Interface- and diffusion-limited capillary rise of reactive melts with a transient contact angle

The kinetics of unidirectional capillary penetration by a reactive fluid under the limiting cases of diffusion control and interface control has been derived for the reactive infiltration phenomenon characterized by a shrinking capillary radius due to interphase formation and an exponentially decaying contact angle. The computational outcomes for the reactive penetration of Si₃N₄ capillaries by AgCuTi brazes and of carbon capillaries by Si show that greater lengths are attained at lower values of the parabolic rate constant (under diffusion control), and the limiting length is reached earlier at larger values of the linear rate constant (under interface control). A capillary-driven flow analysis (Washburn equation) overestimates the infiltration kinetics, whereas an analysis that considers pore shrinkage but assumes the contact angle and the capillary pressure to be constant during flow underestimates the kinetics. The penetration lengths predicted by the analysis at pore closure due to reaction choking exhibit a slightly better agreement with the recent measurements in the Si/C system than the models of reactive flows currently in vogue.