High-purity pivalic acid (PVA) dendrites were observed growing under convection-free conditions during the isothermal dendritic growth experiment (IDGE) flown on NASA's space shuttle Columbia on STS-87. The IDGE was part of the complement of primary scientific experiments designated as the United States Microgravity Payload Mission (USMP4) launched late in 1997. The IDGE video data show that PVA dendrites may be melted without exhibiting any detectable relative motion with respect to the surrounding quiescent melt phase. Thus, melting occurs by heat conduction alone. When a small fixed superheating is imposed on pre-existing dendritic fragments, they melt steadily toward extinction. Individual fragments steadily decrease in size according to a square-root of time dependence predicted using quasi-static conduction-limited theory. Agreement between analytic melting theory and microgravity experiments was found originally if the melting process occurs under the restriction of shape-preserving conditions, where needle-like crystal fragments may be approximated as ellipsoids with a constant axial ratio. Among the new results reported here is the influence of capillarity effects on melting in needle-like crystallites, observed as a dramatic change in their axial ratio, when the size scale of a crystallite decreases below a critical value. In microgravity melting experiments, the axial ratio of individual crystallites does not remain constant, because of interactions with neighboring fragments within the mushy zone. The kinetic data were then "sectorized" to divide the total melting process into a series of short intervals. Each melting sector for a crystallite could then be approximated by a constant average value of the axial ratio. Sectorization also allows accurate prediction of melting kinetics by applying quasi-static heat conduction theory, despite the suspected presence of capillarity and the occurrence of fragmentation. These additional processes that accompany the melting of slender crystallites currently lie outside conventional melting theory. The data presented show that melting kinetics of small crystallites remains dominated by heat conduction from the surrounding melt, which is modified by the appearance of additional heat fluxes. These additional heat fluxes flow within the crystallites. They arise from capillary effects induced by steep interfacial curvature gradients that accompany the small crystallite size scales prior to their extinction. (c) 2004 Elsevier B.V. All rights reserved.