BIRD, BCAM's Institutional Repository Data
http://bird.bcamath.org:80
The BIRD digital repository system captures, stores, indexes, preserves, and distributes digital research material.2019-01-16T14:00:47ZNormal lubrication force between spherical particles immersed in a shear-thickening fluid
http://hdl.handle.net/20.500.11824/912
Normal lubrication force between spherical particles immersed in a shear-thickening fluid
Vázquez-Quesada A.; Wagner N.J.; Ellero M.
In this work, the inverse bi-viscous model [Physics of Fluids 29, 103104 (2017)] is used to describe a shear-thickening fluid. An analytical velocity profile in a planar Poiseuille flow is utilized to calculate an approximate solution to the generalized lubrication force between two close spheres interacting hydrodynamically in such a medium. This approximate analytical expression is compared to the exact numerical solution.The flow topology of the shear-thickening transition within the interparticle gap is also shown and discussed in relation to the behaviour of the lubrication force. The present result can allow in the future to perform numerical simulations of dense particle suspensions immersed in a shear-thickening matrix based on an effective lubrication force acting between pairwise interacting particles. This model may find additional value in representing experimental systems consisting of suspensions in shear thickening media, polymer coated suspensions, and industrial systems such as concrete.
2018-12-07T00:00:00ZApparent slip mechanism between two spheres based on solvent rheology: Theory and implication for the shear thinning of non-Brownian suspensions
http://hdl.handle.net/20.500.11824/911
Apparent slip mechanism between two spheres based on solvent rheology: Theory and implication for the shear thinning of non-Brownian suspensions
Vázquez-Quesada A.; Español P.; Ellero M.
Analytical results for the apparent slip between two spheres in a simple biviscous model of a shear thinning fluid are presented. Velocity profiles and apparent slip lengths along the surfaces are analyzed in order to characterize the physical mechanism. It is shown that in this non-Newtonian model, the effect of shear-thinning limited to high-shear rates in the interstitial regions between close spheres can be alternatively interpreted as the onset of an apparent shear-rate dependent slippage effect. The results of the theory compare well with experiments from the literature showing the presence of surface slip on a particle approaching a planar wall. In terms of implications on suspensions rheology, the present results bridge the ’hidden’ solvent shear-thinning theory [A. Va ́zquez-Quesada et al. , Phys. Rev. Lett., 117, 108001-5 (2016)] with slip-based models presented recently in [M. Kroupa et al., Phys. Chem. Chem. Phys. 19, 5979-5984 (2017)] as a possible explanation on the mechanism behind the shear-thinning in hard-sphere non-Brownian suspensions.
2018-12-10T00:00:00ZA jacobian module for disentanglements and applications to Mond's conjecture
http://hdl.handle.net/20.500.11824/910
A jacobian module for disentanglements and applications to Mond's conjecture
Fernández de Bobadilla J.; Nuño Ballesteros J. J.; Peñafort Sanchis G.
Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$-module $M(g)$ with the property that $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, with equality if
$f$ is weighted homogeneous.
We also define a relative version $M_y(G)$ for unfoldings $F$, in such a way that $M_y(G)$ specialises to $M(g)$ when $G$ specialises to $g$. The main result is that if $(n,n+1)$ are
nice dimensions, then $\dim_\mathbb C M(g)\ge \mu_I(f)$, with equality if and only if $M_y(G)$ is Cohen-Macaulay, for some stable unfolding $F$. Here, $\mu_I(f)$ denotes the image
Milnor number of $f$, so that if $M_y(G)$ is Cohen-Macaulay, then Mond's conjecture holds for $f$; furthermore, if $f$ is weighted homogeneous, Mond's conjecture for $f$ is
equivalent to the fact that $M_y(G)$ is Cohen-Macaulay. Finally, we observe that to prove Mond's conjecture, it is enough to
prove it in a suitable family of examples.
2019-01-01T00:00:00ZA least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
http://hdl.handle.net/20.500.11824/909
A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
Petras A.; Ling L.; Piret C.; Ruuth S.J.
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. Recently, a closest point method with explicit time-stepping was proposed that uses finite differences derived from radial basis functions (RBF-FD). Here, we propose a least-squares implicit formulation of the closest point method to impose the constant-along-normal extension of the solution on the surface into the embedding space. Our proposed method is particularly flexible with respect to the choice of the computational grid in the embedding space. In particular, we may compute over a computational tube that contains problematic nodes. This fact enables us to combine the proposed method with the grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]) to obtain a numerical method for approximating PDEs on moving surfaces. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for advection-diffusion equations and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented.
2018-10-01T00:00:00Z