Nonlinear Model of Ice Surface Softening during Friction Taking into Account Spatial Heterogeneity of Temperature
| Authors | A.V. Khomenko , D.T. Logvinenko, Ya.V. Khyzhnya |
| Affiliations |
Sumy State University, 2, Rymsky-Korsakov St., 40007 Sumy, Ukraine |
| Е-mail | |
| Issue | Volume 12, Year 2020, Number 4 |
| Dates | Received 18 June 2020; revised manuscript received 15 August 2020; published online 25 August 2020 |
| Citation | A.V. Khomenko, D.T. Logvinenko, Ya.V. Khyzhnya, J. Nano- Electron. Phys. 12 No 4, 04002 (2020) |
| DOI | https://doi.org/10.21272/jnep.12(4).04002 |
| PACS Number(s) | 05.65. + b, 05.70.Ln, 46.55. + d, 62.20.F –, 64.60. – i, 81.40.Pq |
| Keywords | Ice friction, Phase transition (6) , Rheology, Plasticity, Friction force, Shear strain and stress. |
| Annotation |
A nonlinear model of a viscoelastic medium is proposed, which describes softening of a thin layer of the ice surface during friction. The description of this transformation is based on the three following basic equations: the Kelvin-Voigt equation for a viscoelastic medium, the relaxation equations of Landau-Khalatnikov-type and for heat conductivity. It is revealed that mentioned equations coincide formally with the synergetic Lorenz system, where the order parameter is reduced to the shear strain, the stress acts as the conjugate field, and the temperature plays the role of the control parameter. The work further develops a nonlinear model of ice surface softening during friction, taking into account the spatial inhomogeneity of temperature in the equation of heat conductivity. In the framework of one-mode and adiabatic approximations an analytical soliton solution of a one-dimensional parabolic equation for the spatial normal distribution of shear strain to the ice surface is found. Due to the numerical solution of the one-dimensional Ginzburg-Landau differential equation, the distribution of friction force over the softened surface layer of ice is obtained and described. Two physical situations are considered: 1) the upper and lower surfaces move with equal velocities in opposite directions; 2) the upper surface is sheared along the fixed lower one. The coordinate dependencies of the friction force at different times are constructed and the evolution of the system to a stationary state is described. It is shown that the growth of time and background ice temperature leads to a sharper change of the friction force along the thickness of the premelted surface layer of ice, i.e. the relative shear velocity of the rubbing surfaces increases. |
|
List of References |
Other articles from this number
1) Fabrication and Characterization of Polyaniline Nanofiber Films by Various Techniques [04001-1-04001-5]2) Effect of Different Heat Treatment Regimes on Electrical Properties and Microstructure of n-Si [04003-1-04003-5]
3) Synthesis and Characterization of Temperature Controlled SnO2 Nanoparticles by Solid-state Reaction Method [04004-1-04004-6]
4) Simulation of Fracture Dynamics of Two-dimensional Titanium Carbide Ti2C under Different Types of Tensile Loading [04005-1-04005-4]
5) Features of Structural Organization of Nanodiamonds in the Polyethylene Glycol Matrix [04006-1-04006-6]
6) Characterization of Crystal Structure and Magnetic Properties of Zn(1 – x)MnxO (x = 0.086 and 0.090) Nanoparticles Synthesis Results Using Coprecipitation Method [04007-1-04007-4]
7) Effect of pH on Structural Morphology and Magnetic Properties of Ordered Phase of Cobalt Doped Lithium Ferrite Nanoparticles Synthesized by Sol-gel Auto-combustion Method [04008-1-04008-7]
8) A Low-profile Ultra-wideband LTCC Based Microstrip Antenna for Millimeter-wave Applications under 100 GHz [04009-1-04009-6]
9) Fabrication and Interpretation of Zinc-Cerium Composite: Structural and Thermal Studies [04010-1-04010-5]
10) Features of the Initial Stage of the Formation of Ti-Zr-Ni Quasicrystalline Thin Films [04011-1-04011-6]
11) Structural Studies of Mechanically Alloyed Fe1–xAlx Powder [04012-1-04012-5]
12) Hydrogen Adsorption on Li+ and Na+ Decorated Coronene and Corannulene: DFT, SAPT0, and IGM Study [04013-1-04013-6]
13) Realization of the Kelvin Probe System for the Surface Treatment of a Semiconductor [04014-1-04014-6]
14) Effect of Weak Confinement on the Optical Properties of Chemically Synthesized ZnS Nanoparticles [04015-1-04015-5]
15) Influence of the Vector Order Parameter on the Dynamics of 3D Ultrashort Pulses in Carbon Nanotubes [04016-1-04016-4]
16) Structural, Optical and Electrical Properties of Ce Doped SnO2 Nanoparticles Prepared by Surfactant Assisted Gel Combustion Method [04017-1-04017-6]
17) Sintering Temperature Dependent Structural and Mechanical Studies of BaxPb1 − xTiO3 Ferroelectrics [04018-1-04018-5]
18) Impact of Concentration of Nanoparticles on Characteristics of Transformer Oil [04019-1-04019-4]
19) Effect of the Porous Silicon Layer Structure on Gas Adsorption [04020-1-04020-5]
20) Light Emission from Silicon Structures with Dielectric Insulation [04021-1-04021-5]
21) Crystal Growth and Electro-optical Characterization of In2Se2.7Sb0.3 Compound [04022-1-04022-4]
22) Electron Energy in Rectangular and Cylindrical Quantum Wires [04023-1-04023-5]
23) An Ultra-low Power, High SNM, High Speed and High Temperature of 6T-SRAM Cell in 3C-SiC 130 nm CMOS Technology [04024-1-04024-4]
24) Measurement of the Angle of Attack of an Aerophysical Missile Complex in Flight Based on the Hall Effect Sensor and Electronic Measurement System [04025-1-04025-5]
25) Peculiarity of Elastic and Inelastic Properties of Radiation Cross-linked Hydrogels [04026-1-04026-5]
26) Structural and Optical Properties of Polycrystalline ZnO Nanopowder Synthesized by Direct Precipitation Technique [04027-1-04027-5]
27) Improving the Solar Collector Base Model for PVT System [04028-1-04028-5]
28) The Effect of Graphene Oxide on the Properties and Release of Drugs from Apatite-Polymer Composites [04029-1-04029-7]
29) Adhesion Strength of TiZrN/TiSiN Nanocomposite Coatings on a Steel Substrate with Transition Layer [04030-1-04030-6]
30) Thermal Effects on the Surface Morphology of an Ion-plasma Coating [04031-1-04031-5]
31) Some Properties and Structural Features of Poly(Vinyl Chloride)/Cu Films with Copper Nanoparticles Obtained by Exploding Wire Methodu [04032-1-04032-5]
32) Some Types of Carbon-based Nanomaterials as Contrast Agents for Photoacoustic Tomography [04033-1-04033-6]
33) Dynamics of Receiving Electroelastic Spherical Shell with a Filler [04034-1-04034-7]
34) The Effect of Chemical Composition and Electrolyte Temperature on the Size and Structure of Cadmium Sulfide Nanocrystals Obtained by the Electrolytic Method [04035-1-04035-6]
35) Morphological Features of the Nanoporous Structure in the Ammonium Nitrate Granules at the Final Drying Stage in Multistage Devices [04036-1-04036-6]
36) On Theory of Superheterodyne FELs with Longitudinal Electrostatic Undulator [04037-1-04037-5]
37) Experimental Investigation of the Distribution of Energy Deposited by FIB in Ion-beam Lithography [04038-1-04038-3]
38) Peculiarities of Magnetocaloric Effect in Ferromagnetic Cylindrical Nanowires with a Domain Wall [04039-1-04039-3]
