Magnetic compensation of gravity forces in „p-… hydrogen near its critical point: Application to weightless conditions R. Wunenburger, 1 D. Chatain, 2 Y. Garrabos, 1 and D. Beysens 2 1 ESEME, Institut de Chimie de la Matie `re Condense ´e de Bordeaux, UPR 9048, Centre National de la Recherche Scientifique, Universite ´ Bordeaux I, Avenue Dr. A. Schweitzer, F-33608 Pessac Cedex, France 2 ESEME, Service des Basses Tempe ´ratures, DRFMC, CEA-Grenoble, 17 rue des Martyrs, F-38054 Grenoble Cedex 09, France Received 28 October 1999 We report a study concerning the compensation of gravity forces in two-phase p- hydrogen. The sample is placed near one end of the vertical z axis of a superconducting coil, where there is a near-uniform magnetic field gradient. A variable effective gravity level g can thus be applied to the two-phase fluid system. The vanishing behavior of the capillary length l C at the critical point is compensated by a decrease in g and l C is kept much smaller than the cell dimension. For g ranging from 1 to 0.25 times Earth’s gravity modulus g 0  we compare the actual shape of the meniscus to the expected shape in a homogeneous gravity field. We determine l C in a wide range of reduced temperature  =( T C -T )/ T C = 10 -4 – 0.02 from a fit of the meniscus shape. The data are in agreement with previous measurements further from T C performed in n-H 2 under Earth’s gravity. The effective gravity is homogeneous within 10 -2 g 0 for a 3 mm diameter and 2 mm thickness sample and is in good agreement with the computed one, validating the use of the apparatus as a variable gravity facility. In the vicinity of the levitation point where magnetic forces exactly compensate Earth’s gravity, the computed axial component of the acceleration is found to be quadratic in z, whereas its radial component is proportional to the distance to the axis, which explains the gas-liquid patterns observed near the critical point. PACS numbers: 68.10.-m, 64.60.Fr, 07.20.Mc I. INTRODUCTION Magnetic levitation of matter consists of the compensa- tion of its weight by magnetic forces. Because of the weak diamagnetic susceptibility of many nonmagnetic substances, strong magnetic fields are needed for magnetic levitation. Such field intensities have been attained only recently. Since the first demonstration of magnetic levitation of diamagnetic substances 1,2, this technique has chiefly been applied to the containerless handling of liquids, solids, or living bodies 1–7, the simulation of low gravity or weightless conditions for life science 3, and fluid physics noncoalescence of liq- uid drops in contact 5,6, deformations modes of drops 7, investigation of the lambda transition in helium 8. In some previous work using magnetic weightlessness, precise mea- surements of the magnetic field 8 as well as detailed ana- lytical and numerical calculations of the force field applied to the sample were performed 1,4,6,8. However, no measure- ment of the residual gravity has been performed. In this pa- per, we present a simple method to check the homogeneity of the total acceleration field. It is based on the analysis of the shape of the gas-liquid interface and on the vanishing behav- ior of the capillary length of a liquid-gas mixture of hydro- gen in equilibrium near its critical point. Containerless handling applications require only a global compensation of the total weight of the body and a stable levitation to be met, whereas gravity compensation needs more conditions to be fulfilled. Indeed, when a diamagnetic sample is placed in a magnetic field B, each of its molecules is subjected to a force that is proportional to its magnetic susceptibility  and to the local gradient of B 2 . The resulting magnetic acceleration vector a m induced by the magnetic field B is a m =   0  “ 1 2 B 2  , 1 where  is the sample density and  0 =4  10 -7 Hm -1 . The total acceleration vector applied to the sample on the Earth is g=g 0 +a m , 2 where g 0 is the gravitational acceleration vector. Let g * be the reduced acceleration modulus effective gravity level g * =  g  g 0  , 3 which can be larger or smaller than 1 due to the vectorial character of Eq. 2. The acceleration field g is homogeneous at the length scale of the sample provided that the B 2 gradi- ent and the chemical composition of the sample are homo- geneous at the sample length scale. Under these conditions, Earth’s gravitational acceleration can be increased, partially compensated, or exactly cancelled in the same manner at each point of the sample. This leads to the accomplishment of a tunable artificial gravity, ranging from large to low val- ues of g * , and ultimately reaching weightlessness ( g * =0). Since a homogeneous acceleration field can be achieved only within a given precision, it is useful to evaluate the maximum deviation of g * from its mean value within the sample  g * = max sample  |  g *  sample -g *|  . 4 PHYSICAL REVIEW E JULY 2000 VOLUME 62, NUMBER 1 PRE 62 1063-651X/2000/621/4698/$15.00 469 ©2000 The American Physical Society