https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Mon, 13 Jul 2026 06:59:26 GMT 2026-07-13T06:59:26Z http://hdl.handle.net/10985/24485 Coherent Particle Structures in High-Prandtl-Number Liquid Bridges BARMAK, Ilya; ROMANO, Francesco; KANNAN, Parvathy Kunchi; KUHLMANN, Hendrik C. Clustering of small rigid spherical particles into particle accumulation structures (PAS) is studied numerically for a high-Prandtl-number (Pr = 68) thermocapillary liquid bridge. The one-way-coupling approach is used for calculation of the particle motion, modeling PAS as an attractor for a single particle. The attractor is created by dissipative forces acting on the particle near the boundary due to the finite size of the particle. These forces can dramatically deflect the particle trajectory from a fluid pathline and transfer it to certain tubular flow structures, called Kolmogorov–Arnold–Moser (KAM) tori, in which the particle is focused and from which it might not escape anymore. The transfer of particles can take place if a KAM torus, which is a property of the flow without particles, enters the narrow boundary layer on the flow boundaries in which the particle experiences extra forces. Since the PAS obtained in this system depends mainly on the finite particle size, it can be classified as a finite-size coherent structure (FSCS). Mon, 01 Feb 2021 00:00:00 GMT http://hdl.handle.net/10985/24485 2021-02-01T00:00:00Z BARMAK, Ilya ROMANO, Francesco KANNAN, Parvathy Kunchi KUHLMANN, Hendrik C. Clustering of small rigid spherical particles into particle accumulation structures (PAS) is studied numerically for a high-Prandtl-number (Pr = 68) thermocapillary liquid bridge. The one-way-coupling approach is used for calculation of the particle motion, modeling PAS as an attractor for a single particle. The attractor is created by dissipative forces acting on the particle near the boundary due to the finite size of the particle. These forces can dramatically deflect the particle trajectory from a fluid pathline and transfer it to certain tubular flow structures, called Kolmogorov–Arnold–Moser (KAM) tori, in which the particle is focused and from which it might not escape anymore. The transfer of particles can take place if a KAM torus, which is a property of the flow without particles, enters the narrow boundary layer on the flow boundaries in which the particle experiences extra forces. Since the PAS obtained in this system depends mainly on the finite particle size, it can be classified as a finite-size coherent structure (FSCS). http://hdl.handle.net/10985/24322 Attractors for the motion of a finite-size particle in a cuboidal lid-driven cavity WU, Haotian; ROMANO, Francesco; KUHLMANN, Hendrik C. The motion of a finite-size particle in the cuboidal lid-driven cavity flow is investigated experimentally for Reynolds numbers 100 and 200 for which the flow is steady. These steady three-dimensional flows exhibit chaotic and regular streamlines, where the latter are confined to Kolmogorov–Arnold–Moser (KAM) tori. The interaction between the moving wall and the particle creates global particle attractors. For neutrally buoyant particles, these attractors are periodic or quasi-periodic, strongly attracting and located in or near KAM tori of the flow. As the density mismatch between particle and fluid increases, buoyancy and inertia become important, and the attractors evolve from those for neutrally buoyant particles, changing their shape, position and attraction rates. Sun, 01 Jan 2023 00:00:00 GMT http://hdl.handle.net/10985/24322 2023-01-01T00:00:00Z WU, Haotian ROMANO, Francesco KUHLMANN, Hendrik C. The motion of a finite-size particle in the cuboidal lid-driven cavity flow is investigated experimentally for Reynolds numbers 100 and 200 for which the flow is steady. These steady three-dimensional flows exhibit chaotic and regular streamlines, where the latter are confined to Kolmogorov–Arnold–Moser (KAM) tori. The interaction between the moving wall and the particle creates global particle attractors. For neutrally buoyant particles, these attractors are periodic or quasi-periodic, strongly attracting and located in or near KAM tori of the flow. As the density mismatch between particle and fluid increases, buoyancy and inertia become important, and the attractors evolve from those for neutrally buoyant particles, changing their shape, position and attraction rates. http://hdl.handle.net/10985/24504 MaranStable: A linear stability solver for multiphase flows in canonical geometries STOJANOVIĆ, Mario; ROMANO, Francesco; KUHLMANN, Hendrik C. MaranStable is a software to perform three-dimensional linear stability analyses of steady two-dimensional non-isothermal multiphase flows in canonical geometries. Different approximations to the Navier–Stokes equations can be selected, which are discretized by finite volumes on a staggered grid. The stability of the basic flow, obtained by Newton—Raphson iteration, is computed by solving the linearized three-dimensional perturbation equations using normal modes. All calculations are based on Matlab and make extensive use of the already parallelized backslash and eigs operators, and the graphical user interface eases the access to MaranStable. Sat, 01 Jul 2023 00:00:00 GMT http://hdl.handle.net/10985/24504 2023-07-01T00:00:00Z STOJANOVIĆ, Mario ROMANO, Francesco KUHLMANN, Hendrik C. MaranStable is a software to perform three-dimensional linear stability analyses of steady two-dimensional non-isothermal multiphase flows in canonical geometries. Different approximations to the Navier–Stokes equations can be selected, which are discretized by finite volumes on a staggered grid. The stability of the basic flow, obtained by Newton—Raphson iteration, is computed by solving the linearized three-dimensional perturbation equations using normal modes. All calculations are based on Matlab and make extensive use of the already parallelized backslash and eigs operators, and the graphical user interface eases the access to MaranStable. http://hdl.handle.net/10985/24488 Stokesian motion of a spherical particle near a right corner made by tangentially moving walls ROMANO, Francesco; DES BOSCS, Pierre-Emmanuel; KUHLMANN, Hendrik C. The slow motion of a small buoyant sphere near a right dihedral corner made by tangentially sliding walls is investigated. Under creeping-flow conditions the force and torque on the sphere can be decomposed into eleven elementary types of motion involving simple particle translations, particle rotations and wall movements. Force and torque balances are employed to find the velocity and rotation of the particle as functions of its location. Depending on the ratio of the wall velocities and the gravitational settling velocity of the sphere, different dynamical regimes are identified. In particular, a non-trivial line attractor/repeller for the particle motion exists at a location detached from both the walls. The existence, location and stability of the corresponding two-dimensional fixed point are studied depending on the wall velocities and the buoyancy force. The impact of the line attractors/repellers on the motion of small particles in cavities and its relevance for corner cleaning applications are discussed. Wed, 01 Sep 2021 00:00:00 GMT http://hdl.handle.net/10985/24488 2021-09-01T00:00:00Z ROMANO, Francesco DES BOSCS, Pierre-Emmanuel KUHLMANN, Hendrik C. The slow motion of a small buoyant sphere near a right dihedral corner made by tangentially sliding walls is investigated. Under creeping-flow conditions the force and torque on the sphere can be decomposed into eleven elementary types of motion involving simple particle translations, particle rotations and wall movements. Force and torque balances are employed to find the velocity and rotation of the particle as functions of its location. Depending on the ratio of the wall velocities and the gravitational settling velocity of the sphere, different dynamical regimes are identified. In particular, a non-trivial line attractor/repeller for the particle motion exists at a location detached from both the walls. The existence, location and stability of the corresponding two-dimensional fixed point are studied depending on the wall velocities and the buoyancy force. The impact of the line attractors/repellers on the motion of small particles in cavities and its relevance for corner cleaning applications are discussed. http://hdl.handle.net/10985/24324 Stability of thermocapillary flow in liquid bridges fully coupled to the gas phase STOJANOVIĆ, Mario; ROMANO, Francesco; KUHLMANN, Hendrik C. The linear stability of the axisymmetric steady thermocapillary flow in a liquid bridge made from 2 cSt silicone oil (Prandtl number 28) is investigated numerically in the framework of the Boussinesq approximation. The flow and temperature fields in the surrounding gas phase (air) are taken into account for a generic cylindrical container hosting the liquid bridge. The flows in the liquid and in the gas are fully coupled across the hydrostatically deformed liquid–gas interface, neglecting dynamic interface deformations. Originating from a common reference case, the linear stability boundary is computed varying the length of the liquid bridge (aspect ratio), its volume and the gravity level, providing accurate critical data. The qualitative dependence of the critical threshold on these parameters is explained in terms of the characteristics of the critical mode. The heat exchange between the ambient gas and the liquid bridge that is fully resolved has an important influence on the critical conditions. Thu, 01 Sep 2022 00:00:00 GMT http://hdl.handle.net/10985/24324 2022-09-01T00:00:00Z STOJANOVIĆ, Mario ROMANO, Francesco KUHLMANN, Hendrik C. The linear stability of the axisymmetric steady thermocapillary flow in a liquid bridge made from 2 cSt silicone oil (Prandtl number 28) is investigated numerically in the framework of the Boussinesq approximation. The flow and temperature fields in the surrounding gas phase (air) are taken into account for a generic cylindrical container hosting the liquid bridge. The flows in the liquid and in the gas are fully coupled across the hydrostatically deformed liquid–gas interface, neglecting dynamic interface deformations. Originating from a common reference case, the linear stability boundary is computed varying the length of the liquid bridge (aspect ratio), its volume and the gravity level, providing accurate critical data. The qualitative dependence of the critical threshold on these parameters is explained in terms of the characteristics of the critical mode. The heat exchange between the ambient gas and the liquid bridge that is fully resolved has an important influence on the critical conditions. http://hdl.handle.net/10985/24482 Instability of axisymmetric flow in thermocapillary liquid bridges: Kinetic and thermal energy budgets for two-phase flow with temperature-dependent material properties STOJANOVIĆ, Mario; ROMANO, Francesco; KUHLMANN, Hendrik C. In numerical linear stability investigations, the rates of change of the kinetic and thermal energy of the perturbation flow are often used to identify the dominant mechanisms by which kinetic or thermal energy is exchanged between the basic and the perturbation flow. Extending the conventional energy analysis for a single-phase Boussinesq fluid, the energy budgets of arbitrary infinitesimal perturbations to the basic two-phase liquid–gas flow are derived for an axisymmetric thermocapillary bridge when the material parameters in both phases depend on the temperature. This allows identifying individual transport terms and assessing their contributions to the instability if the basic flow and the critical mode are evaluated at criticality. The full closed-form energy budgets of linear modes have been derived for thermocapillary two-phase flow taking into account the temperature dependence of all thermophysical parameters. The influence of different approximations to the temperature dependence on the linear stability boundary of the axisymmetric flow in thermocapillary liquid bridges is tested regarding their accuracy. The general mechanism of symmetry breaking turns out to be very robust. Sat, 01 Jul 2023 00:00:00 GMT http://hdl.handle.net/10985/24482 2023-07-01T00:00:00Z STOJANOVIĆ, Mario ROMANO, Francesco KUHLMANN, Hendrik C. In numerical linear stability investigations, the rates of change of the kinetic and thermal energy of the perturbation flow are often used to identify the dominant mechanisms by which kinetic or thermal energy is exchanged between the basic and the perturbation flow. Extending the conventional energy analysis for a single-phase Boussinesq fluid, the energy budgets of arbitrary infinitesimal perturbations to the basic two-phase liquid–gas flow are derived for an axisymmetric thermocapillary bridge when the material parameters in both phases depend on the temperature. This allows identifying individual transport terms and assessing their contributions to the instability if the basic flow and the critical mode are evaluated at criticality. The full closed-form energy budgets of linear modes have been derived for thermocapillary two-phase flow taking into account the temperature dependence of all thermophysical parameters. The influence of different approximations to the temperature dependence on the linear stability boundary of the axisymmetric flow in thermocapillary liquid bridges is tested regarding their accuracy. The general mechanism of symmetry breaking turns out to be very robust. http://hdl.handle.net/10985/24487 Attractors for the motion of a finite-size particle in a two-sided lid-driven cavity WU, Haotian; ROMANO, Francesco; KUHLMANN, Hendrik C. The motion of a single spherical particle in a two-sided lid-driven cavity is investigated experimentally. The flow in which the particle moves is created by two facing cavity sidewalls which move with equal velocity in opposite directions. For a long cavity with width-to-height cross-sectional aspect ratio Γ=W/H=1.6 the flow field at Reynolds number Re=400 consists of steady spatially periodic three-dimensional convection cells. Nearly neutrally buoyant particles with radius in units of H ranging from 1.1×10−2 to 7.1×10−2 are found to be attracted to periodic or quasi-periodic orbits in close vicinity of Kolmogorov–Arnold–Moser (KAM) tori of the unperturbed flow. Like the KAM tori the attractors of neutrally buoyant particles arise in mirror-symmetric pairs within each convection cell. The particle attractors are created by a dissipative effect in the dynamical system describing the particle motion which arises when the finite-size particle closely passes the moving walls. When the particle density deviates from that of the fluid, inertial attractors arise whose symmetry is broken by buoyancy, and other periodic attractors are created which do not have KAM tori as counterparts. Sun, 01 Nov 2020 00:00:00 GMT http://hdl.handle.net/10985/24487 2020-11-01T00:00:00Z WU, Haotian ROMANO, Francesco KUHLMANN, Hendrik C. The motion of a single spherical particle in a two-sided lid-driven cavity is investigated experimentally. The flow in which the particle moves is created by two facing cavity sidewalls which move with equal velocity in opposite directions. For a long cavity with width-to-height cross-sectional aspect ratio Γ=W/H=1.6 the flow field at Reynolds number Re=400 consists of steady spatially periodic three-dimensional convection cells. Nearly neutrally buoyant particles with radius in units of H ranging from 1.1×10−2 to 7.1×10−2 are found to be attracted to periodic or quasi-periodic orbits in close vicinity of Kolmogorov–Arnold–Moser (KAM) tori of the unperturbed flow. Like the KAM tori the attractors of neutrally buoyant particles arise in mirror-symmetric pairs within each convection cell. The particle attractors are created by a dissipative effect in the dynamical system describing the particle motion which arises when the finite-size particle closely passes the moving walls. When the particle density deviates from that of the fluid, inertial attractors arise whose symmetry is broken by buoyancy, and other periodic attractors are created which do not have KAM tori as counterparts. http://hdl.handle.net/10985/24423 Finite-size coherent particle structures in high-Prandtl-number liquid bridges BARMAK, Ilya; ROMANO, Francesco; KUHLMANN, Hendrik C. The transport of liquid and of small rigid spherical particles in a high-Prandtl-number (Pr = 68) thermocapillary liquid bridge under zero gravity is studied by highly resolved numerical simulations when the flow arises as an azimuthally traveling hydrothermal wave with azimuthal wave number one. The Langrangian transport of fluid elements reveals the coexistence of regular and chaotic streamlines in the frame of reference rotating with the wave. The structure of the KAM (Kolmogorov-Arnold-Moser) tori is unraveled for several Reynolds numbers for which the flow is periodic in time and space. Based on the streamline topology the segregation of small rigid spherical particles of a dilute suspension into particle accumulation structures (PASs) is studied, based on the steric finite-particle-size effect when the particles moves close to the free surface. It is shown that the intricate KAM structures have their counterparts in a multitude of different attractors for the particle motion. Examples of PASs are provided, and their dependence on particle size, particle-to-fluid density ratio, and Reynolds number are discussed. A large parametric study reveals the most probable combinations of particle size and density ratio which lead to particle clustering. Sun, 01 Aug 2021 00:00:00 GMT http://hdl.handle.net/10985/24423 2021-08-01T00:00:00Z BARMAK, Ilya ROMANO, Francesco KUHLMANN, Hendrik C. The transport of liquid and of small rigid spherical particles in a high-Prandtl-number (Pr = 68) thermocapillary liquid bridge under zero gravity is studied by highly resolved numerical simulations when the flow arises as an azimuthally traveling hydrothermal wave with azimuthal wave number one. The Langrangian transport of fluid elements reveals the coexistence of regular and chaotic streamlines in the frame of reference rotating with the wave. The structure of the KAM (Kolmogorov-Arnold-Moser) tori is unraveled for several Reynolds numbers for which the flow is periodic in time and space. Based on the streamline topology the segregation of small rigid spherical particles of a dilute suspension into particle accumulation structures (PASs) is studied, based on the steric finite-particle-size effect when the particles moves close to the free surface. It is shown that the intricate KAM structures have their counterparts in a multitude of different attractors for the particle motion. Examples of PASs are provided, and their dependence on particle size, particle-to-fluid density ratio, and Reynolds number are discussed. A large parametric study reveals the most probable combinations of particle size and density ratio which lead to particle clustering. http://hdl.handle.net/10985/24424 Lagrangian chaos in steady three-dimensional lid-driven cavity flow ROMANO, Francesco; TÜRKBAY, Tuǧçe; KUHLMANN, Hendrik C. Steady three-dimensional flows in lid-driven cavities are investigated numerically using a high-order spectral-element solver for the incompressible Navier–Stokes equations. The focus is placed on critical points in the flow field, critical limit cycles, their heteroclinic connections, and on the existence, shape, and dependence on the Reynolds number of Kolmogorov–Arnold–Moser (KAM) tori. In finite-length cuboidal cavities at small Reynolds numbers, a thin layer of chaotic streamlines covers all walls. As the Reynolds number is increased, the chaotic layer widens and the complementary KAM tori shrink, eventually undergoing resonances, until they vanish. Accurate data for the location of closed streamlines and of KAM tori are provided, both of which reach very close to the moving lid. For steady periodic Taylor–Görtler vortices in spanwise infinitely extended cavities with a square cross section, chaotic streamlines occupy a large part of the flow domain immediately after the onset of Taylor–Görtler vortices. As the Reynolds number increases, the remaining KAM tori vanish from the Taylor–Görtler vortices, while KAM tori grow in the central region further away from the solid walls. Wed, 01 Jul 2020 00:00:00 GMT http://hdl.handle.net/10985/24424 2020-07-01T00:00:00Z ROMANO, Francesco TÜRKBAY, Tuǧçe KUHLMANN, Hendrik C. Steady three-dimensional flows in lid-driven cavities are investigated numerically using a high-order spectral-element solver for the incompressible Navier–Stokes equations. The focus is placed on critical points in the flow field, critical limit cycles, their heteroclinic connections, and on the existence, shape, and dependence on the Reynolds number of Kolmogorov–Arnold–Moser (KAM) tori. In finite-length cuboidal cavities at small Reynolds numbers, a thin layer of chaotic streamlines covers all walls. As the Reynolds number is increased, the chaotic layer widens and the complementary KAM tori shrink, eventually undergoing resonances, until they vanish. Accurate data for the location of closed streamlines and of KAM tori are provided, both of which reach very close to the moving lid. For steady periodic Taylor–Görtler vortices in spanwise infinitely extended cavities with a square cross section, chaotic streamlines occupy a large part of the flow domain immediately after the onset of Taylor–Görtler vortices. As the Reynolds number increases, the remaining KAM tori vanish from the Taylor–Görtler vortices, while KAM tori grow in the central region further away from the solid walls.