Physical and mechanical properties such as yield strength, compression stress, thermal and electrical conductivities, and absorption coefficient strongly depend on directions and shapes of a pore. Pores formation during horizontal solidification often occurs in welding, casting, 3-D printing, biology, tissue, MEM, micro- or nano-engineering, foods, geophysics, aerospace, and outer space, etc. Since base area of a bubble on the solidification front moving in horizontal direction deviates from the center of mass of the bubble, torque induced by external forces such as gravity force increases, leading to different behavior of bubble entrapment from that of vertical solidification.

Using available scaling in the literature, velocity of free convection driven by heat transfer or mass transfer is much less than that induced by force convection by considering the same magnitudes between buoyancy and viscous force, and convection and diffusion in thermal and concentration boundary layers, respectively [Wei and Lin, 2022]. The variation of gravitational acceleration on the pore shape under a terrestrial condition during horizontal solidification is thus negligibly small. Development of the pore shape is therefore investigated by significantly boosting gravitational acceleration, which can be produced by centrifuges used in sciences, medicine to separation of single cell suspensions and macromolecules from blood or solutions, etc., and big centrifuges to test the tolerance of astronauts with accelerations larger than that of Earth’s gravity.

Solute transport coupling with shape development of a pore resulting from a bubble entrapped by a solidification front proceeding in horizontal direction can be thoroughly investigated by solving transport equations of mass, momentum, energy, concentration and phase field equations [Wei and Lin, 2022]. Fluid flow across the cap of a bubble filled with high solute gas pressure after supersaturated nucleation is usually outward, leading to bubble growth in the early stage. Provided that gravitational acceleration significantly increases, flow away from the bubble becomes downward. A closed bottom boundary thus forces the flow to change into inward and upward directions. Increased hydrostatic pressure with gravitational acceleration may override solute gas pressure in the pore, resulting in receding the lower part of the bubble cap. The bubble cap surrounded by a circulation flow becomes a non-circular shape growing in the upper part whereas receding in the lower part. In the absence of flow circulations, the pore deforms slightly for an opening condition at the bottom. There also finds high concentration regions in triangular shape covering solid and liquid near the triple-phase line. Solute segregation in solid and liquid around the isolated pore is significantly affected by different transport and materials properties. Iso-concentration lines exhibit different semi-enclosures in solidified solid as a result of oscillatory solidification front. The pore shape and solute concentration thus can be controlled by adjusting ambient pressure, fluid flow imposed on boundaries, and material and transport properties.

About the author

Mr. Pin-Yi Lin received B.S. from Mechanical and Electro-Mechanical Engineering Department in Tamkang University, Taipei, Taiwan. He is a graduate student in National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC. His major is thermal sciences in manufacturing processes.



About the author

Dr. Peng-Sheng Wei received Ph.D. in Mechanical Engineering Department at University of California, Davis. He is a professor in the Department of Mechanical and Electro-Mechanical Engineering of National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC. Dr. Wei has contributed to advancing studies of thermal and fluid flow processes, and formations of the defects such as humping, rippling, spiking and porosity during solidification. Dr. Wei has published more than 90 SCI journal papers. He is a Fellow of AWS and ASME. He received the Outstanding Research Achievement Awards from both the National Science Council, and NSYSU, the Outstanding Scholar Research Project Winner Award from NSC, the Adams Memorial Membership Award, the Warren F. Savage Memorial Award, and the William Irrgang Memorial Award from AWS, and the Elihu Thomson Resistance Welding Award from RWMA and AWS. He has been the Xi-Wan Chair Professor of NSYSU, and Invited Distinguished Professor in the Beijing University of Technology, China.


Wei, P. S., and P. Y. Lin, Transport processes for a bubble entrapment during horizontal solidification, Int. J. Therm. Sci., 172(2022)107314.

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