Статті в журналах: "Fluids motion"

1

Fetecau, Constantin, Tahir Mushtaq Qureshi, Abdul Rauf, and Dumitru Vieru. "On the Modified Stokes Second Problem for Maxwell Fluids with Linear Dependence of Viscosity on the Pressure." Symmetry 14, no. 2 (January 24, 2022): 219. http://dx.doi.org/10.3390/sym14020219.

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The modified Stokes second problem for incompressible upper-convected Maxwell (UCM) fluids with linear dependence of viscosity on the pressure is analytically and numerically investigated. The fluid motion, between infinite horizontal parallel plates, is generated by the lower wall, which oscillates in its plane. The movement region of the fluid is symmetric with respect to the median plane, but its motion is asymmetric due to the boundary conditions. Closed-form expressions are found for the steady-state components of start-up solutions for non-dimensional velocity and the corresponding non-trivial shear and normal stresses. Similar solutions for the simple Couette flow are obtained as limiting cases of the solutions corresponding to the motion due to cosine oscillations of the wall. For validation, it is graphically proved that the start-up solutions (numerical solutions) converge to their steady-state components. Solutions for motions of ordinary incompressible UCM fluids performing the same motions are obtained as special cases of present results using asymptotic approximations of standard Bessel functions. The time needed to reach the permanent or steady state is also determined. This time is higher for motions of ordinary fluids, compared with motions of liquids with pressure-dependent viscosity. The impact of physical parameters on the fluid motion and the spatial–temporal distribution of start-up solutions are graphically investigated and discussed. Ordinary fluids move slower than fluids with pressure-dependent viscosity.

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2

Fetecau, Constantin, Dumitru Vieru, Abdul Rauf, and Tahir Mushtaq Qureshi. "STEADY-STATE SOLUTIONS FOR SOME MOTIONS OF MAXWELL FLUIDS WITH PRESSURE-DEPENDENCE OF VISCOSITY." Journal of Mathematical Sciences: Advances and Applications 68, no. 1 (November 30, 2021): 1–28. http://dx.doi.org/10.18642/jmsaa_7100122224.

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Two isothermal motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are investigated when gravity effects are taken into account. The fluid motion, between two infinite horizontal parallel plates, is generated by the lower plate that applies a time-dependent shear stress to the fluid. Exact expressions are established for the steady-state components of the dimensionless start-up velocity, shear stress, and normal stress. They are used to find the needed time to touch the steady-state and to provide corresponding solutions for the motion of the same fluids induced by an exponential shear stress on the boundary. This time is useful for experimentalists who want to eliminate transients from their experiments. It is higher for motions of ordinary fluids as compared to fluids with pressure-dependent viscosity. The variation of starting solutions (numerical solutions) in time and space is graphically represented and some characteristics of the fluid motion are brought to light.

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3

Fetecau, Constantin, Dumitru Vieru, Waqas Nazeer, and Shehraz Akhtar. "Long-time solutions for some mixed boundary value problems depicting motions of a class of Maxwell fluids with pressure dependent viscosity." Open Journal of Mathematical Sciences 6, no. 1 (June 21, 2022): 192–204. http://dx.doi.org/10.30538/oms2022.0188.

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Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

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4

Fetecau, Constantin, Dumitru Vieru, and Ahmed Zeeshan. "Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel." Mathematical Problems in Engineering 2021 (April 24, 2021): 1–13. http://dx.doi.org/10.1155/2021/5539007.

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Two unsteady motions of incompressible Maxwell fluids between infinite horizontal parallel plates embedded in a porous medium are analytically studied to get exact solutions using the finite Fourier cosine transform. The motion is induced by the lower plate that applies time-dependent shear stresses to the fluid. The solutions that have been obtained satisfy all imposed initial and boundary conditions. They can be easily reduced as limiting cases to known solutions for the incompressible Newtonian fluids. For a check of their correctness, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The effects of physical parameters on the fluid motion are graphically emphasized and discussed. Required time to reach the steady-state is also determined. It is found that the steady-state is rather obtained for Newtonian fluids as compared with Maxwell fluids. Furthermore, the effect of the side walls on the fluid motion is more effective in the case of Newtonian fluids.

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5

Fetecau, Constantin, Dumitru Vieru, Tehseen Abbas, and Rahmat Ellahi. "Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure." Mathematics 9, no. 4 (February 7, 2021): 334. http://dx.doi.org/10.3390/math9040334.

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Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

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6

Fetecau, Constantin, and Dumitru Vieru. "General Solutions for Some MHD Motions of Second-Grade Fluids between Parallel Plates Embedded in a Porous Medium." Symmetry 15, no. 1 (January 8, 2023): 183. http://dx.doi.org/10.3390/sym15010183.

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General solutions are established for an initial boundary value problem by means of the integral transforms. They correspond to the isothermal MHD unidirectional motion of incompressible second-grade fluids between infinite horizontal parallel plates embedded in a porous medium. The fluid motion, which in some situations becomes symmetric with respect to the median plane, is generated by the two plates that apply time-dependent arbitrary shear stresses to the fluid. Closed-form expressions are established both for the fluid velocity and the corresponding non-trivial shear stress. Using an important remark regarding the governing equations of velocity and shear stress, exact general solutions are developed for similar motions of the same fluids when both plates move in their planes with arbitrary time-dependent velocities. The results that have been obtained here can generate exact solutions for any motion with the technical relevance of this type of incompressible second-grade fluids and their correctness being proved by comparing them with the numerical solution or with known results from the existing literature. Consequently, both motion problems of these fluids with shear stress or velocity on the boundary are completely solved.

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7

Fetecau, Constantin, Rahmat Ellahi, and Sadiq M. Sait. "Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall." Mathematics 9, no. 1 (January 4, 2021): 90. http://dx.doi.org/10.3390/math9010090.

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Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the plates which is moving in its plane and the obtained solutions satisfy all imposed initial and boundary conditions. The starting solutions corresponding to the oscillatory motion are presented as sum of their steady-state and transient components. They can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for the incompressible Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. The influence of physical parameters on the fluid motion is graphically shown and discussed. It is found that the Maxwell fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state.

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8

Caimmi, R. "R fluids." Serbian Astronomical Journal, no. 176 (2008): 23–35. http://dx.doi.org/10.2298/saj0876023c.

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A theory of collisionless fluids is developed in a unified picture, where nonrotating (?f1 = ?f2 = ?f3 = 0) figures with some given random velocity component distributions, and rotating (?f1 = ?f2 = ?f3 ) figures with a different random velocity component distributions, make adjoint configurations to the same system. R fluids are defined as ideal, self-gravitating fluids satisfying the virial theorem assumptions, in presence of systematic rotation around each of the principal axes of inertia. To this aim, mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The figure rotation is defined as the mean angular velocity, weighted on the moment of inertia, with respect to a selected axis. The generalized tensor virial equations (Caimmi and Marmo 2005) are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general hypotheses, by reversing the sign of tangential or axial velocity components of an assigned fraction of particles, leaving the distribution function and other parameters unchanged (Meza 2002). The application of the reversion process to tangential velocity components is found to imply the conversion of random motion rotation kinetic energy into systematic motion rotation kinetic energy. The application of the reversion process to axial velocity components is found to imply the conversion of random motion translation kinetic energy into systematic motion translation kinetic energy, and the loss related to a change of reference frame is expressed in terms of systematic motion (imaginary) rotation kinetic energy. A number of special situations are investigated in greater detail. It is found that an R fluid always admits an adjoint configuration where figure rotation occurs around only one principal axis of inertia (R3 fluid), which implies that all the results related to R3 fluids (Caimmi 2007) may be ex- tended to R fluids. Finally, a procedure is sketched for deriving the spin parameter distribution (including imaginary rotation) from a sample of observed or simulated large-scale collisionless fluids i.e. galaxies and galaxy clusters.

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9

Fetecau, Constantin, Dumitru Vieru, Abdul Rauf, and Tahir Mushtaq Qureshi. "Mixed initial-boundary value problems describing motions of Maxwell fluids with linear dependence of viscosity on the pressure." Zeitschrift für Naturforschung A 76, no. 12 (October 13, 2021): 1107–24. http://dx.doi.org/10.1515/zna-2021-0212.

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Abstract Some mixed initial-boundary value problems are analytically studied. They correspond to unsteady motions of the incompressible upper-convected Maxwell (IUCM) fluids with linear dependence of viscosity on the pressure between infinite horizontal parallel plates. The fluid motion is generated by the upper plate that applies time-dependent shear stresses to the fluid. Exact solutions are established for the dimensionless velocity and nontrivial shear stress fields using a suitable change of the spatial variable and the Laplace transform technique. They are presented as sum of the steady-state and transient components and are used to determine the required time to reach the permanent state. Comparisons between exact and numerical solutions indicate an excellent agreement. Analytical solutions for the unsteady motion of the same fluids induced by an exponential shear stress on the boundary are obtained as limiting cases of the general solutions. Moreover, the steady-state solutions corresponding to the ordinary IUCM fluids performing the initial motions are provided by means of asymptotic approximations of standard Bessel functions. Finally, spatial variation of starting solutions and the influence of physical parameters on the fluid motion are graphically underlined and discussed.

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10

Fetecau, Constantin, and Dumitru Vieru. "Steady-state solutions for modified Stokes’ second problem of Maxwell fluids with power-law dependence of viscosity on the pressure." Open Journal of Mathematical Sciences 6, no. 1 (March 3, 2022): 14–24. http://dx.doi.org/10.30538/oms2022.0175.

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Analytical expressions for the steady-state solutions of modified Stokes’ second problem of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are determined when the gravity effects are considered. Fluid motion is generated by a flat plate that oscillates in its plane. We discuss similar solutions for the simple Couette flow of the same fluids. Obtained results can be used by the experimentalists who want to know the required time to reach the steady or permanent state. Furthermore, we discuss the accuracy of results by graphical comparisons between the solutions corresponding to the motion due to cosine oscillations of the plate and simple Couette flow. Similar solutions for incompressible Newtonian fluids with power-law dependence of viscosity on the pressure performing the same motions and some known solutions from the literature are obtained as limiting cases of the present results. The influence of pertinent parameters on fluid motion is graphically underlined and discussed.

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11

Zhang, Xiangxiang, Kai Gu, Chengyu Liu, Yangbing Cao, J. G. Wang, and Feng Gao. "Study on Fluid Front Motion of Water, Nitrogen, and CO2 during Anisotropic Flow in Shale Reservoirs." Geofluids 2022 (December 5, 2022): 1–9. http://dx.doi.org/10.1155/2022/7202972.

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The fluid front motion is an important phenomenon during anisotropic fluid flow in rock engineering. The pore pressure and mechanical responses may be significantly influenced and show an obvious difference near the moving fluid front. However, few studies have been conducted to investigate the front motion of different types of fluids during anisotropic fluid flow. In this work, a numerical model was proposed to detect the front motion of water, nitrogen, and CO2 in anisotropic shale reservoirs. The full coupling effects among mechanical deformation, fluid flow, and moving boundary in anisotropic porous media were considered in the model construction. The impacts of different fluid properties among water, nitrogen, and CO2 on the anisotropic fluid flow have been discussed. Then, the proposed model was applied to study the differences in front motion among different types of fluids in anisotropic shales. The impacts of permeability and mobility on fluid front motion were investigated. The theoretical equations for predicting the fluid front motion of different types of fluids were established by introducing corresponding correction coefficients to the previous formulas. The results showed that the model can well describe the anisotropic fluid permeation process. The fluid front motion increased with the increase of permeability and mobility. At the same permeability or mobility, the nitrogen front motion was the largest and the water front motion was the smallest. The difference in fluid front motion among water, nitrogen, and CO2 was caused by the difference of their viscosity and compressibility. The proposed formulas can fast and accurately predict the evolution of fluid front motion for different types of fluids.

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12

Fetecau, Constantin, and Abdul Rauf. ""Permanent solutions for some motions of UCM fluids with power-law dependence of viscosity on the pressure"." Studia Universitatis Babes-Bolyai Matematica 66, no. 1 (March 20, 2021): 197–209. http://dx.doi.org/10.24193/subbmath.2021.1.16.

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Steady motion of two types of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure is analytically studied between infinite horizontal parallel plates when the gravity effects are taken into consideration. Simple and exact expressions are established for the permanent components of starting solutions corresponding to two oscillatory motions induced by the lower plate that oscillates in its plane. Such solutions are very important for the experimentalists who want to eliminate the transients from their experiments. The similar solutions for the simple Couette flow of the same fluids, as well as the permanent solutions corresponding to ordinary incompressible Maxwell fluids performing the same motions, are obtained as limiting cases of general solutions. The convergence of starting solutions to their permanent components as well as the influence of physical parameters on the fluid motion is graphically underlined and discussed.

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13

Fetecau, Constantin, and Costică Moroşanu. "Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate." Symmetry 15, no. 6 (June 16, 2023): 1269. http://dx.doi.org/10.3390/sym15061269.

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The main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an infinite flat plate are analytically investigated when porous effects are taken into consideration. The fluid motion is due to the plate moving in its plane with an arbitrary time-dependent velocity or applying a time-dependent shear stress to the fluid. Closed-form expressions are established both for the dimensionless velocity and shear stress fields and the Darcy’s resistance corresponding to the first motion. The dimensionless shear stress corresponding to the second motion has been immediately obtained using a perfect symmetry between the governing equations of velocity and the non-trivial shear stress. Furthermore, the obtained results provide the first exact general solutions for MHD motions of second grade fluids through porous media. Finally, for illustration, as well as for their use in engineering applications, the starting and/or steady state solutions of some problems with technical relevance are provided, and the validation of the results is graphically proved. The influence of magnetic field and porous medium on the steady state and the flow resistance of fluid are graphically underlined and discussed. It was found that the flow resistance of the fluid declines or increases in the presence of a magnetic field or porous medium, respectively. In addition, the steady state is obtained earlier in the presence of a magnetic field or porous medium.

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14

Nelson, J. K. "Dielectric fluids in motion." IEEE Electrical Insulation Magazine 10, no. 3 (May 1994): 16–28. http://dx.doi.org/10.1109/57.285419.

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15

Fetecau, Corina, Qammar Rubbab, Shahraz Akhter, and Constantin Fetecau. "New methods to provide exact solutions for some unidirectional motions of rate type fluids." Thermal Science 20, no. 1 (2016): 7–20. http://dx.doi.org/10.2298/tsci130225130f.

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Based on three immediate consequences of the governing equations corresponding to some unidirectional motions of rate type fluids, new motion problems are tackled for exact solutions. For generality purposes, exact solutions are developed for shear stress boundary value problems of generalized Burgers fluids. Such solutions, for which the shear stress instead of its differential expressions is given on the boundary, are lack in the literature for such fluids. Consequently, the first exact solutions for motions of rate type fluids induced by an infinite plate or a circular cylinder that applies a constant shear f or an oscillating shear f sin(?t) to the fluid are here presented. In addition, all steady-state solutions can easily be reduced to known solutions for second grade and Newtonian fluids.

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16

Rana, Mehwish, Nazish Shahid, and Azhar Ali Zafar. "Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid." Zeitschrift für Naturforschung A 68, no. 12 (December 1, 2013): 725–34. http://dx.doi.org/10.5560/zna.2013-0052.

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Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

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17

Hohmann, Manuel. "Non-metric fluid dynamics and cosmology on Finsler spacetimes." International Journal of Modern Physics A 31, no. 02n03 (January 20, 2016): 1641012. http://dx.doi.org/10.1142/s0217751x16410128.

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We generalize the kinetic theory of fluids, in which the description of fluids is based on the geodesic motion of particles, to spacetimes modeled by Finsler geometry. Our results show that Finsler spacetimes are a suitable background for fluid dynamics and that the equation of motion for a collisionless fluid is given by the Liouville equation, as it is also the case for a metric background geometry. We finally apply this model to collisionless dust and a general fluid with cosmological symmetry and derive the corresponding equations of motion. It turns out that the equation of motion for a dust fluid is a simple generalization of the well-known Euler equations.

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18

Mammadova, Maleyka. "ABOUT DARSY’S LAW DURING FLUIDS MOTION IN THE MICRO-CRACKED CHANNELS." EUREKA: Physics and Engineering 5 (September 30, 2020): 3–11. http://dx.doi.org/10.21303/2461-4262.2020.001386.

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Firstly it has been experimentally revealed that during fluid motion in the micro-cracked channel and in the equivalent porous medium an unknown additional resistance arises in the scientific technical literature that is the “microcrack-fluid” effect. It has been demonstrated that the determined “microcrack-fluid” effect is the cause of linear Darcy’s law violation in the micro-cracked channels. It has been revealed in the work that during fluids moving in the microcracked channel there is a critical size of crack for the homogeneous fluid (water, viscous and anomalous fluids) and a hydrodynamic effect as so-called “microcrack-fluid” is manifested. So for the first time we determined the critical value of opening − hcr on the basis of experimental investigations in cracks. It was found that at h<hcr the anomalous properties are manifested for viscous fluids and rheological parameters are increased for anomalous fluids, and at h≥hcr these effects disappear. It has been established that the reason of the anomalous behavior of fluids in the microcrack with h<hcr opening is the effect occurred in the “microcrack-fluid” system. It is shown that microcrack with certain opening can be considered as a model but the ultra-low permeable porous medium is nature. It has been determined that the critical value of the Reynolds number calculated for viscous and abnormal fluids in the microcracked channel and in the equivalent porous medium in the microcrack is Re<1. The new fact about Darcy’s law violation during fluids flow in microcrack with h<hcr opening has been experimentally revealed i.e. micro-cracked effect of “microcrack-fluid” system is a cause of Darcy’s law violation. It is recommended to taking into consideration the microcracked effect in the “fluid-medium” system for regulation and creation of the new technical and technological processes in the different branches of industry

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19

Vieru, D., C. Fetecau, and C. Bridges. "Analytical Solutions for a General Mixed Boundary Value Problem Associated with Motions of Fluids with Linear Dependence of Viscosity on the Pressure." International Journal of Applied Mechanics and Engineering 25, no. 3 (September 1, 2020): 181–97. http://dx.doi.org/10.2478/ijame-2020-0042.

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AbstractAn unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finite Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.

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20

Godin, Oleg A. "Finite-amplitude acoustic-gravity waves: exact solutions." Journal of Fluid Mechanics 767 (February 12, 2015): 52–64. http://dx.doi.org/10.1017/jfm.2015.40.

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AbstractWe consider strongly nonlinear waves in fluids in a uniform gravity field, and demonstrate that an incompressible wave motion, in which pressure remains constant in each fluid parcel, is supported by compressible fluids with free and rigid boundaries. We present exact analytic solutions of nonlinear hydrodynamics equations which describe the incompressible wave motion. The solutions provide an extension of the Gerstner wave in an incompressible fluid with a free boundary to waves in compressible three-dimensionally inhomogeneous moving fluids such as oceans and planetary atmospheres.

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21

Gad-el-Hak, Mohamed. "Splendor of fluids in motion." Progress in Aerospace Sciences 29, no. 2 (January 1992): 81–123. http://dx.doi.org/10.1016/0376-0421(92)90004-2.

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22

Kramer, Dietrich. "Perfect fluids with conformal motion." General Relativity and Gravitation 22, no. 10 (October 1990): 1157–62. http://dx.doi.org/10.1007/bf00759016.

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23

Millán-Rodríguez, Juan, Michael Bestehorn, Carlos Pérez-García, Rudolf Friedrich, and Marc Neufeld. "Defect Motion in Rotating Fluids." Physical Review Letters 74, no. 4 (January 23, 1995): 530–33. http://dx.doi.org/10.1103/physrevlett.74.530.

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24

Velescu, Cornel, and Nicolae Calin Popa. "Laminar Motion of the Incompressible Fluids in Self-Acting Thrust Bearings with Spiral Grooves." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/478401.

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We analyze the laminar motion of incompressible fluids in self-acting thrust bearings with spiral grooves with inner or external pumping. The purpose of the study is to find some mathematical relations useful to approach the theoretical functionality of these bearings having magnetic controllable fluids as incompressible fluids, in the presence of a controllable magnetic field. This theoretical study approaches the permanent motion regime. To validate the theoretical results, we compare them to some experimental results presented in previous papers. The laminar motion of incompressible fluids in bearings is described by the fundamental equations of fluid dynamics. We developed and particularized these equations by taking into consideration the geometrical and functional characteristics of these hydrodynamic bearings. Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the “pumping” direction. These pressure and speed distributions offer important information, both quantitative (concerning the bearing performances) and qualitative (evidence of the viscous-inertial effects, the fluid compressibility, etc.), for the laminar and permanent motion regime.

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25

Bush, J. W. M., H. A. Stone, and J. Bloxham. "Axial drop motion in rotating fluids." Journal of Fluid Mechanics 282 (January 10, 1995): 247–78. http://dx.doi.org/10.1017/s0022112095000139.

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A theoretical and experimental investigation of drop motion in rotating fluids is presented. The theory describing the vertical on-axis translation of an axisymmetric rigid body through a rapidly rotating low-viscosity fluid is extended to the case of a buoyant deformable fluid drop of arbitrary viscosity. In the case that inertial and viscous effects are negligible within the bulk external flow, motions are constrained to be two-dimensional in compliance with the Taylor–Proudman theorem, and the rising drop is circumscribed by a Taylor column. Calculations for the drop shape and rise speed decouple, so that theoretical predictions for both are obtained analytically. Drop shapes are set by a balance between centrifugal and interfacial tension forces, and correspond to the family of prolate ellipsoids which would arise in the absence of drop translation. In the case of a drop rising through an unbounded fluid, the Taylor column is dissipated at a distance determined by the outer fluid viscosity, and the rise speed corresponds to that of an identically shaped rigid body. In the case of a drop rising through a sufficiently shallow plane layer of fluid, the Taylor column extends to the boundaries. In such bounded systems, the rise speed depends further on the fluid and drop viscosities, which together prescribe the efficiency of the Ekman transport over the drop and container surfaces.A set of complementary experiments is also presented, which illustrate the effects of drop viscosity on steady drop motion in bounded rotating systems. The experimental results provide qualitative agreement with the theoretical predictions; in particular, the poloidal circulation observed inside low-viscosity drops is consistent with the presence of a double Ekman layer at the interface, and is opposite to that expected to arise in non-rotating systems. The steady rise speeds observed are larger than those predicted theoretically owing to the persistence of finite inertial effects.

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26

Walicka, A. "Basic Flows of Generalized Second Grade Fluids Based on a Sisko Model." International Journal of Applied Mechanics and Engineering 22, no. 4 (December 20, 2017): 1019–33. http://dx.doi.org/10.1515/ijame-2017-0065.

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Abstract The present investigation is concerned with basic flows of generalized second grade fluids based on a Sisko fluid. After formulation of the general equations of motion three simple flows of viscoplastic fluids of a Sisko type or fluids similar to them are considered. These flows are: Poiseuille flow in a plane channel, Poiseuille flow in a circular pipe and rotating Couette flow between two coaxial cylinders. After presentation the Sisko model one was presented some models of fluids similar to this model. Next it was given the solutions of equations of motion for three flows mentioned above.

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27

Koutselos, A. D., and J. Samios. "Transport properties of diatomic ions in moderately dense gases in an electrostatic field." Pure and Applied Chemistry 76, no. 1 (January 1, 2004): 223–29. http://dx.doi.org/10.1351/pac200476010223.

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The motion of diatomic ions in moderately dense fluids under the action of an electrostatic field is studied through a nonequilibrium molecular dynamics simulation method. The method simulates the motion of the ions and the fluid molecules that constitute their immediate environment. Thus, effectively, the dissipation of the excess energy of the ions is reproduced leading to steady drift motion. Results revealed the effect of the fluid density on mobility, ion-effective temperatures and diffusion coefficients parallel and perpendicular to the field at various field strengths for a model diatomic ion in Ar. Extension of the method to dense fluids and to polyatomic ions and neutral molecules is discussed.

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28

Yasappan, Justine, Ángela Jiménez-Casas, and Mario Castro. "Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments." Abstract and Applied Analysis 2013 (2013): 1–20. http://dx.doi.org/10.1155/2013/748683.

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Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient.

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29

Naumov I.V., Sharifullin B.R., and Shtern V.N. "Influence of the upper liquid layer on vortex breakdown in the bioreactor model." Technical Physics Letters 48, no. 10 (2022): 42. http://dx.doi.org/10.21883/tpl.2022.10.54797.19259.

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The motion caused by rotation of the upper disk in a stationary vertical cylindrical container filled with two immiscible fluids is studied experimentally. The vortex breakdown the emergence of reversed motion on the cylinder axis in the lower liquid is investigated as a function of the thickness of the upper liquid layer. It is found that despite the fact that the motion of the upper fluid converges spirally to the cylinder axis near the interface, the vortex breakdown in the lower fluid occurs similarly to what is observed in the case of a single fluid, with the upper disk swirling. This curious result may be practically important for the operation of vortex bioreactors. Keywords: Confined swirling flow, vortex dynamics, bubbly vortex breakdown, immiscible fluids.

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30

Kararsiz, Gokhan, Yasin Cagatay Duygu, Zhengguang Wang, Louis William Rogowski, Sung Jea Park, and Min Jun Kim. "Navigation and Control of Motion Modes with Soft Microrobots at Low Reynolds Numbers." Micromachines 14, no. 6 (June 7, 2023): 1209. http://dx.doi.org/10.3390/mi14061209.

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This study investigates the motion characteristics of soft alginate microrobots in complex fluidic environments utilizing wireless magnetic fields for actuation. The aim is to explore the diverse motion modes that arise due to shear forces in viscoelastic fluids by employing snowman-shaped microrobots. Polyacrylamide (PAA), a water-soluble polymer, is used to create a dynamic environment with non-Newtonian fluid properties. Microrobots are fabricated via an extrusion-based microcentrifugal droplet method, successfully demonstrating the feasibility of both wiggling and tumbling motions. Specifically, the wiggling motion primarily results from the interplay between the viscoelastic fluid environment and the microrobots’ non-uniform magnetization. Furthermore, it is discovered that the viscoelasticity properties of the fluid influence the motion behavior of the microrobots, leading to non-uniform behavior in complex environments for microrobot swarms. Through velocity analysis, valuable insights into the relationship between applied magnetic fields and motion characteristics are obtained, facilitating a more realistic understanding of surface locomotion for targeted drug delivery purposes while accounting for swarm dynamics and non-uniform behavior.

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31

Fetecau, Constantin, and Dumitru Vieru. "Symmetric and Non-Symmetric Flows of Burgers’ Fluids through Porous Media between Parallel Plates." Symmetry 13, no. 7 (June 22, 2021): 1109. http://dx.doi.org/10.3390/sym13071109.

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Unidirectional unsteady flows of the incompressible Burgers’ fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy’s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers’ fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy’s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.

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32

FORBES, LAWRENCE K., RHYS A. PAUL, MICHAEL J. CHEN, and DAVID E. HORSLEY. "KELVIN–HELMHOLTZ CREEPING FLOW AT THE INTERFACE BETWEEN TWO VISCOUS FLUIDS." ANZIAM Journal 56, no. 4 (April 2015): 317–58. http://dx.doi.org/10.1017/s1446181115000085.

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The Kelvin–Helmholtz flow is a shearing instability that occurs at the interface between two fluids moving with different speeds. Here, the two fluids are each of finite depth, but are highly viscous. Consequently, their motion is caused by the horizontal speeds of the two walls above and below each fluid layer. The motion of the fluids is assumed to be governed by the Stokes approximation for slow viscous flow, and the fluid motion is thus responsible for movement of the interface between them. A linearized solution is presented, from which the decay rate and the group speed of the wave system may be obtained. The nonlinear equations are solved using a novel spectral representation for the streamfunctions in each of the two fluid layers, and the exact boundary conditions are applied at the unknown interface location. Results are presented for the wave profiles, and the behaviour of the curvature of the interface is discussed. These results are compared to the Boussinesq–Stokes approximation which is also solved by a novel spectral technique, and agreement between the results supports the numerical calculations.

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33

Feireisl, E. "Mathematical Theory of Fluids in Motion." Siberian Advances in Mathematics 28, no. 4 (October 2018): 233–64. http://dx.doi.org/10.3103/s1055134418040016.

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34

Millan‐Rodriguez, Juan, Carlos Pérez‐García, Michael Bestehorn, Marc Neufeld, and Rudolf Friedrich. "Motion of defects in rotating fluids." Chaos: An Interdisciplinary Journal of Nonlinear Science 4, no. 2 (June 1994): 369–76. http://dx.doi.org/10.1063/1.166014.

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35

Ernst, Dominique, Marcel Hellmann, Jürgen Köhler, and Matthias Weiss. "Fractional Brownian motion in crowded fluids." Soft Matter 8, no. 18 (2012): 4886. http://dx.doi.org/10.1039/c2sm25220a.

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36

Guo, Junke. "Motion of spheres falling through fluids." Journal of Hydraulic Research 49, no. 1 (February 2011): 32–41. http://dx.doi.org/10.1080/00221686.2010.538572.

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37

Euler, Leonhard. "Principles of the motion of fluids." Physica D: Nonlinear Phenomena 237, no. 14-17 (August 2008): 1840–54. http://dx.doi.org/10.1016/j.physd.2008.04.019.

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38

Chen, Yu, Qinjun Kang, Qingdong Cai, Moran Wang, and Dongxiao Zhang. "Lattice Boltzmann Simulation of Particle Motion in Binary Immiscible Fluids." Communications in Computational Physics 18, no. 3 (September 2015): 757–86. http://dx.doi.org/10.4208/cicp.101114.150415a.

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AbstractWe combine the Shan-Chen multicomponent lattice Boltzmann model and the link-based bounce-back particle suspension model to simulate particle motion in binary immiscible fluids. The impact of the slightly mixing nature of the Shan-Chen model and the fluid density variations near the solid surface caused by the fluid-solid interaction, on the particle motion in binary fluids is comprehensively studied. Our simulations show that existing models suffer significant fluid mass drift as the particle moves across nodes, and the obtained particle trajectories deviate away from the correct ones. A modified wetting model is then proposed to reduce the non-physical effects, and its effectiveness is validated by comparison with existing wetting models. Furthermore, the first-order refill method for the newly created lattice node combined with the new wetting model significantly improves mass conservation and accuracy.

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39

Tripathi, M. K., K. C. Sahu, G. Karapetsas, K. Sefiane, and O. K. Matar. "Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature." Journal of Fluid Mechanics 763 (December 10, 2014): 82–108. http://dx.doi.org/10.1017/jfm.2014.659.

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AbstractWe study the motion of a bubble driven by buoyancy and thermocapillarity in a tube with a non-uniformly heated walls, containing a so-called ‘self-rewetting fluid’; the surface tension of the latter exhibits a parabolic dependence on temperature, with a well-defined minimum. In the Stokes flow limit, we derive the conditions under which a spherical bubble can come to rest in a self-rewetting fluid whose temperature varies linearly in the vertical direction, and demonstrate that this is possible for both positive and negative temperature gradients. This is in contrast to the case of simple fluids whose surface tension decreases linearly with temperature, for which bubble motion is arrested only for negative temperature gradients. In the case of self-rewetting fluids, we propose an analytical expression for the position of bubble arrestment as a function of other dimensionless numbers. We also perform direct numerical simulation of axisymmetric bubble motion in a fluid whose temperature increases linearly with vertical distance from the bottom of the tube; this is done for a range of Bond and Galileo numbers, as well as for various parameters that govern the functional dependence of surface tension on temperature. We demonstrate that bubble motion can be reversed and then arrested only in self-rewetting fluids, and not in linear fluids, for sufficiently small Bond numbers. We also demonstrate that considerable bubble elongation is possible under significant wall confinement, and for strongly self-rewetting fluids and large Bond numbers. The mechanisms underlying the phenomena observed are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow.

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40

Fetecau, Constantin, Abdul Rauf, Tahir Mushtaq Qureshi, and Masood Khan. "Permanent solutions for some oscillatory motions of fluids with power-law dependence of viscosity on the pressure and shear stress on the boundary." Zeitschrift für Naturforschung A 75, no. 8 (September 25, 2020): 757–69. http://dx.doi.org/10.1515/zna-2020-0135.

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AbstractIn this paper, we provide simple expressions for the permanent solutions corresponding to some oscillatory motions of two classes of Newtonian fluids with power-law dependence of viscosity on the pressure between two infinite horizontal parallel plates. The fluid motion is generated by the lower plate that applies an oscillatory shear stress to the fluid. Such solutions, which are lack in the existing literature, can be useful both for those who want to eliminate the transients from their experiments and as tests to verify numerical schemes that are developed to study complex unsteady flow problems of these fluids. The similar solutions corresponding to the motion due to a constant shear stress on the boundary are also determined and, contrary to our expectations, the shear stresses are constant on the whole flow domain although the associated velocity fields depend both of the spatial variable and the dimensionless pressure-viscosity coefficient. Finally, for validation, some comparative graphical illustrations are included and the convergence of starting solutions to the permanent solutions is graphically proved. Spatial profiles of starting solutions are also provided.

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41

Jamil, Muhammad, and Najeeb Alam Khan. "Slip Effects on Fractional Viscoelastic Fluids." International Journal of Differential Equations 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/193813.

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Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions , by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is . Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally, the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations.

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42

Cui, Wenzheng, Minli Bai, Jizu Lv, and Xiaojie Li. "On the Microscopic Flow Characteristics of Nanofluids by Molecular Dynamics Simulation on Couette Flow." Open Fuels & Energy Science Journal 5, no. 1 (April 19, 2012): 21–27. http://dx.doi.org/10.2174/1876973x01205010021.

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Adding a small amount of nanoparticles to conventional fluids (nanofluids) has been proved to be an effective way for improving capability of heat transferring in base fluids. The change in micro structure of base fluids and micro motion of nanoparticles may be key factors for heat transfer enhancement of nanofluids. Therefore, it is essential to examine these mechanisms on microscopic level. The present work performed a Molecular Dynamics simulation on Couette flow of nanofluids and investigated the microscopic flow characteristics through visual observation and statistic analysis. It was found that the even-distributed liquid argon atoms near solid surfaces of nanoparticles could be seemed as a reform to base liquid and had contributed to heat transfer enhancement. In the process of Couette flow, nanoparticles moved quickly in the shear direction accompanying with motions of rotation and vibration in the other two directions. When the shearing velocity was increased, the motions of nanoparticles were strengthened significantly. The motions of nanoparticles could disturb the continuity of fluid and strengthen partial flowing around nanoparticles, and further enhanced heat transferring in nanofluids.

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43

Main, B. G. "Explosion Hazards in Offshore Motion Compensators." Proceedings of the Institution of Mechanical Engineers, Part A: Power and Process Engineering 199, no. 4 (November 1985): 229–35. http://dx.doi.org/10.1243/pime_proc_1985_199_029_02.

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Auto-ignition data for phosphate ester hydraulic fluids and explosion initiators in high pressure hydraulic/pneumatic motion compensators are reviewed. Data obtained in this study highlight the potential increased danger due to contamination of fire-resistant fluids.

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44

Song, Sanggeun, Seong Jun Park, Minjung Kim, Jun Soo Kim, Bong June Sung, Sangyoub Lee, Ji-Hyun Kim, and Jaeyoung Sung. "Transport dynamics of complex fluids." Proceedings of the National Academy of Sciences 116, no. 26 (June 7, 2019): 12733–42. http://dx.doi.org/10.1073/pnas.1900239116.

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Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate subdiffusive, and long-time diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a challenging problem. Here, we present a transport equation and its solutions, which yield a unified quantitative explanation of the mean-square displacement (MSD), the non-Gaussian parameter (NGP), and the displacement distribution of complex fluids. In our approach, the environment-coupled diffusion kernel and its time correlation function (TCF) are the essential quantities that determine transport dynamics and characterize mobility fluctuation of complex fluids; their time profiles are directly extractable from a model-free analysis of the MSD and NGP or, with greater computational expense, from the two-point and four-point velocity autocorrelation functions. We construct a general, explicit model of the diffusion kernel, comprising one unbound-mode and multiple bound-mode components, which provides an excellent approximate description of transport dynamics of various complex fluidic systems such as supercooled water, colloidal beads diffusing on lipid tubes, and dense hard disk fluid. We also introduce the concepts of intrinsic disorder and extrinsic disorder that have distinct effects on transport dynamics and different dependencies on temperature and density. This work presents an unexplored direction for quantitative understanding of transport and transport-coupled processes in complex disordered media.

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45

Harnoy, A. "Squeeze Film Flow of Elastic Fluids at Steady Motion and Dynamic Loads." Journal of Tribology 109, no. 4 (October 1, 1987): 691–95. http://dx.doi.org/10.1115/1.3261539.

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The role of the elasticity of the fluid is investigated in a squeeze film flow, between two parallel coaxial disks. An analysis is done for elastic fluids of low Deborah numbers, where the stress relaxation process is a first order effect to the dominant zero order effect of the viscosity. The constitutive equation of the fluid does not consider the normal-stresses. The results, which show a reduction in the load capacity for a steady speed squeeze action, are consistent with previous experiments in oil-polymer solutions. An improvement in the lubrication performance at dynamic loads is predicted and unlike in Newtonian fluids, the acceleration of the upper disk has a significant effect.

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46

Imran, M., M. Kamran, M. Athar, and A. A. Zafar. "Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple." Nonlinear Analysis: Modelling and Control 16, no. 1 (January 25, 2011): 47–58. http://dx.doi.org/10.15388/na.16.1.14114.

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Анотація:

Exact solutions for the velocity field and the associated shear stress, corresponding to the flow of a fractional second grade fluid between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a time-dependent torque per unit length 2πR1ft2. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1, respectively β → 1 and α1 → 0, the corresponding solutions for ordinary second grade fluids and Newtonian fluids, performing the same motion, are obtained as limiting cases.

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47

Gondret, P., M. Lance, and L. Petit. "Bouncing motion of spherical particles in fluids." Physics of Fluids 14, no. 2 (February 2002): 643–52. http://dx.doi.org/10.1063/1.1427920.

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48

Euler, Leonhard. "General principles of the motion of fluids." Physica D: Nonlinear Phenomena 237, no. 14-17 (August 2008): 1825–39. http://dx.doi.org/10.1016/j.physd.2008.02.023.

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49

Khasanov, M. M. "Specific features of motion of rheopectic fluids." Journal of Engineering Physics and Thermophysics 66, no. 6 (June 1994): 638–43. http://dx.doi.org/10.1007/bf00867964.

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50

De Boer, P. C. T. "Thermally driven motion of highly viscous fluids." International Journal of Heat and Mass Transfer 29, no. 5 (May 1986): 681–88. http://dx.doi.org/10.1016/0017-9310(86)90120-1.

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