The two coefficients of viscosity for an incompressible fluid containing air bubbles

1954 ◽  
Vol 226 (1164) ◽  
pp. 34-37 ◽  
Keyword(s):  
Relaxation Time ◽  
Incompressible Fluid ◽  
Small Proportion ◽  
Incompressible Fluids ◽  
Air Bubbles ◽  
Maximum Value ◽  
Volume Viscosity ◽  
Coefficient Of Viscosity ◽  
Surrounding Fluid

Incompressible fluids possess only one coefficient of viscosity because, by definition, no changes in volume can occur. If such a fluid contains air bubbles it becomes compressible, and any changes in volume involves a contraction or expansion of the bubbles which is resisted by the ordinary viscosity of the surrounding fluid. The resulting second coefficient of viscosity is found to be 4μ/3v, where μ is the viscosity of the incompressible fluid and v the (small) proportion of the total volume which is occupied by the bubbles. The effect of compressibility in the fluid is discussed in Notes by Sir Geoffrey Taylor and Dr R. O. Davies. In the second of these it is shown that a relaxation time must exist and in the first the volume viscosity of water containing air bubbles is calculated. This is found to reach a maximum value of 6700 times the viscosity of water when v = 5 x 10 -5 .

scholarly journals Damping of waves due to a soluble film

1980 ◽  
Vol 3 (2) ◽  
pp. 383-396 ◽  
Author(s):  
K. K. Puri
Keyword(s):  
Thin Film ◽  
Porous Medium ◽  
Relaxation Time ◽  
Free Surface ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Damping Coefficient ◽  
Free Surface Oscillations ◽  
The Waves ◽  
Soluble Material

The damping of avity waves, forming on the surface of a layer of viscous, incompressible fluid which rests on top of a porous medium, is studied. It is assumed that the 'free' surface of the fluid has a thin film of soluble material adsorbed on it and the relaxation time for the equilibrium of the film is negligible in comparison to the free surface oscillations. The damping coefficient of the waves is calculated as a function of the parameters associated with the surfactant and the permeability.

INCOMPRESSIBLE FLUIDS

2005 ◽  
Vol 20 (27) ◽  
pp. 6122-6132 ◽  
Author(s):  
S. G. RAJEEV
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Quantum Groups ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Two Dimensional ◽  
Incompressible Fluid Flow ◽  
Fluid System ◽  
Random Forces ◽  
Turbulent Incompressible Fluid

We propose a model for random forces in a turbulent incompressible fluid by balancing the energy gain from fluctuations against dissipation by viscosity. This leads to a more singular covariance distribution for the random forces than is ordinarily allowed. We then propose regularization of the fluid system by matrix models. A formula for entropy of a two dimensional fluid is derived and then a vorticity profile of a hurricane that maximizes entropy. A regularization of three dimensional incompressible fluid flow using quantum groups is also proposed.

Simulation of Interactions Between Microbubbles and Turbulent Flows

1994 ◽  
Vol 47 (6S) ◽  
pp. S70-S74 ◽  
Author(s):  
M. R. Maxey ◽  
E. J. Chang ◽  
L. -P. Wang
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Small Scale ◽  
Air Bubbles ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Flow ◽  
Drag Forces ◽  
Spherical Inclusions ◽  
Average Rise ◽  
Surrounding Fluid

Microbubbles formed by small air bubbles in water are characterized as spherical inclusions that are essentially rigid due to the effects of surfactants, and respond to the action of drag forces and added-mass effects from the motion relative to the surrounding fluid. Direct numerical simulations of homogeneous, isotropic turbulence are used to study the effects of the small-scale, dissipation range turbulence on microbubble transport and in particular the average rise velocity of microbubbles. It is found that microbubbles rise significantly more slowly than in still fluid even in the absence of a mean flow, due to a strong interaction with the small-scale vorticity. The way in which microbubbles might modify the underlying turbulence by the variations in their local distribution is discussed for dilute, dispersed systems and some estimates for the enhanced viscous dissipation given.

Hybrid solutions of a (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation in an incompressible fluid

2021 ◽  
pp. 2150126
Author(s):  
Chong-Dong Cheng ◽  
Bo Tian ◽  
Cong-Cong Hu ◽  
Xin Zhao
Keyword(s):  
Incompressible Fluid ◽  
Bilinear Form ◽  
Periodic Wave ◽  
Incompressible Fluids ◽  
Ocean Engineering ◽  
Hybrid Solutions ◽  
Kink Wave ◽  
Kink Waves ◽  
Lump Wave

Incompressible fluids are studied in such disciplines as ocean engineering, astrophysics and aerodynamics. Under investigation in this paper is a [Formula: see text]-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation in an incompressible fluid. Based on the known bilinear form, BLMP hybrid solutions comprising a lump wave, a periodic wave and two kink waves, and hybrid solutions comprising a breather wave and multi-kink waves are derived. We observe the interaction among a lump wave, a periodic wave and two kink waves. Fission of a kink wave is observed: A kink wave divides into a breather wave and three kink waves. On the contrary, we see the fusion among a breather wave and three kink waves: The breather wave and three kink waves merge into a kink wave. Finally, we observe the interaction among a breather wave and four kink waves.

scholarly journals Dielectric loss due to polar molecules in solid paraffin wax

1939 ◽  
Vol 172 (951) ◽  
pp. 502-517 ◽  
Keyword(s):  
Relaxation Time ◽  
Dielectric Loss ◽  
Maximum Rate ◽  
Angular Frequency ◽  
Rate Of Change ◽  
Polar Molecules ◽  
Dielectric Polarization ◽  
Specific Energy Loss ◽  
Maximum Value ◽  
Time Required

According to most theories of dielectric loss the maximum rate of change of dielectric constant and the maximum value of the specific energy loss per unit volume occur at an angular frequency ω (= 2 πv ) which is the inverse of a quantity r known as the relaxation time of the dielectric. The relaxation time is the time required for the polarization of the dielectric to revert to 1/ ϵ of its value after the removal of the applied electric field: and this is a quantity which can be determined experimentally. According to Debye’s theory of polar molecules, part of the dielectric polarization is due to the orientation of the dipoles in line with the applied field and the relaxation time is related closely to the time taken for the molecules to revert to their random positions after removal of the field.

Ultrasonic Absorption and Relaxation Phenomena in Molten Nitrate Mixtures

1986 ◽  
Vol 41 (3) ◽  
pp. 535-544 ◽  
Author(s):  
J. Richter ◽  
B. Fuchs
Keyword(s):  
Relaxation Time ◽  
Molten Salt ◽  
Structural Relaxation ◽  
Composition Range ◽  
Frequency Interval ◽  
Relaxation Phenomena ◽  
Ultrasonic Absorption ◽  
Volume Viscosity ◽  
Salt Mixtures ◽  
Total Composition

An optical device based on the Debye-Sears effect is developed to determine the ultrasonic absorption and velocity in molten alkali nitrate + silver nitrat mixtures. RbNO3 + AgNO3 and CsNO3 + AgNO3 are investigated in the total composition range between 480 K and 580 K within a frequency interval from 10 MHz to 35 MHz. In the concentration range of high ultrasonic absorption we find dispersion and a frequency dependent step in the absorption curve caused by relaxation. The relaxation time of the structural relaxation in the molten salt mixtures investigated here is in the order of 10-8 s.The volume viscosity, the adiabatic constant, and the compressibilities are calculated.

Incompressible-Fluid Symbolic Computation and Bäcklund Transformation: (3+1)-Dimensional Variable-Coefficient Boiti–Leon–Manna–Pempinelli Model

2015 ◽  
Vol 70 (1) ◽  
pp. 59-61 ◽  
Author(s):  
Xin-Yi Gao
Keyword(s):  
Shock Wave ◽  
Incompressible Fluid ◽  
Symbolic Computation ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Incompressible Fluids ◽  
Current Interest ◽  
Backlund Transformation ◽  
Wave Type ◽  
Dimensional Variable

AbstractIncompressible fluids are of current interest. Considering a (3+1)-dimensional variable-coefficient Boiti–Leon–Manna–Pempinelli model for an incompressible fluid, we perform symbolic computation to work out a variable-coefficient-dependent auto-Bäcklund transformation, along with two variable-coefficient-dependent classes of the shock-wave-type solutions. Our auto-Bäcklund transformation is different from the recently reported bilinear one.

A theoretical analysis of the mechanical relaxation of single-crystalline ice

1958 ◽  
Vol 247 (1251) ◽  
pp. 462-464 ◽  
Keyword(s):  
Relaxation Time ◽  
Loss Factor ◽  
Mechanical Deformation ◽  
Lattice Defects ◽  
Mechanical Relaxation ◽  
Hydrogen Atoms ◽  
Maximum Loss ◽  
Maximum Value ◽  
Modes Of Vibration ◽  
Characteristic Maximum

Kneser, Magun & Ziegler (1955) have found a mechanical relaxation of single crystals of ice. Torsional vibrations of cylindrical specimens, cut parallel to the c -axis, were employed and the logarithmic decrement showed the characteristic maximum associated with a single relaxation time. Similar results have since beer obtained by Schiller (yet unpublished) for various modes of vibration and various crystallographic orientations. The frequency for maximum loss factor and the energy of activation are approximately equal for the mechanical and dielectric relaxation. It seems obvious to associate both relaxations with movements of the hydrogen atoms. In the mechanical case, this may be done in two different ways. As a first possibility I have assumed that an equilibrium exists between a large number of possible hydrogen arrangements and that this equilibrium is disturbed by and mechanical deformation of the crystal lattice. The rearrangement of the hydrogen atoms throughout the lattice then gives rise to the observed relaxation. A second possible mechanism is connected with the distribution of lattice defects such as doubly occupied and vacant bonds between neighbouring oxygen atoms. Normally the probability of finding a given type of defect on a given bond would be approxi­mately the same for all bonds. In the deformed lattice, bonds with a certain orientation would be preferred and the resulting rearrangement of the defects would cause the observed relaxation. With the first mechanism, lattice defects can serve as catalysts in bringing about configurational changes and their presence (in small numbers) will thus affect the relaxation time, but not the magnitude of the decrement. With the second mechanism, however, the magnitude of the decrement is proportional to the number of defects present. I have calculated the maximum value of the decrement for the first mechanism, which implies a general rearrange­ment of the hydrogen atoms, and shall show that the result agrees well with the measurements. On the other hand, estimates based on the second mechanism are clearly inconsistent with the experimental evidence.

scholarly journals Safe Hb Concentration Measurement during Bladder Irrigation Using Artificial Intelligence

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5723
Author(s):  
Gerd Reis ◽  
Xiaoying Tan ◽  
Lea Kraft ◽  
Mehmet Yilmaz ◽  
Dominik Stephan Schoeb ◽  
...  
Keyword(s):  
Neural Network ◽  
Bubble Formation ◽  
Concentration Measurement ◽  
Air Bubbles ◽  
Irrigation Systems ◽  
Bladder Irrigation ◽  
Non Invasive ◽  
Maximum Value ◽  
Temporal Features ◽  
Hb Concentration

We have developed a sensor for monitoring the hemoglobin (Hb) concentration in the effluent of a continuous bladder irrigation. The Hb concentration measurement is based on light absorption within a fixed measuring distance. The light frequency used is selected so that both arterial and venous Hb are equally detected. The sensor allows the measurement of the Hb concentration up to a maximum value of 3.2 g/dL (equivalent to ≈20% blood concentration). Since bubble formation in the outflow tract cannot be avoided with current irrigation systems, a neural network is implemented that can robustly detect air bubbles within the measurement section. The network considers both optical and temporal features and is able to effectively safeguard the measurement process. The sensor supports the use of different irrigants (salt and electrolyte-free solutions) as well as measurement through glass shielding. The sensor can be used in a non-invasive way with current irrigation systems. The sensor is positively tested in a clinical study.

Flight Research at High Subsonic Speeds

1948 ◽  
Vol 52 (452) ◽  
pp. 483-512 ◽  
Author(s):  
H. Davies
Keyword(s):  
Incompressible Fluid ◽  
Special Reference ◽  
Speed Of Sound ◽  
Incompressible Fluids ◽  
Level Flight ◽  
The Past ◽  
Work Done ◽  
Made In ◽  
As If

Until about ten years ago the highest speeds achieved by aircraft, even in dives, rarely exceeded half the speed of sound. Under these conditions the air round the aircraft behaved very much as if it were incompressible, and the forces acting on the aircraft could be derived on the basis of laws governing the aerodynamics of incompressible fluids.During the 1939-45 War great advances were made in the performance of aircraft and eventually speeds of over three-quarters of the speed of sound were being reached, even in level flight. At these speeds the air no longer behaves as an incompressible fluid; the aerodynamic laws involved become much more complicated and the aircraft designer is faced with a mass of new problems, involving many strange and unexpected effects.The purpose of this lecture is to discuss the contribution which research in flight can make towards the elucidation of these problems, with special reference to work done at the Royal Aircraft Establishment during the past few years.

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