Dominant Diffusing Mode in the Self-Similar Phase Separation of a Magnetic Suspension in a Magnetic Field

Langmuir ◽  
1998 ◽  
Vol 14 (3) ◽  
pp. 578-581 ◽  
Author(s):  
Adriana S. Silva ◽  
Denis Wirtz
Keyword(s):  
Magnetic Field ◽  
Phase Separation ◽  
Magnetic Suspension ◽  
The Self ◽  
Self Similar ◽  
Similar Phase

Hydromagnetic effects on non-Newtonian Hiemenz flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Magnetic Field ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Uniform Magnetic Field ◽  
Magnetic Parameter ◽  
Similarity Transformation ◽  
The Self ◽  
Free Boundary Value Problem ◽  
Uniqueness Of The Solution ◽  
Self Similar

Abstract The stagnation point flow of a non-Newtonian Reiner–Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the self-similar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.

scholarly journals ON THE SELF-SIMILAR HEAT BOUNDARY LAYER PROBLEMS IN MAGNETOHYDRODYNAMICS

2002 ◽  
Vol 7 (1) ◽  
pp. 93-102
Author(s):  
V. Kremenetsky
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Temperature Field ◽  
Joule Heat ◽  
The Self ◽  
Horizontal Flows ◽  
Self Similar Solution ◽  
Steady Magnetic Field ◽  
Self Similar ◽  
Boundary Layer Problems

Usually all self‐similar heat boundary layer problems in presence of magnetic field are solved neglecting the Joule heat, created by current, induced in fluid by interaction of velocity and magnetic field. But the analysis of this heat shows that its influence to the temperature field is very important. For vertical flows it is impossible to find self‐similar solution of boundary layer problems due to the Joule heat influence in temperature field. For horizontal flows only two self‐similar boundary layer problems can be formulated: flow near the critical point in magnetic field with the neutral point and in the transverse steady magnetic field.

Dynamical effects of the ambipolar diffusion in a protoplanetary disc

2020 ◽  
Vol 497 (2) ◽  
pp. 1634-1653 ◽  
Author(s):  
Mahmoud Gholipour
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Outer Region ◽  
Ambipolar Diffusion ◽  
The Self ◽  
Mhd Equations ◽  
Solution Technique ◽  
Self Similar

ABSTRACT Several recent simulation works in the non-ideal magnetohydrodynamic (MHD) formalism have shown the importance of ambipolar diffusion (AD) within the protoplanetary discs (PPDs) at large radii. In this study, we model the time evolution of a polytropic PPD in the presence of the AD. In this regard, the non-ideal MHD equations are investigated in the outer region of a PPD where the magnetic field evolution is dominated by the AD. The self-similar solution technique is used for a polytropic fluid including the self-gravity and viscosity. The ambipolar diffusivity and its derivative are crucial for the formulation of this study. Hence, this variable is scaled by an important factor, that is the Elsasser number. The self-similar equations are derived, and the semi-analytical and numerical solutions are presented for the isothermal and polytropic cases. The analytical approach enables us to know the asymptotic behaviour of the physical variables in a PPD, such as the angular momentum and magnetic field. Furthermore, the coupling/decoupling of magnetic field with the angular momentum was discussed analytically to find a corresponding model for the angular momentum loss at large radii of a PPD. Regarding this approach, we found that the magnetic braking induced by the AD at large radii has a high potential to loss the angular momentum even if the turbulent viscosity is not efficient. Also, the sign and values of vertical velocity strongly depends on the sign and values of radial field in the polytropic case.

scholarly journals The self-similar structure of advection-dominated discs with outflow and radial viscosity

2020 ◽  
Vol 493 (4) ◽  
pp. 5107-5119
Author(s):  
S M Ghoreyshi ◽  
M Shadmehri
Keyword(s):  
Magnetic Field ◽  
Similarity Solutions ◽  
Observational Evidence ◽  
The Self ◽  
Accretion Discs ◽  
Gas Velocity ◽  
State Structure ◽  
Self Similar ◽  
Strong Winds ◽  
The Magnetic Field

ABSTRACT Observational evidence and theoretical arguments postulate that outflows may play a significant role in the advection-dominated accretion discs (ADAFs). While the azimuthal viscosity is the main focus of most previous studies in this context, recent studies indicated that disc structure can also be affected by the radial viscosity. In this work, we incorporate these physical ingredients and the toroidal component of the magnetic field to explore their roles in the steady-state structure of ADAFs. We thereby present a set of similarity solutions where outflows contribute to the mass loss, angular momentum removal, and the energy extraction. Our solutions indicate that the radial viscosity causes the disc to rotate with a slower rate, whereas the radial gas velocity increases. For strong winds, the infall velocity may be of order the Keplerian speed if the radial viscosity is considered and the saturated conduction parameter is high enough. We show that the strength of magnetic field and of wind can affect the effectiveness of radial viscosity.

Annular self-similar solutions in ideal magnetogasdynamics

2008 ◽  
Vol 74 (4) ◽  
pp. 531-554 ◽  
Author(s):  
R. M. LOCK ◽  
A. J. MESTEL
Keyword(s):  
Magnetic Field ◽  
Initial Value Problem ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
The Self ◽  
Initial Value ◽  
Azimuthal Magnetic Field ◽  
Self Similar ◽  
Similar Solutions ◽  
Z Pinch

AbstractWe consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are singular at the annular boundaries. Numerical solutions of the full ideal MGD initial value problem indicate that the self-similar solutions are not attractive for arbitrary initial conditions, possibly as a result of flux-freezing.

The self-similar problem of the expanding elliptical crack in an anisotropic solid

1969 ◽  
Vol 66 (2) ◽  
pp. 443-468 ◽  
Author(s):  
R. Burridge ◽  
J. R. Willis
Keyword(s):  
Phase Transformation ◽  
Inverse Method ◽  
Crack Edge ◽  
Elliptical Crack ◽  
The Self ◽  
Stress Singularities ◽  
Anisotropic Solid ◽  
Title Problem ◽  
Self Similar ◽  
Similar Phase

AbstractThe title problem is solved by a semi-inverse method involving plane wave expansions. Expressions are given for stress singularities near the crack edge and for the radiation patterns produced by the crack. The case of an elliptical crack in an isotropic medium expanding under shear is examined in detail. Finally, some generalizations are discussed. Solutions are outlined for when the centre of the crack is allowed to move and for a self-similar phase transformation problem, in which a phase change takes place in an expanding ellipsoidal region.

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

scholarly journals Influence of Salt on the Self-Organization in Solutions of Star-Shaped Poly-2-alkyl-2-oxazoline and Poly-2-alkyl-2-oxazine on Heating

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1152
Author(s):  
Tatyana Kirila ◽  
Anna Smirnova ◽  
Alla Razina ◽  
Andrey Tenkovtsev ◽  
Alexander Filippov
Keyword(s):  
Phase Separation ◽  
Salt Concentration ◽  
Monomer Unit ◽  
Salt Content ◽  
The Self ◽  
Self Organization ◽  
Phase Separation Temperature ◽  
The Core ◽  
Separation Temperature ◽  
Water Salt

The water–salt solutions of star-shaped six-arm poly-2-alkyl-2-oxazines and poly-2-alkyl-2-oxazolines were studied by light scattering and turbidimetry. The core was hexaaza[26]orthoparacyclophane and the arms were poly-2-ethyl-2-oxazine, poly-2-isopropyl-2-oxazine, poly-2-ethyl-2-oxazoline, and poly-2-isopropyl-2-oxazoline. NaCl and N-methylpyridinium p-toluenesulfonate were used as salts. Their concentration varied from 0–0.154 M. On heating, a phase transition was observed in all studied solutions. It was found that the effect of salt on the thermosensitivity of the investigated stars depends on the structure of the salt and polymer and on the salt content in the solution. The phase separation temperature decreased with an increase in the hydrophobicity of the polymers, which is caused by both a growth of the side radical size and an elongation of the monomer unit. For NaCl solutions, the phase separation temperature monotonically decreased with growth of salt concentration. In solutions with methylpyridinium p-toluenesulfonate, the dependence of the phase separation temperature on the salt concentration was non-monotonic with minimum at salt concentration corresponding to one salt molecule per one arm of a polymer star. Poly-2-alkyl-2-oxazine and poly-2-alkyl-2-oxazoline stars with a hexaaza[26]orthoparacyclophane core are more sensitive to the presence of salt in solution than the similar stars with a calix[n]arene branching center.

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