A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number

This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.Comment: 41 pages, 15 figure

Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method

We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection ($10^4-10 ^5$) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.Comment: 37 pages, 21 figure

Light scattering from cold rolled aluminum surfaces

We present experimental light scattering measurements from aluminum surfaces obtained by cold rolling. We show that our results are consistent with a scale invariant description of the roughness of these surfaces. The roughness parameters that we obtain from the light scattering experiment are consistent with those obtained from Atomic Force Microscopy measurements

Symmetry breaking and electrostatic attraction between two identical surfaces

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.By allowing the surface charge of one surface to affect the adsorption equilibrium of the other, we establish the existence of a long-range attractive interaction between two identical surfaces in an electrolyte containing polyvalent counter ions with a mean-field Poisson-Boltzmann approach. A Stern electrostatic condition from linearization of the mass-action adsorption isotherm is used to capture how polyvalent ion condensation affects and reverses the surface charge. We furthermore establish a direct mapping between this Stern layer conditions and previously derived modified Mean-field formulations associated with correlated fluctuations theory. For a sufficiently potential-sensitive isotherm, antisymmetric charge inversion can occur to produce an attractive force that increases with decreasing ionic strengths. Analyses of a mass-action isotherm produce force-separation relations, including an exponential far-field force decay distinct but consistent with previously proposed correlated fluctuation theories, and in quantitative agreement with experimental data

Blood pressure distribution in microvascular networks

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Blood rheology is complex and nonlinear. The effective viscosity variations are important due to red blood cells packing inside capillaries, the socalled FåhræusLindquist effect, whilst concomitantly phase segregation appears in bifurcations. We have performed direct numerical simulations of different nonlinear rheological models of the blood on realistic threedimensional microvascular networks. These simulations point out two significant results. First, various rheological models lead to very similar pressure distributions over the whole range of physiologically relevant hematocrits. Secondly, different models for phase segregation lead to very distinct hematocrit distributions in the microvascular network. Moreover, for all the investigated rheological models, the hematocrit distribution very weakly affects the pressure distribution, when prescribing uniform pressure boundary conditions.The research was supported by GDR n° 2760 Biomécanique des fluides et des transferts Interaction fluide/structure biologique, the ASUPS A03 and A05 of Paul Sabatier University, Toulouse, France and the ANR project ANR06BLAN023801

Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization

Stress condensation in crushed elastic manifolds

We discuss an M-dimensional phantom elastic manifold of linear size L crushed into a small sphere of radius R << L in N-dimensional space. We investigate the low elastic energy states of 2-sheets (M=2) and 3-sheets (M=3) using analytic methods and lattice simulations. When N \geq 2M the curvature energy is uniformly distributed in the sheet and the strain energy is negligible. But when N=M+1 and M>1, both energies appear to be condensed into a network of narrow M-1 dimensional ridges. The ridges appear straight over distances comparable to the confining radius R.Comment: 4 pages, RevTeX + epsf, 4 figures, Submitted to Phys. Rev. Let

Mechanical Integrity of 3D Rough Surfaces during Contact

Rough surfaces are in contact locally by the peaks of roughness. At this local scale, the pressure of contact can be sharply superior to the macroscopic pressure. If the roughness is assumed to be a random morphology, a well-established observation in many practical cases, mechanical indicators built from the contact zone are then also random variables. Consequently, the probability density function (PDF) of any mechanical random variable obviously depends upon the morphological structure of the surface. The contact pressure PDF, or the probability of damage of this surface can be determined for example when plastic deformation occurs. In this study, the contact pressure PDF is modeled using a particular probability density function, the generalized Lambda distributions (GLD). The GLD are generic and polymorphic. They approach a large number of known distributions (Weibull, Normal, and Lognormal). The later were successfully used to model damage in materials. A semi-analytical model of elastic contact which takes into account the morphology of real surfaces is used to compute the contact pressure. In a first step, surfaces are simulated by Weierstrass functions which have been previously used to model a wide range of surfaces met in tribology. The Lambda distributions adequacy is qualified to model contact pressure. Using these functions, a statistical analysis allows us to extract the probability density of the maximal pressure. It turns out that this density can be described by a GLD. It is then possible to determine the probability that the contact pressure generates plastic deformation

Permeability Estimates of Self-Affine Fracture Faults Based on Generalization of the Bottle Neck Concept

We propose a method for calculating the effective permeability of two-dimensional self-affine permeability fields based on generalizing the one-dimensional concept of a bottleneck. We test the method on fracture faults where the local permeability field is given by the cube of the aperture field. The method remains accurate even when there is substantial mechanical overlap between the two fracture surfaces. The computational efficiency of the method is comparable to calculating a simple average and is more than two orders of magnitude faster than solving the Reynolds equations using a finite-difference scheme