An exact solution for the shape of a crystal growing in a forced flow
References (10)
- et al.
J. Crystal Growth
(1986) Dokl. Akad. Nauk SSSR
(1947)- et al.
Ann. Rev. Fluid Mech.
(1986) Phys. Rev.
(1986)- et al.
Phys. Rev.
(1986)
Cited by (47)
Equiaxed dendritic growth in nearly isothermal conditions: A study combining in situ and real-time experiment with large-scale phase-field simulation
2021, Materials Today CommunicationsCitation Excerpt :A comprehensive and in-depth understanding of equiaxed dendritic growth is of vital importance to control the casting processing for optimizing the quality of final products [1,2]. Many theoretical progresses have been gained on the steady-state growth of a dendrite growing freely during solidification of pure substances and alloys [3–6], even with considering the influence of melt convection [7–11]. Meanwhile, amounts of solidification experiments of transparent organic alloys [12,13] were performed to validate these theories.
Free dendritic growth model considering both interfacial nonisothermal nature and effect of convection for binary alloy
2021, Transactions of Nonferrous Metals Society of China (English Edition)Concentration and fluid flow effects on kinetics, dendrite remelting and stress accumulation upon rapid solidification of deeply undercooled alloys
2018, Journal of Alloys and CompoundsCitation Excerpt :Rapid solidification has been a key subject in the solidification field [1–44].
Solute redistribution around crystal shapes growing under hyperbolic mass transport
2015, International Journal of Heat and Mass TransferCitation Excerpt :Analytical solutions of Ivantsov [1–3] about shapes of crystals growing in concentration and heat fields play an exceptional role in solidification theory and have various practical applications. Indeed, Ivantsov solutions present zero order approximation of the stability theory of growing crystals [4,5], they are main equations for the development of dendritic growth models [6], they are the basis for the development of the theory of anisotropic growth of dendritic crystals [7] and crystals under forced convective transport [8], they present basic solutions for numerical tests [9] and they play an extraordinary role in interpretation of experimental data [10,11]. Ivantsov [1–3] and also Horvay and Cahn [12] have found solutions for seven main shapes of crystals which satisfy the balance conditions at the phase interface under diffusional transfer of heat or mass in the bulk system.
Foreword
2015, International Journal of Non-Linear MechanicsMathematical modeling of solidification process near the inner core boundary of the Earth
2013, Applied Mathematical Modelling