Magnetic fluid droplet deformation in electrostatic field

The stability of the ferrofluid (FF) subjected to the electric field is crucial for the application in high voltage (HV) technology. There are several cases where the fluid interacts with solid interfaces. We examined experimentally FF drop on a glass surface. The drop was exposed to the steady electric field. During tests the suspended particles started to aggregate. Changing drop's shape was recorded during a time period. It was observed that the further deformation development depends on aggregates shape and location. The results are compared with the behaviour of pure carrier fluid. Understanding the phenomenon associated with FF drop deformation can help more reliable HV component design.     

Influence of surface tension on the conical meniscus of a magnetic fluid in the field of a current-carrying wire

We study the influence of surface tension on the shape of the conical meniscus built up by a magnetic fluid surrounding a current-carrying wire. Minimization of the total energy of the system leads to a singular second order boundary value problem for the function ζ(r)$\zeta (r)$ describing the axially symmetric shape of the free surface. An appropriate transformation regularizes the problem and allows a straightforward numerical solution. We also study the effects a superimposed second liquid, a nonlinear magnetization law of the magnetic fluid, and the influence of the diameter of the wire on the free surface profile.     

Heating of magnetic fluid systems driven by circularly polarized magnetic field

A theory is presented to calculate the heat dissipation of a magnetic suspension, a ferrofluid, driven by circularly polarized magnetic field. Theory is tested by in vitro experiments and it is shown that, regardless of the character of the relaxation process, linearly and circularly polarized magnetic field excitations, having the same root-mean-square magnitude, are equivalent in terms of heating efficiency.     

Numerical approach and experimental verification for interface shape determination between layered fluids subject to a magnetic field

Various applications of magnetic fluids involve interface phenomena. The analysis of the hydrostatic interface shape between two immiscible liquid layers, especially under magnetic field influence, is the first step to understand the accompanying complex dynamic phenomena as well as to providing reliable numerical capabilities for their accurate prediction. This study presents a relatively simple numerical approach, and the accompanying theory, to reliably define the meniscus shape in a two-layered fluid system in presence of a horizontal magnetic field with a vertical gradient. In the course of the study, two dimensionless parameters have been derived to describe the magnetic pressure jump at the interface and the magnetic body force throughout the volume. These parameters are used to interpret the results of the analysis and to show that a horizontal magnetic field tends to flatten the meniscus shape at the interface despite of the direction of its vertical gradient.     

Parametric investigation of heating due to magnetic fluid hyperthermia in a tumor with blood perfusion

Magnetic fluid hyperthermia (MFH) is a cancer treatment that can selectively elevate the tumor temperature without significantly damaging the surrounding healthy tissue. Optimal MFH design requires a fundamental parametric investigation of the heating of soft materials by magnetic fluids. We model the problem of a spherical tumor and its surrounding healthy tissue that are heated by exciting a homogeneous dispersion of magnetic nanoparticles infused only into the tumor with an external AC magnetic field. The key dimensionless parameters influencing thermotherapy are the Péclet, Fourier, and Joule numbers. Analytical solutions for transient and steady hyperthermia provide correlations between these parameters and the portions of tumor and healthy tissue that are subjected to a threshold temperature beyond which they are damaged. Increasing the ratio of the Fourier and Joule numbers also increases the tumor temperature, but doing so can damage the healthy tissue. Higher magnetic heating is required for larger Péclet numbers due to the larger convection heat loss that occurs through blood perfusion. A comparison of the model predictions with previous experimental data for MFH applied to rabbit tumors shows good agreement. The optimal MFH conditions are identified based on two indices, the fraction I_T of the tumor volume in which the local temperature is above a threshold temperature and the ratio I_N of the damaged normal tissue volume to the tumor tissue volume that also lies above it. The spatial variation in the nanoparticle concentration is also considered. A Gaussian distribution provides efficacy while minimizing the possibility of generating a tumor hot spot. Varying the thermal properties of tumor and normal tissue alters I_Tand I_N but the nature of the temperature distribution remains unchanged.     

Dynamics of a nonmagnetic drop suspended in a magnetic fluid in a rotating magnetic field

The behavior of a nonmagnetic drop suspended in a magnetic fluid and subjected to the action of a rotating magnetic field is studied experimentally. The configurations of the drop in the form of prolate and oblate ellipsoids of revolution in the rotating field are investigated, and disintegration of the drop in the rotating field and the development of comb instability of its surface under certain conditions are observed.     

Capillary disintegration of a suspended filamentary drop of a viscous magnetic fluid in a longitudinal magnetic field

A differential equation that describes the axisymmetric motion of two immiscible magnetic fluids of the same density and viscosity is derived. It includes in explicit form the contribution of capillary forces localized at the interface between the fluids, which has the form of a weakly distorted cylindrical surface. With this equation, a dispersion relation for the problem of capillary instability of an extended axisymmetric drop placed in a uniform longitudinal magnetic field is obtained. The effect of magnetic forces on the capillary disintegration of the drop for the extreme cases (large and small Ohnesorge numbers) is analyzed.     

Deformation and breakup of aqueous drops in viscous oil under a uniform AC electric field

Electric coalescence in alternating current (AC) electric fields is an important electrical dehydration technology. The deformation and breakup of water drops are crucial to the application of this process. In this study, these procedures were examined experimentally in an AC electric field using a high-speed camera. The deformation and breakup of drops depend on the intensity and frequency of this field. Deformation is aggravated by the increase in frequency under a constant electric field strength. Furthermore, the electric strength of breakup weakens as the frequency increases. Thus, understanding the deformation process can help advance electrocoalescencer design.     

A kinetic approach to the calculation of surface tension of a spherical drop

In literature, surface tension has been investigated mainly from a Thermodynamics standpoint, more rarely with kinetic methods. In the present work, surface tension of drops is studied in the framework of kinetic theory, starting from the Sutherland approximation to Van Der Waals interaction between molecules. Surface tension is calculated as a function of drop radius: it is found that it approaches swiftly an asymptotic value, for radii of several times the distance of minimum approach D of the Sutherland potential. This theoretical asymptotic value is compared to experimental values of surface tension in plane surfaces of a few liquids, and is found in reasonable agreement.     

VOF法模拟剪切流动下液滴的变形和断裂运动

本文对剪切作用下悬浮液滴在另一种不相融的液体中的变形和断裂过程进行了数值模拟.采用VOF(Volume ofFluid)法中的三维PLIC(Piecewise Linear Interface Calculation)算法实现界面的重构和输运,交错网格下投影法离散表面张力为源项的不可压缩Navier-Stokes方程....     

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).     

The stability of ferrofluid flow in a vertical layer subject to lateral heating and horizontal magnetic field

We use the Langevin law of magnetization to study the linear stability of a convective flow in a flat vertical layer of ferrofluid subject to a transverse temperature gradient and a uniform magnetic field. The stability of the flow against planar, spiral and three-dimensional perturbations is examined, and the stability boundaries and characteristics of critical disturbances are determined. The competition between the monotonic mode and two types of wave modes is analyzed taking into account the properties of the fluid (magnetic susceptibility and Prandtl number) and the magnetic field strength. The domain of parameters where the oscillatory thermomagnetic wave instability exists is found.     

On the stability of a free surface of a magnetic fluid under microgravity

We have investigated the behavior of a free surface of a suspension of ferrimagnetic particles in heptane under strongly reduced gravity. It was found that the free surface is destabilized when a homogeneous magnetic field parallel to the surface is applied. The strength of the critical magnetic field parallel to the surface varies with the volume concentration of magnetic particles in the suspension. We show that the destabilization of the fluid layer is forced by the influence of the suspension on the homogeneity of the magnetic field producing a magnetic field component normal to the fluid surface. The dependence of the critical magnetic field on the volume concentration of magnetic particles can be explained by applying the theory of the normal-field instability to this field component under conditions of strongly reduced gravity. The experiments were carried out at the drop tower ‘Bremen’ of the Center of Applied Space Technology and Microgravity (ZARM) in Bremen.     

A stochastic method to determine the shape of a drop on a wall

We present results of a stochastic simulation which determines the shape of a liquid drop, subject to gravity, on a wall. The system is modeled using an Ising model in a field gradient, with Kawasaki dynamics governing the time dependence. We can locate a phase transition between a hanging and a sliding phase with high precision and determine its critical exponents.     

Steady parallel flow in an evaporating fluid heated from sidewalls

Evaporation is ubiquitous in nature, but very few attempts have been made in the past to couple the effects of evaporation with fluid flow behavior. In this theoretical paper we have discussed the effects of evaporation on the dynamics of steady state thermocapillary convection in a two-dimensional rectangular container. The liquid is heated by differentially heated sidewalls and mass loss from the interface due to evaporation is compensated by the liquid entering into the container through a lower inlet, thus keeping the thickness of the liquid layer constant. We show that for an evaporating liquid one can obtain a plane parallel base state profile which depends on the evaporative mass flux.     

Effect of surface tension on a liquid-jet produced by the collapse of a laser-induced bubble against a rigid boundary

The effect of surface tension on the behavior of a liquid-jet is investigated experimentally by means of a fiber-coupled optical beam deflection (OBD) technique. It is found that a target under water is impacted in turn by a laser-plasma ablation force and by a high-speed liquid-jet impulse induced by bubble collapse in the vicinity of a rigid boundary. The liquid-jet impact is found to be the main damage mechanism in cavitation erosion. Furthermore, the liquid-jet increases monotonously with surface tension, so cavitation erosion rises sharply with increasing surface tension. Surface tension also reduces bubble collapse duration. From the experimental results and the modified Rayleigh theory, the maximum bubble radius is obtained and it is found to reduce with increasing surface tension.     

Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces

A lattice Boltzmann equation (LBE) method for incompressible binary fluids is proposed to model the contact line dynamics on partially wetting surfaces. Intermolecular interactions between a wall and fluids are represented by the inclusion of the cubic wall energy in the expression of the total free energy. The proposed boundary conditions eliminate the parasitic currents in the vicinity of the contact line. The LBE method is applied to micron-scale drop impact on dry surfaces, which is commonly encountered in drop-on-demand inkjet applications. For comparison with the existing experimental results [H. Dong, W.W. Carr, D.G. Bucknall, J.F. Morris, Temporally-resolved inkjet drop impaction on surfaces, AIChE J. 53 (2007) 2606–2617], computations are performed in the range of equilibrium contact angles from 31° to 107° for a fixed density ratio of 842, viscosity ratio of 51, Ohnesorge number (Oh) of 0.015, and two Weber numbers (We) of 13 and 103.     

Evaporation coefficient of a spherical fluid drop

The distribution of the number of particles in a fluid drop and in the vapor-gas layer adjoining the drop is simulated by the distribution of catastrophe, generation, and immigration known from the theory of random processes. An expression is obtained for the evaporation rate and an explicit analytic dependence for the evaporation coefficient.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 109–112, November, 1978.The authors are grateful to A. V. Chalom for useful discussions of the results.     

Flexural rigidity of a liquid surface

The energy of a mass of liquid is evaluated asymptotically in powers of the range of the intermolecular potential divided by a typical dimension of the liquid. The leading term is the internal energy, proportional to the liquid volume. The second term is the energy of surface tension, proportional to the area of the liquid surface. The third term is proportional to an integral over this surface of the square of the mean curvature of the surface minus one-third of its Gaussian curvature. This new term has exactly the form of the bending energy of a thin elastic plate. Comparing it with the bending energy yields expressions for the flexural rigidity and the Poisson ratio of the liquid surface. This flexural rigidity of the surface leads to new terms in the equation of equilibrium of the liquid surface, in addition to the usual surface tension terms.     

Correlation for Nusselt number in pure magnetic convection ferrofluid flow in a square cavity by a numerical investigation

Magnetic convection heat transfer in a two-dimensional square cavity induced by magnetic field gradient is investigated numerically using a semi-implicit finite volume method. The side walls of the cavity are heated with different temperatures, the top and bottom walls are isolated, and a permanent magnet is located near the bottom wall. Thermal buoyancy-induced flow is neglected due to the nongravity condition on the plane of the cavity. Conditions for the different values of non-dimensional variables in a variety of ferrofluid properties and magnetic field parameters are studied. Based on this numerical analysis, a general correlation for the overall Nusselt number on the side walls is introduced for a wide range of effective parameters. Results showed that maximum error produced by use of this correlation is about 6 percent.