arXiv subjects

I. Karlin

Publications and source records attributed to I. Karlin.

5 recordsLinked to original sources

arXiv2026

Effects of anisotropic confinement on droplet rebound from superhydrophobic surfaces

On flat superhydrophobic surfaces, droplet rebound is well described by a single inertio-capillary time scale, yielding a contact-time that is independent of impact energy. This single-mode response reflects the radial symmetry of flat-plate impacts. We demonstrate that an anisotropic geometric constraint, imposing a fixed spreading length along one axis, breaks this degeneracy and splits the rebound into a reciprocal pair of inertio-capillary modes. The fixed length also couples the contact-time to the Weber-dependent maximum spread, introducing an impact-energy dependence absent on the flat plate. We realize this constraint with grooved substrates, simulated using a non-ideal, entropic, multiple-relaxation-time lattice Boltzmann method and validated against the experiments of Chantelot et al. Extending their blob model from a single transverse scale to the reciprocal pair, we organize both modes through a geometric blob number and relate their time scales to the Weber number and groove width. We show that on non-wetting grooves the reciprocal modes are recovered directly, and explore the effects of finite wall affinity, using competition between the two modes to explain an observed two-branch structure in the contact-time response on mildly wetting, superhydrophobic grooves. Predictions tied to global energy balance reproduce cleanly across all conditions, while those tied to the details of the droplet's spread morphology are approximate but directionally correct. These results show that anisotropic confinement turns contact-time reduction from a question of accelerating a single rebound mode into one of selecting between conjugate inertio-capillary modes.

physics.flu-dyn↗

arXiv2023

Lattice Boltzmann methods for combustion applications

The lattice Boltzmann method, after close to thirty years of presence in computational fluid dynamics has turned into a versatile, efficient and quite popular numerical tool for fluid flow simulations. The lattice Boltzmann method owes its popularity in the past decade to its efficiency, low numerical dissipation and simplicity of its algorithm. Progress in recent years has opened the door for yet another very challenging area of application: Combustion simulations. Combustion is known to be a challenge for numerical tools due to, among many others, the large number of variables and scales both in time and space, leading to a stiff multi-scale problem. In the present work we present a comprehensive overview of models and strategies developed in the past years to model combustion with the lattice Boltzmann method and discuss some of the most recent applications, remaining challenges and prospects.

physics.flu-dyn↗

arXiv2013

Hilbert's 6th Problem: Exact and Approximate Hydrodynamic Manifolds for Kinetic Equations

The problem of the derivation of hydrodynamics from the Boltzmann equation and related dissipative systems is formulated as the problem of slow invariant manifold in the space of distributions. We review a few instances where such hydrodynamic manifolds were found analytically both as the result of summation of the Chapman--Enskog asymptotic expansion and by the direct solution of the invariance equation. These model cases, comprising Grad's moment systems, both linear and nonlinear, are studied in depth in order to gain understanding of what can be expected for the Boltzmann equation. Particularly, the dispersive dominance and saturation of dissipation rate of the exact hydrodynamics in the short-wave limit and the viscosity modification at high divergence of the flow velocity are indicated as severe obstacles to the resolution of Hilbert's 6th Problem. Furthermore, we review the derivation of the approximate hydrodynamic manifold for the Boltzmann equation using Newton's iteration and avoiding smallness parameters, and compare this to the exact solutions. Additionally, we discuss the problem of projection of the Boltzmann equation onto the approximate hydrodynamic invariant manifold using entropy concepts. Finally, a set of hypotheses is put forward where we describe open questions and set a horizon for what can be derived exactly or proven about the hydrodynamic manifolds for the Boltzmann equation in the future.

math-ph↗

arXiv2013

Ultrarelativistic Transport Coefficients in Two Dimensions

We compute the shear and bulk viscosities, as well as the thermal conductivity of an ultrarelativistic fluid obeying the relativistic Boltzmann equation in 2+1 space-time dimensions. The relativistic Boltzmann equation is taken in the single relaxation time approximation, based on two approaches, the first, due to Marle and using the Eckart decomposition, and the second, proposed by Anderson and Witting and using the Landau-Lifshitz decomposition. In both cases, the local equilibrium is given by a Maxwell-Juettner distribution. It is shown that, apart from slightly different numerical prefactors, the two models lead to a different dependence of the transport coefficients on the fluid temperature, quadratic and linear, for the case of Marle and Anderson-Witting, respectively. However, by modifying the Marle model according to the prescriptions given in Ref.[1], it is found that the temperature dependence becomes the same as for the Anderson-Witting model.

cond-mat.stat-mech↗

arXiv2013

Relativistic Lattice Boltzmann Model with Improved Dissipation

We develop a relativistic lattice Boltzmann (LB) model, providing a more accurate description of dissipative phenomena in relativistic hydrodynamics than previously available with existing LB schemes. The procedure applies to the ultra-relativistic regime, in which the kinetic energy (temperature) far exceeds the rest mass energy, although the extension to massive particles and/or low temperatures is conceptually straightforward. In order to improve the description of dissipative effects, the Maxwell-Juettner distribution is expanded in a basis of orthonormal polynomials, so as to correctly recover the third order moment of the distribution function. In addition, a time dilatation is also applied, in order to preserve the compatibility of the scheme with a cartesian cubic lattice. To the purpose of comparing the present LB model with previous ones, the time transformation is also applied to a lattice model which recovers terms up to second order, namely up to energy-momentum tensor. The approach is validated through quantitative comparison between the second and third order schemes with BAMPS (the solution of the full relativistic Boltzmann equation), for moderately high viscosity and velocities, and also with previous LB models in the literature. Excellent agreement with BAMPS and more accurate results than previous relativistic lattice Boltzmann models are reported.

physics.comp-ph↗