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Srboljub Simić

Publications and source records attributed to Srboljub Simić.

8 recordsLinked to original sources
arXiv2026

Constitutive Modelling of Korteweg Fluids Using Liu's Method

The paper studies constitutive modelling of Korteweg fluids. Thermodynamic consistency, i.e. compatibility with entropy balance law, is achieved using Liu's method of multipliers. Appropriate constitutive assumptions facilitated inclusion of the capillary effects in the specific entropy. Korteweg stresses are derived from the equilibrium conditions -- vanishing of the entropy production and its minimization in equilibrium. Material parameter in Korteweg stresses is allowed to depend on temperature, which turns out to be consistent with kinetic-theory results and leads to cross-coupling of mechanical and thermal effects. The generalized Gibbs' relation, which inherits the capillary effects, is derived as consequence, which is a peculiar feature of the Liu's method.

physics.flu-dyn↗
arXiv2025

Capillary Rise in Pipes with Variable Cross Section

This work proposes an ODE model for a capillary rise in pipes with variable cross section and compares it to the lubrication theory model. Two key assumptions are made: (1) radius of the pipe varies with axial coordinate, and (2) pipe's convergence angle is small. The model reduction process involves the identification of critical parameters and simplifies the governing equations by neglecting higher-order terms. Under appropriate scaling, it is shown that generalized Washburn's equation for capillary rise in pipes with variable cross section reduces to the known lubrication theory model.

physics.flu-dyn↗
arXiv2025

Modelling Capillary Rise with a Slip Boundary Condition: Well-posedness and Long-time Dynamics of Solutions to Washburn's Equation

The aim of this paper is to extend Washburn's capillary rise equation by incorporating a slip condition at the pipe wall. The governing equation is derived using fundamental principles from continuum mechanics. A new scaling is introduced, allowing for a systematic analysis of different flow regimes. We prove the global-in-time existence and uniqueness of a bounded positive solution to Washburn's equation that includes the slip parameter, as well as the continuous dependence of the solution in the maximum norm on the initial data. Thus, the initial-value problem for Washburn's equation is shown to be well-posed in the sense of Hadamard. Additionally, we show that the unique equilibrium solution may be reached either monotonically or in an oscillatory fashion, similarly to the no-slip case. Finally, we determine the basin of attraction for the system, ensuring that the equilibrium state will be reached from the initial data we impose. These results hold for any positive value of the nondimensional slip parameter in the model, and for all values of the ratio $h_0/h_e$ in the range $[0,3/2]$, where $h_0$ is the initial height of the fluid column and $h_e$ is its equilibrium height.

math.AP↗
arXiv2023

Energy method for the Boltzmann equation of monatomic gaseous mixtures

In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a global equilibrium is decomposed into the sum of a macroscopic and a microscopic part, for which we obtain a priori estimates at both lower and higher orders. These estimates are obtained under a suitable smallness assumption. The assumption can be justified a posteriori in the higher-order case, leading to the closure of the corresponding estimate.

math.AP↗
arXiv2020

Open mathematical aspects of continuum thermodynamics: hyperbolicity, boundaries and nonlinearities

Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for decades, their mathematical properties and consequences of the generalizations are less-known and are still of high interest in current researches. Therefore, we found it essential to collect the most important and still open mathematical questions related to different continuum thermodynamic approaches. First, we start with the example of Classical Irreversible Thermodynamics (CIT) in order to provide the basis for the more general and complex frameworks, such as the Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and Rational Extended Thermodynamics (RET). Here, we aim to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities. We present these properties and comparing the approach of NET-IV and RET to each other from these points of view.

cond-mat.stat-mech↗
arXiv2020

Non-equilibrium theories of rarefied gases: internal variables and extended thermodynamics

Limits of classical constitutive laws such as Fourier and Navier-Stokes equations are discovered since decades. However, the proper extensions -- generalizations of these are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely the kinetic theory-based Rational Extended Thermodynamics (RET) and non-equilibrium thermodynamics with internal variables (NET-IV). First, the paper starts with the case of rigid heat conductors summarizing the result achieved so far. Then a typical example of compressible bodies is shown by presenting the first generalization for rarefied gases, called Meixner's theory. It is further extended using generalized entropy current in the framework of NET-IV. It is shown how its structure is related to RET and how the compatibility between them can be acquired.

cond-mat.stat-mech↗
arXiv2016

Polyatomic gases with dynamic pressure: Maximum entropy principle and shock structure

This paper is concerned with the analysis of polyatomic gases within the framework of kinetic theory. Internal degrees of freedom are modeled using a single continuous variable corresponding to the molecular internal energy. Non-equilibrium velocity distribution function, compatible with macroscopic field variables, is constructed using the maximum entropy principle. A proper collision cross section is constructed which obeys the micro-reversibility requirement. The source term and entropy production rate are determined in the form which generalizes the results obtained within the framework of extended thermodynamics. They can be adapted to appropriate physical situations due to the presence of parameters. They are also compared with the results obtained using BGK approximation. For the proposed model the shock structure problem is thoroughly analyzed.

math-ph↗