On the spreading of impacting drops under the influence of a vertical magnetic field

2016 ◽  
Vol 809 ◽  
Author(s):  
Jie Zhang ◽  
Tian-Yang Han ◽  
Juan-Cheng Yang ◽  
Ming-Jiu Ni
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Contact Angles ◽  
Vertical Magnetic Field ◽  
Joule Dissipation ◽  
Spreading Factor ◽  
Dissipation Energy ◽  
Capillary Effects ◽  
The Magnetic Field ◽  
Maximum Spreading

A theoretical model is developed to predict the maximum spreading of liquid metal drops when impacting onto dry surfaces under the influence of a vertical magnetic field. This model, which is constructed based on the energy conversion principle, agrees very well with the numerical results, covering a wide range of impact speeds, contact angles and magnetic strengths. When there is no magnetic field, we found that the maximum spreading factor can be predicted well by an interpolating scheme between the viscous and capillary effects, as proposed by Laan et al. (Phys. Rev. Appl., vol. 2 (4), 2014, 044018). However, when gradually increasing the magnetic field strength, the induced Lorentz forces are dominant over the viscous and capillary forces, taking the spreading behaviour into the ‘Joule regime’, where the Joule dissipation is significant. For most situations of practical interest, namely when the strength of the magnetic field is less than 3 T, all three energy conversion routes are important. Therefore, we determine the correct scaling behaviours for the magnetic influence by first equating the loss of kinetic energy to the Joule dissipation in the Joule regime, then by interpolating it with the viscous dissipation and the capillary effects, which allows for a universal rescaling. By plotting the numerical results against the theoretical model, all the results can be rescaled onto a single curve regardless of the materials of the liquid metals or the contact angles of the surfaces, proving that our theoretical model is correct in predicting the maximum spreading factor by constructing a balanced formula between kinetic energy, capillary energy, viscous dissipation energy and Joule dissipation energy.

Effect of magnetic field on parametrically driven surface waves

2006 ◽  
Vol 463 (2079) ◽  
pp. 711-722 ◽  
Author(s):  
Supriyo Paul ◽  
Krishna Kumar
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Liquid Metals ◽  
Tricritical Point ◽  
Thin Layers ◽  
Vertical Magnetic Field ◽  
Harmonic Solution ◽  
Chandrasekhar Number ◽  
The Magnetic Field ◽  
Primary Instability

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

scholarly journals Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

2018 ◽  
Vol 620 ◽  
pp. A191 ◽  
Author(s):  
M. Benko ◽  
S. J. González Manrique ◽  
H. Balthasar ◽  
P. Gömöry ◽  
C. Kuckein ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Temporal Evolution ◽  
Vertical Component ◽  
Field Vector ◽  
Linear Increase ◽  
Vertical Magnetic Field ◽  
Magnetic Diffusion ◽  
The Magnetic Field ◽  
Linear Decay

Context. It has been empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. Aims. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28–September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to prove the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. Methods. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. Results. We find a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the sunspot decay shown, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what is seen in stable sunspots. Conclusions. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field is found for the inner penumbral boundary.

Instability and transition of a vertical ascension or fall of a free sphere affected by a vertical magnetic field

2018 ◽  
Vol 859 ◽  
pp. 33-48 ◽  
Author(s):  
Jun-Hua Pan ◽  
Nian-Mei Zhang ◽  
Ming-Jiu Ni
Keyword(s):  
Magnetic Field ◽  
Interaction Parameter ◽  
Scaling Law ◽  
Density Ratio ◽  
Vertical Magnetic Field ◽  
Streamwise Vorticity ◽  
Close Relationship ◽  
Wake Patterns ◽  
The Magnetic Field ◽  
Solid System

When the Galileo number is below the first bifurcation, the instability and transition of a vertical ascension or the fall of a free sphere affected by a vertical magnetic field are investigated numerically. A compact model is used to explain that the magnetic field can destabilize the fluid–solid system. When the interaction parameter exceeds a critical value, the sphere trajectory is transitioned from a steady vertical trajectory to a steady oblique one. Furthermore, the trajectory will remain vertical at a sufficiently large magnetic field because of a double effect of the magnetic field on the fluid–solid system. Under the influence of an external vertical magnetic field, four wake patterns at the rear of the sphere are found and the physical behaviour of the free sphere is independent of the density ratio. The wake or trajectory of the free sphere is only determined by the Galileo number $G$ and the interaction parameter $N$. A close relationship between the streamwise vorticity and the sphere motion is found. An interesting ‘agglomeration phenomenon’ is also found, which shows that the vertical velocities are agglomerated into a point for a certain magnetic field regardless of the Galileo number and satisfy a scaling law $V_{z}\sim N^{-1/4}$, when $N>1$. The principal results of the present work are summarized in a map of regimes in the $\{G,N\}$ plane.

The magnetic field profiles of NGC 7331, NGC 2841, and NGC 6946 - A theoretical model

1988 ◽  
Vol 331 ◽  
pp. 116 ◽  
Author(s):  
E. Battaner ◽  
E. Florido ◽  
M. L. Sanchez-Saavedra
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Ngc 6946 ◽  
The Magnetic Field

Coupling of Buoyant Convections in Boron Oxide and a Molten Semiconductor in a Vertical Magnetic Field

2002 ◽  
Vol 124 (4) ◽  
pp. 643-649 ◽  
Author(s):  
Martin V. Farrell ◽  
Nancy Ma
Keyword(s):  
Magnetic Field ◽  
Boron Oxide ◽  
Maximum Velocity ◽  
Horizontal Velocity ◽  
Vertical Magnetic Field ◽  
Electrical Conductor ◽  
Interfacial Velocity ◽  
Rectangular Container ◽  
Vertical Walls ◽  
The Magnetic Field

This paper treats the buoyant convection in a layer of boron oxide, called a liquid encapsulant, which lies above a layer of a molten compound semiconductor (melt) between cold and hot vertical walls in a rectangular container with a steady vertical magnetic field B. The magnetic field provides an electromagnetic (EM) damping of the molten semiconductor which is an excellent electrical conductor but has no direct effect on the motion of the liquid encapsulant. The temperature gradient drives counter clockwise circulations in both the melt and encapsulant. These circulations alone would lead to positive and negative values of the horizontal velocity in the encapsulant and melt, respectively, near the interface. The competition between the two buoyant convections determines the direction of the horizontal velocity of the interface. For B=5 T, there is significant EM damping of the melt motion and the encapsulant drives a positive interfacial velocity and a small clockwise circulation in the melt. For a much weaker field B=0.1 T, the maximum velocity in the melt is hundreds of times larger than that of the encapsulant, thus causing nearly all the encapsulant to circulate in the clockwise direction.

The Comparison of Magnetic Leakage of Different Teeth Structures in Magnetic Fluid Seal

2011 ◽  
Vol 197-198 ◽  
pp. 314-317 ◽  
Author(s):  
Fei Fei Xing ◽  
De Cai Li ◽  
Wen Ming Yang ◽  
Xiao Long Yang
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Theoretical Model ◽  
Field Distribution ◽  
Magnetic Fluid ◽  
Magnetic Field Distribution ◽  
Two Sides ◽  
The Magnetic Field ◽  
Sealing Gap

Based on the theoretical model, magnetic field distribution of rectangular teeth, two-sides dilated shape and one-side dilated shape teeth structure with common other conditions were calculated using finite element method when the sealing gap was 0.1mm and 0.12mm. The comparison of their results with the same sealing gap showed that rectangular teeth structure had the highest magnetic leakage. Moreover, the magnetic field distribution of sealing structures with rectangular stages on both the shaft and pole pieces under the same design and sealing gap were also calculated using the same method, whose result was compared with rectangular stages on pole pieces only. The comparison showed that the former did not have higher pressure capability obviously but led to higher magnetic leakage.

scholarly journals A theoretical model of torsional oscillations from a flux transport dynamo model

2010 ◽  
Vol 6 (S273) ◽  
pp. 366-368
Author(s):  
Piyali Chatterjee ◽  
Sagar Chakraborty ◽  
Arnab Rai Choudhuri
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Lorentz Force ◽  
High Latitude ◽  
Torsional Oscillation ◽  
Sunspot Cycle ◽  
Dynamo Model ◽  
Flux Transport ◽  
Torsional Oscillations ◽  
The Magnetic Field

AbstractAssuming that the torsional oscillation is driven by the Lorentz force of the magnetic field associated with the sunspot cycle, we use a flux transport dynamo to model it and explain its initiation at a high latitude before the beginning of the sunspot cycle.

A model for the texture development of high-Tc superconductors under an elevated magnetic field

1999 ◽  
Vol 14 (7) ◽  
pp. 2751-2763 ◽  
Author(s):  
P. J. Ferreira ◽  
H. B. Liu ◽  
J. B. Vander Sande
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Melt Processing ◽  
High Tc Superconductors ◽  
High Tc ◽  
Grain Alignment ◽  
Grain Rotation ◽  
Stages Of Growth ◽  
Intermediate States ◽  
The Magnetic Field

A theoretical model is proposed to explain the degree of texture achieved in high-Tc superconductors during melt-processing under an elevated magnetic field. The degree of grain alignment is quantified through a factor F which is defined as ranging from 0 (random alignment) to 1 (completely oriented). Intermediate values of F clearly characterize intermediate states of alignment in which there is still some tendency for the grains to align their c axes with the magnetic field. The model suggests that the enhancement in texture is primarily obtained through grain rotation during the early stages of grain growth from the liquid. At the later stages of growth, grains interact with each other, which hinders the phenomena of magnetic-field–induced grain alignment.

Study on Spreading of Liquid Droplet Impacting on a Solid Dry Surface

2011 ◽  
Vol 66-68 ◽  
pp. 888-893
Author(s):  
Yun Chao Song ◽  
Chun Hai Wang ◽  
Zhi Ning
Keyword(s):  
Experimental Data ◽  
Theoretical Model ◽  
Liquid Droplet ◽  
Single Droplet ◽  
Capillary Effects ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Wetting Model ◽  
Theoretical Results ◽  
Maximum Spreading

A numerical computation and theoretical model are presented on spreading of a single droplet impacting on a solid surface at low Weber number. The numerical simulation uses combined Level Set-VOF method and a precise wetting model. The singularity at the moving contact line was analyzed and removed by present wetting model. A theoretical model based on the energy balance was developed to predict the maximum spreading ratio, accounting for wetting effect by a correction factor. The droplets shapes, the dimensionless spreading radius and the dimensionless height of droplet calculated by present numerical method were compared with the experimental data. The theoretical model is used to predict the maximum spreading ratio. The numerical and theoretical results agree well with the experimental data. Present theoretical model indicates that capillary effects may be neglected if 6We(We/3+4)>>Re.

On the Equilibrium of a Linear Extrap Pinch

1982 ◽  
Vol 37 (8) ◽  
pp. 769-779 ◽  
Author(s):  
B. Lehnert
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Heat Balance ◽  
Plasma Column ◽  
Transverse Magnetic ◽  
Substantial Effect ◽  
Linear Dimensions ◽  
Axial Heat ◽  
The Magnetic Field ◽  
Linear Plasma

The equilibrium is studied of a pinched linear plasma column of “Extrap” type which is confined in a purely transverse magnetic field, partly arising from currents in a set of external conductor rods being introduced for stabilizing purposes. The axial and transverse losses are separated in a simplified theoretical model for which stability is assumed as a working hypothesis and anomalous transport as well as impurity radiation are neglected. Then, the reduction of the axial heat transport by the magnetic field will have a substantial effect on the over-all heat balance, thus leading to high temperatures at large axial lengths of the plasma column. Conditions near ignition should become possible at technically realistic linear dimensions and pinch currents

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