Ferrofluid meniscus in a horizontal or vertical magnetic field

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Abstract

An optical system using reflections of a narrow laser beam to measure the height and shape of a ferrofluid meniscus in response to uniform applied magnetic fields finds that meniscus height on a vertical flat wall decreases in horizontal applied field and increases in vertical applied field. An approximate energy minimization analysis predicts meniscus height in directional agreement with measurements. This study is a first step in calculating the tangential surface force acting in flows where magnetization magnitude and direction lag a changing magnetic field direction, and the meniscus shape is magnetically perturbed.

Introduction

Spin-up and related flows in ferrofluids experience tangential force on the free surface ξ(x) that depends on the meniscus geometry [1], giving motivation for this study. We performed experimental measurements of meniscus height h=ξ(0) and shape ξ(x) using narrow diameter laser beam reflections from the meniscus interface as a function of DC applied magnetic fields, see Fig. 1. The angle of deflection of the laser beam from the vertical allows us to compute the shape of the ferrofluid meniscus.

Section snippets

Meniscus measurements

We made measurements with oil- and water-based ferrofluids having the properties listed in Table 1. Three applied magnetic field arrangements are used as shown in Fig. 2. A meniscus forms on the sides of a glass slide immersed in the center of a vessel where negligibly small field gradients are 0.75G/cm at an applied magnetic field of 500 G. Fig. 3 shows for both ferrofluids that applied magnetic field in configuration a has practically no effect on the meniscus shape. Thus, as expected with a

General results

We utilize an approximate analysis with the objective of capturing trends of the data while providing physical insight. The idealized shape of the entire volume of ferrofluid is shown in Fig. 4. The meniscus regions are represented by a triangular zone neglecting the 1.0 mm thick glass slide. Total energy E for unit distance into the plane of Fig. 4 is given by the sumE=ES+EW+EG+EM,where the terms on the right side denote surface, wall, gravitational, and magnetic energies. The system's

Concluding remarks

The data show that theory and experiment are in directional agreement: horizontal field perpendicular to the wall reduces meniscus height; vertical field increases the height, and field parallel to the wall has no effect. Data points in Fig. 5 for water-based ferrofluid show fair agreement with theory, with susceptibility calculated as the geometric mean of initial and tangential values. The variance of the oil-based data from model predictions is currently under study.

Acknowledgements

This research is supported by National Science Foundation Grant# CTS-0084070.

References (3)

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