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The migration of liquid droplets in a solid phase caused by temperature gradient zone melting (TGZM) is simulated by employing adaption of the quantitative phase-field (PF) model proposed by Echebarria et al.The PF simulation results are compared with the predictions of an analytical model that describes the droplet migration for both static and dynamic conditions, allowing the direct solution of the time dependent migration velocity of a liquid droplet that is initially located at an arbitrary position in the mushy zone.