Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field

Ferrofluid spin-up flow is studied within a sphere subjected to a uniform rotating magnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 90° phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1-14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1-4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniform magnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1-20 mm/s) when the field is made non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a non-uniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-up flow in ferrofluids with no free surface, while tangential magnetic surface stress contributes to flow in the presence of a free surface.Recent work has fitted velocity flow measurements of ferrofluid filled finite height cylinders with no free surface, subjected to uniform rotating magnetic fields, neglecting the container shape effects which cause non-uniform demagnetizing fields, and resulting in much larger non-physical effective values of spin viscosity η′∼10⁻⁸−10⁻¹² N s than those obtained from theoretical spin diffusion analysis where η′≤10⁻¹⁸ N s. COMSOL Multiphysics finite element computer simulations of spherical geometry in a uniform rotating magnetic field using non-physically large experimental fit values of spin viscosity η′∼10⁻⁸−10⁻¹² N s with a zero spin-velocity boundary condition at the outer wall predicts measureable flow, while simulations setting spin viscosity to zero (η′=0) results in negligible flow, in agreement with the ultrasound velocimetry measurements. COMSOL simulations also confirm that a non-uniform rotating magnetic field or a uniform rotating magnetic field with a non-uniform distribution of magnetization due to an external magnet or a current carrying coil can drive a measureable flow in an infinitely long ferrofluid cylinder with zero spin viscosity (η′=0).     

Steady flow generated by the differential rotation of a porous disk of finite thickness

When a body of fluid bounded by a porous disk of finite thickness is disturbed from a state of rigid rotation by an enhanced (or reduced) angular velocity of the disk, a few authors followed Darcys model and observed that the centrifugal pumping occurs through the entire porous layer regarded as a convection zone. The shear stress can develop only at the edge of the porous layer. We use a porous disk of high permeability that allows the fluid in the porous disk to deform in response to the changing angular velocity. Based on the Birkmans model, we solve for the steady non-linear flow and observe that there arises (i) a convection zone of nearly uniform angular velocity at the boundary (within the porous layer) and (ii) a transition zone adjacent to the convection zone which provides a smooth transition to the interior. This makes the model relevant to some astrophysical situations as described by some authors [1, 3]. The two point boundary value problem is solved subject to the boundary conditions, the far field conditions, and the matching conditions at the fluid-porous medium interface. The solution is obtained using a numerical procedure known as the method of Adjoints.Received: June 13, 2002; revised: July 7, 2003     

Spin-up and wrapping of cryogenic helium bubble around dewar well from rest in microgravity

Time dependent animation of spherically shaped bubble sitting at one-side of the dewar container, which is spin-up from rest to certain rotating speed of interests, has been investigated. Time dependent deformation of bubble with or without a completion of wrapping around the inner well of the rotating dewar, are numerically studied and simulated. Some similarity parameters are considered for a completion of bubble wrapping around the dewar well. Illustrative examples show that the degree of the completion of bubble wrapping around the dewar well increases with increasing container rotating speed and Weber number.     

Spin-up and spin-down electron transport through a single-atom imperfect metallic wire: An analytical picture

Within a new perspective which includes the consideration of spin-up and spin-down electrons, a quantum-box approach is used to find a closed mathematical expression for the quantized electrical conductance of an imperfect point–metal contact. From this expression, both proper and improper fractions of the fundamental conductance quantum are obtained and discussed in the light of both resonant and off-resonant conduction states. Issues concerning Fermi energy and electrochemical potential are discussed. In addition, essential aspects related to the atom–lead coupling are examined; in particular, a tensor–dyadic formalism is introduced. Our results are found to be in excellent agreement with previous theoretical results and with experimental observations.     

An approach based on the free-electron theory to calculate electron conductance of perfect metallic nanowires

For the first time, the quantum free-electron theory is utilized for determining the quantized electrical conductance in a perfect metallic multi-atom nanowire. In this formulation, both spin-up and spin-down conduction electrons are considered so that our final result comes from a series combination of the contributions to the conductance from the two possible types of spin-oriented electron, assuming a symmetric distribution of the involved counter-ions. In addition, several aspects related to the atom-lead coupling are discussed.     

Spin-up in a semicircular cylinder

This paper addresses the spin-up from rest of a free-surface fluid confined in a cylindrical container with a semicircular cross-section. The flow in the various stages of the spin-up process has been calculated numerically by using the finite-volume technique on a three-dimensional grid. Local grid refinement was applied in order to capture the effects of the boundary layer at the lateral boundaries and of the Ekman layer at the bottom. The numerical results agree very well with laboratory observations.