Instytut Podstawowych Problemów Techniki

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We analyze the three-dimensional (3D) buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Péclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal character of the full 3D spectral problem for a small perturbation of a thin filament from a straight position of arbitrary orientation. We use the eigenvalues and eigenfunctions for the linearized elastica equation in the shear plane, found earlier by Liu et al. [Phys. Rev. Fluids 9, 014101 (2024)] with the Chebyshev spectral collocation method, to solve the full 3D eigenproblem. We provide a simple analytic approximation of the eigenfunctions, represented as Gaussian wave packets. As the main result of the paper, we derive the square-root dependence of the eigenfunction wave number on the parameter χ˜ = −η sin 2φ sin2 θ, where

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The long-time behavior of highly elastic fibers in a shear flow is investigated experimentally and numerically. Characteristic attractors of the dynamics are found. It is shown that for a small ratio of bending to hydrodynamic forces, most fibers form a spinning elongated double helix, performing an effective Jeffery orbit very close to the vorticity direction. Recognition of these oriented shapes, and how they form in time, may prove useful in the future for understanding the time history of complex microstructures in fluid flows and considering processing steps for their synthesis.

Słowa kluczowe:

Stokes equations, shear flow, elastic fibers

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Streszczenie:

We present the spectral analysis of three-dimensional dynamics of an elastic filament in a shear flow of a viscous fluid at a low Reynolds number in the absence of Brownian motion. The elastica model is used. The fiber initially is almost straight at an arbitrary orientation, with small perpendicular perturbations in the shear plane and out-of-plane. To analyze the stability of both perturbations, equations for the eigenvalues and eigenfunctions are derived and solved by the Chebyshev spectral collocation method. It is shown that their crucial features are the same as in the case of the two-dimensional elastica dynamics in shear flow [Becker and Shelley, Phys. Rev. Lett. 87, 198301 (2001)] and the three-dimensional elastica dynamics in the compressional flow [Chakrabarti et al., Nat. Phys. 16, 689 (2020)]. We find a similar dependence of the buckled shapes on the ratio of bending to hydrodynamic forces as in the simulations for elastic fibers of a nonzero thickness [Słowicka et al., New J. Phys. 24, 013013 (2022)].

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The hydrostatic bearing is the core component of ultra-precision computer numerical control (CNC) machine tools. Because the temperature rise in the oil film of hydrostatic bearings seriously affects the working accuracy of the bearings, it is important to study the flow and heat transfer characteristics of the oil film. Based on the physical model of an incompressible viscous fluid flowing in a flat microfluidic boundary layer, velocity, temperature and heat flux distribution equations of oil film are constructed by theories of heat transfer and hydrodynamics. Then, the effects of several parameters on velocity distribution, temperature distribution and heat flux distribution are analyzed, such as the upper plate velocity, the channel length, and so on. The results show that the dimensionless velocity of the oil film decreases with the increase in the upper plate velocity and the channel length. The oil film temperature distribution can be divided into three zones: the increasing zone, stabilizing zone and decreasing zone. The heat flux decreases linearly with the increase in the plate thickness, and increases linearly with the increase in the temperature difference.

Słowa kluczowe:

microfluidic boundary layer,hydrostatic oil film,velocity,temperature,heat flux

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A study is reported on modeling a laminar viscoelastic wake flow in intermediate and far regions behind a cylinder by the matched asymptotic expansion method. With the Oldroyd-B model chosen as the constitutive model, a globally valid, composite, reduced-order solution is constructed up to the third order. When viscoelasticity is disabled in the model, the resultant solution to the Newtonian flow can be favorably compared with previous experimental, analytical, and numerical investigations. Results show that the elastic effect begins to surface at the third order in our expansion scheme. For the flow field, the model predicts that the viscoelasticity has a positive effect on the growth of the longitudinal velocity and that the viscosity ratio has a negative effect. As the inertial effect increases, the longitudinal velocity increases. The elastic effects exerting on the vorticity distribution in the wake flow are also predicted by the theoretical model. For the conformation tensor field, the model dictates that a larger elastic effect leads to a greater extension of the polymer molecules, but predicts no influence of the viscosity ratio on the polymer extension because the solutions are only expanded till the third order. The reduced-order solutions establish a theoretical guidance for the complex viscoelastic wake flow, which is beneficial for the investigation of the drag reduction in the viscoelastic wake flow past a bluff body.

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Hydrophilicity/hydrophobicity is a common physical property of the material. Water droplets roll on lotus leaf, and a lot of dust and dirt on the surface of the lotus leaf will be taken away, playing a certain cleaning role. The hydrophobic surface has drag reduction effect that would produce slip on the hydrophobic wall. There are some studies on hydrophilicity/hydrophobicity in channels, most of which focus on the effect of surface drag reduction and heat transfer on microchannels. However, few people pay attention to the effect of the hydrophilicity/hydrophobicity of the injector inner wall on the atomization performance. In this paper, three groups of the open-end swirl injector with different tangential channels were designed to study the effect of hydrophilicity/hydrophobicity on atomization performance. The hydrophobic coating was prepared and used on the inner wall of the injector, and the atomization experimental system was built. In the experiment, the liquid film thickness was measured using the conductance method. Details of the liquid film breakup and spray development were recorded with a high-speed camera. The average droplet diameter was measured by the Malvern particle size analyzer. The atomization performance of injectors with different tangential channels on the hydrophilicity/hydrophobicity was compared, and the effect of the velocity profile on the jet stability is discussed.

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Streszczenie:

Stokes equations, Euler-Bernoulli beam, elastica, elastic filament, shear flow, buckling

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