Modeling the interaction of biological cells with a solidifying interface

Chang, A. T.; Dantzig, Jonathan A.; Darr, Brian T.; Hubel, Allison

doi:10.1016/j.jcp.2007.05.039

Cited by 23 publications

(17 citation statements)

References 56 publications

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“…Sharp treatment of the boundary conditions is also done in the ghost-fluid approach of [72,74,75], which has also been applied to the case where the grid is encoded by quadtrees in the case of the solidification of a unary system [51,76]. In [77], the authors also used the boundary treatment of [72,74] to simulate the growth of a binary system on graded quadtree grids. The work of [77] is applied to cryopreservation, in which the temperature field is assumed to be unaffected by the solidification process.…”

Section: Description Of the Solidification Frontmentioning

confidence: 99%

“…In [77], the authors also used the boundary treatment of [72,74] to simulate the growth of a binary system on graded quadtree grids. The work of [77] is applied to cryopreservation, in which the temperature field is assumed to be unaffected by the solidification process. In the present paper, we focus on the solidification of binary alloys, for which this assumption is invalid, as can been seen in Eqs.…”

Section: Description Of the Solidification Frontmentioning

confidence: 99%

See 1 more Smart Citation

A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys

2014

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We present a numerical method for the simulation of binary alloys. We make use of the level-set method to capture the evolution of the solidification front and of an adaptive mesh refinement framework based on non-graded quadtree grids to efficiently capture the multiscale nature of the alloys' concentration profile. In addition, our approach is based on a sharp treatment of the boundary conditions at the solidification front. We apply this algorithm to the solidification of an Ni-Cu alloy and report results that agree quantitatively with theoretical analyses. We also apply this algorithm to show that solidification mechanism maps predicting growth regimes as a function of tip velocities and thermal gradients can be accurately computed with this method; these include the important transitions from planar to cellular to dendritic regimes.

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Section: Description Of the Solidification Frontmentioning

confidence: 99%

Section: Description Of the Solidification Frontmentioning

confidence: 99%

A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys

2014

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“…However, it is still a rather difficult task to track the evolution of the solidification front and characterize the interaction between the cell membrane and ice in detail. Recently, the progress [35,36] gave some promising research directions to solve this issue.…”

Section: The Interaction Between Ice Growths With Cellmentioning

confidence: 99%

“…Another important process is from Chang et al [36]. They developed a modified level set method for modeling the interaction of biological cells with ice front during a directional solidification.…”

Section: The Interaction Between Ice Growths With Cellmentioning

confidence: 99%

Modeling Ice Crystal Formation of Water in Biological System

He¹,

Liu²

2013

Advanced Topics on Crystal Growth

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“…Mazur's model above and modern nonideal models such as the one proposed and examined by Weng et al [121], for example, assume that there is no solute polarization or other chemical potential gradient generated by the sequestration of water into the incoming ice front. Models addressing concentration gradients generated by ice fronts have been proposed (see for example [15]), but these are the exception rather than the rule. At the cell-media interface, there is a large body of literature on so-called unstirred layers in the physiology literature (see, e.g.…”

Section: Introductionmentioning

confidence: 99%