TY - GEN A1 - Bestehorn, Michael A1 - Sharma, Deewakar A1 - Borcia, Rodica A1 - Amiroudine, Sakir T1 - Faraday instability of binary miscible/immiscible fluids with phase field approach T2 - Physical Review Fluids N2 - The objective in the present paper is to study binary fluids with phase field modeling coupled with Navier-Stokes equations. An extended free energy is proposed to account for the continuous path from immiscible to miscible states. We consider fluid pairs that are immiscible for temperatures below the critical one (consolute temperature) and miscible above it. Our extended phase field equation permits us to move from the immiscible state (governed by the Cahn-Hilliard equation) to the miscible state (defined by the species diffusion equation). The scaling of interface tension and interface width with the distance to the critical point is highlighted. The whole system is mechanically excited showing Faraday instability of a flat interface. A linear stability analysis is performed for the stable case (interface waves) as well as for the unstable Faraday one. For the latter, a Floquet analysis shows the well-known Arnold's tongues as a function of the consolute temperature and depth layer. Moreover, two-dimensional finite difference simulations have been performed allowing us to model nonlinear flow patterns both in miscible and immiscible phases. Linear theory and nonlinear simulations show interesting results such as the diminishing of the wavelength of Faraday waves or a shift of the critical vibration amplitude when the consolute temperature is approached. KW - Binary fluids KW - Hydrodynamic waves KW - Instability of free-surface flows KW - Surface tension effects Y1 - 2021 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.6.064002 U6 - https://doi.org/10.1103/PhysRevFluids.6.064002 SN - 2469-990X VL - 6 IS - 6 SP - 1 EP - 26 ER - TY - GEN A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Bestehorn, Michael A1 - Sharma, Deewakar A1 - Amiroudine, Sakir T1 - Phase field modeling in liquid binary mixtures: isothermal and non-isothermal problems T2 - Physical Review Fluids N2 - The objective in the present paper is to study binary fluids with phase field modeling coupled with Navier-Stokes equations. An extended free energy is proposed to account for the continuous path from immiscible to miscible states. We consider fluid pairs that are immiscible for temperatures below the critical one (consolute temperature) and miscible above it. Our extended phase field equation permits us to move from the immiscible state (governed by the Cahn-Hilliard equation) to the miscible state (defined by the species diffusion equation). The scaling of interface tension and interface width with the distance to the critical point is highlighted. The whole system is mechanically excited showing Faraday instability of a flat interface. A linear stability analysis is performed for the stable case (interface waves) as well as for the unstable Faraday one. For the latter, a Floquet analysis shows the well-known Arnold's tongues as a function of the consolute temperature and depth layer. Moreover, two-dimensional finite difference simulations have been performed allowing us to model nonlinear flow patterns both in miscible and immiscible phases. Linear theory and nonlinear simulations show interesting results such as the diminishing of the wavelength of Faraday waves or a shift of the critical vibration amplitude when the consolute temperature is approached. KW - Binary fluids KW - Drop coalescence KW - Drop interactions KW - Drops & bubbles KW - Microfluidics Y1 - 2022 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.064005 U6 - https://doi.org/10.1103/PhysRevFluids.7.064005 SN - 2469-990X VL - 7 IS - 6 SP - 1 EP - 19 ER - TY - GEN A1 - Bestehorn, Michael A1 - Oron, Alexander T1 - Hopf instability of a Rayleigh–Taylor unstable thin film heated from the gas side T2 - European Physical Journal Special Topics N2 - A thin liquid film located on the underside of a horizontal solid substrate can be stabilized by the Marangoni effect if the liquid is heated at its free surface. Applying long-wave approximation and projecting the velocity and temperature fields onto a basis of low-order polynomials, we derive a dimension-reduced set of three coupled evolution equations where nonlinearities of both the Navier–Stokes and the heat equation are included. We find that in a certain range of fluid parameters and layer depth, the first bifurcation from the motionless state is oscillatory which sets in with a finite but small wave number. The oscillatory branch is determined using a linear stability analysis of the long-wave model, but also by solving the linearized original hydrodynamic equations. Finally, numerical solutions of the reduced nonlinear model equations in three spatial dimensions are presented. Y1 - 2023 UR - https://epjst.epj.org/articles/epjst/abs/2023/04/11734_2023_Article_782/11734_2023_Article_782.html U6 - https://doi.org/10.1140/epjs/s11734-023-00782-z SN - 1951-6401 SN - 1951-6355 VL - 232 IS - 4 SP - 367 EP - 374 ER - TY - GEN A1 - Schön, Franz-Theo A1 - Harlander, Uwe A1 - Borcia, Ion Dan A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Mean fluid transport in an oscillating circular channel with asymmetric forcing T2 - Water waves : an interdisciplinary journal N2 - We investigate surface waves in an oscillating circular channel with local topography. The focus is on spatially or temporally breaking this dynamic system’s symmetry. Asymmetrical wave dynamics and a mean flux excitation are detected to varying degrees, depending on the two input parameters, fluid depth and the tank’s oscillation frequency. The fluid resonates around multiples of the fundamental eigenfrequency of the channel. The development of solitary wave-trains (undular bores) is observed in these resonance bands. A particle image velocimetry system measures the velocity field in the vertical plane of the free surface flow. Moreover, we are using 17 evenly distributed ultrasonic sensors to measure the surface displacement. This makes it possible to find out how strongly the mean flux depends on the resonance frequencies and to study the influence of the surface waves on the symmetry breaking. A numerical long-wave model helps to isolate the various factors influencing the mean flux. Y1 - 2025 U6 - https://doi.org/10.1007/s42286-025-00121-w SN - 2523-3688 VL - 2025 SP - 1 EP - 21 PB - Birkhäuser, part of Springer Nature CY - Basel ER -