ON FARADAY INSTABILITY IN MAGNETIC LIQUIDS: INCE-ERDELYI APPROACH APPLIED TO THE HILL EQUATION DESCRIBING OSCILLATIONS OF A FERROFLUID FREE SURFACE

2013 ◽  
Vol 43 (4) ◽  
pp. 29-48
Author(s):  
M. Hennenberg ◽  
S. Slavtchev ◽  
G. Valchev
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Surface Deformation ◽  
Classical Method ◽  
Physical Phenomenon ◽  
Periodic Part ◽  
Faraday Instability ◽  
Constant Part ◽  
Free Surface Oscillations ◽  
Newtonian Liquids

Abstract When an isothermal ferrofluid is submitted to an oscillating magnetic field, the initially motionless liquid free surface can start to oscillate. This physical phenomenon is similar to the Faraday instability for usual Newtonian liquids subjected to a mechanical oscillation. In the present paper, we consider the magnetic field as a sum of a constant part and a time periodic part. Two different cases for the constant part of the field, being vertical in the first one or horizontal in the second one are studied. Assuming both ferrofluid magnetization and magnetic field to be collinear, we develop the linear stability analysis of the motionless reference state taking into account the Kelvin magnetic forces. The Laplace law describing the free surface deformation reduces to Hill’s equation, which is studied using the classical method of Ince and Erdelyi. Inside this framework, we obtain the transition conditions leading to the free surface oscillations.

scholarly journals The effect of uniform magnetic field on spatial-temporal evolution of thermocapillary convection with the silicon oil based ferrofluid

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 4159-4171
Author(s):  
Shuo Yang ◽  
Rui Ma ◽  
Qiaosheng Deng ◽  
Guofeng Wang ◽  
Yu Gao ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Transverse Magnetic Field ◽  
Liquid Bridge ◽  
Thermocapillary Convection ◽  
Surface Deformation ◽  
Axial Magnetic Field ◽  
Transverse Magnetic ◽  
Surface Flow ◽  
Silicon Oil

A uniform axial or transverse magnetic field is applied on the silicon oil based ferrofluid of high Prandtl number fluid (Pr ? 111.67), and the effect of magnetic field on the thermocapillary convection is investigated. It is shown that the location of vortex core of thermocapillary convection is mainly near the free surface of liquid bridge due to the inhibition of the axial magnetic field. A velocity stagnation region is formed inside the liquid bridge under the axial magnetic field (B = 0.3-0.5 T). The disturbance of bulk reflux and surface flow is suppressed by the increasing axial magnetic field. There is a dynamic response of free surface deformation to the axial magnetic field, and then the contact angle variation of the free surface at the hot corner is as following, ?hot, B = 0.5 T = 83.34? > ?hot, B = 0.3 T = 72.16? > > ?hot,B = 0.1 T = 54.21? > ?hot, B = 0 T = 43.33?. The results show that temperature distribution near the free surface is less and less affected by thermocapillary convection with the increasing magnetic field, and it presents a characteristic of heat-conduction. In addition, the transverse magnetic field does not realize the fundamental inhibition for thermocapillary convection, but it transfers the influence of thermocapillary convection to the free surface.

Free-surface deformation measurement

1997 ◽  
Author(s):  
H. Stahl ◽  
Kevin Stultz ◽  
H. Stahl ◽  
Kevin Stultz
Keyword(s):  
Free Surface ◽  
Surface Deformation ◽  
Deformation Measurement ◽  
Free Surface Deformation

Observation of surface deformation of tungsten exposed to single pulsed high heat flux and magnetic field for divertor design

2021 ◽  
Vol 171 ◽  
pp. 112547
Author(s):  
Takafumi Okita ◽  
Yuki Matsuda ◽  
Sho Saito ◽  
Eiji Hoashi ◽  
Kenzo Ibano ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Surface Deformation ◽  
High Heat ◽  
High Heat Flux

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

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