles in shear flow. The influence of such a modeling is shown by studying an example with 13 particles in 3D. Studying a concentrated suspension in 2D, we demonstrate that contact modelling as well as choice of boundary conditions influences the macroscopic properties of the suspension.
ESAIM: Proceedings, 2009
We simulate the sedimentation in a parallelepipedic container of spheres and nonconvex particles ... more We simulate the sedimentation in a parallelepipedic container of spheres and nonconvex particles constituted by two overlapping spheres. We use the self-written code SCoPI. Thanks to an efficient handling of contacts between particles, it allowed us to consider up to 100, 000 spheres and 10, 000 nonconvex particles. The packing fraction (in bulk and close to a wall) as well as the mean value and the distribution of contacts of the final packings are reported. The results obtained for the classical case of spherical particles (packing fraction: 63.7%, mean number of contacts: 6) are in agreement with previous studies and validate the algorithm. The packing fraction for nonconvex particles increases and then decreases with respect to the aspect ratio, which is similar to the ellipsoid (convex) case. The number of contacts is different from the number of neighbours, which is of course never the case for spherical particles (convex particles). The number of contacts is discontinuous when slightly increasing the aspect ratio from the spherical case: it is equal to 6 in the spherical case and to 10 in the nonconvex case. These values correspond to the isocounting values, i.e. the number of contacts is twice the number of degrees of freedom. This contrasts with the ellipsoid case, where it sharply but continuously increases. Concerning the number of neighbours, it continuously increases for small aspect ratio (which is similar to the convex particle case), but decreases for higher aspect ratio.
ESAIM: Proceedings, 2009
We consider the problem of swimming at low Reynolds numbers. This is the relevant asymptotic for ... more We consider the problem of swimming at low Reynolds numbers. This is the relevant asymptotic for micro-and nano-robots needing to navigate in an aqueous medium. As a model, we propose a robot composed of three balls. The relative positions of these balls can change according to three degrees of freedom. We prove that this robot is able to navigate in a plane by modifying the conformation of its shape.
Revue européenne de mécanique numérique, 2010
This paper focuses on improving the description of the contact between solid particles in a fluid... more This paper focuses on improving the description of the contact between solid particles in a fluid flow. The numerical approach used is related to the fictitious domain method for the fluid-solid problem. It is associated to a gluey particle model in order to improve the behaviour of the particles during their contacts as a Lagrangian method is applied for their displacement. The numerical methodology is validated through 2D and 3D computations describing interactions of two particles in a shear flow. The results obtained show the ability of the scheme to recover the reversibility of the Stokes equations, even for 3D configurations. Finally, another example is studied with larger number of particles.
Discrete and Continuous Dynamical Systems - Series B, 2013
We study self propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, ... more We study self propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow's theorem in an analytic framework, similarly to what has been done in for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically the analyticity result given in and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.
Esaim: Proceedings, 2009
We consider the problem of swimming at low Reynolds numbers. This is the relevant asymptotic for ... more We consider the problem of swimming at low Reynolds numbers. This is the relevant asymptotic for micro-and nano-robots needing to navigate in an aqueous medium. As a model, we propose a robot composed of three balls. The relative positions of these balls can change according to three degrees of freedom. We prove that this robot is able to navigate in a plane by modifying the conformation of its shape.
International Journal for Numerical Methods in Fluids, 2014
The aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting wit... more The aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting with a newtonian fluid. The inextensible membrane is modeled by a chain of circular rigid particles which are maintained in cohesion by using two different type of forces. First, a spring force is imposed between neighboring particles in the chain. Second, in order to model the bending of the membrane, each triplet of successive particles is submitted to an angular force.
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Papers by Aline Lefebvre-Lepot