Stability of the needle crystal

Kotler, G.R.; Tiller, W. A.

doi:10.1016/0022-0248(68)90017-1

Cited by 32 publications

(8 citation statements)

References 5 publications

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“…Already during the later 1960s, it was hypothesised that morphological stability rather than extremum growth was the key element in modelling dendrite tip behaviour. Kotler and Tiller [62] concluded, ' … a true time-dependent perturbation analysis is vital to the development of a … detailed theory of dendritic growth'. Oldfield, a Ph.D. student of Tiller, undertook the first numerical simulations of dendrites in the mid-1960s.…”

Section: Marginal Stabilitymentioning

confidence: 99%

Progress in modelling solidification microstructures in metals and alloys: dendrites and cells from 1700 to 2000

Kurz

Fisher

Trivedi

2018

International Materials Reviews

155

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This is the first account of the history of our understanding of, and ability to model, solidification microstructures. Its objective is to retrace the scientific steps made, from the earliest observations of the eighteenth century to our present-day understanding of dendrites and eutectics. Because of the abundance of information, especially that added during the present century, sub-division was essential: this being the first of three articles. They cover dendrites and cells from 1700 to 2000, and then from 2001 to 2015 and finally eutectics and peritectics from 1700 to 2015. The authors have striven always to identify the genesis of every advance made, being aware that such a compact history must leave many worthy contributions by the wayside; others will doubtless complete the history. This review shows how crossfertilisation between theory and experiment, and basic and applied research led to both the posing and answering of challenging fundamental questions, thus rewarding society with beneficial results.

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Section: Marginal Stabilitymentioning

confidence: 99%

Progress in modelling solidification microstructures in metals and alloys: dendrites and cells from 1700 to 2000

Kurz

Fisher

Trivedi

2018

International Materials Reviews

155

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“…Once a planar solid-liquid interface has become unstable, the theoretical description of the solidification process becomes more difficult as the geometry of the developing protrusions has to be taken into account. A number of models have been presented for the growth of single needle-shaped crystals (Ivantsov, 1947;Kotler & Tiller, 1968) and for a cellular growth morphology (Boiling & Tiller, i960). As mentioned above, the needle-or tongue-like protrusions tend to become unstable themselves such that perturbations, particularly in the 'shoulder' region, result in the formation of side-branches and dendritic structures (cf.…”

Section: Non-planar Growth Of Icementioning

confidence: 99%

Phenomena at the advancing ice–liquid interface: solutes, particles and biological cells

Körber

1988

Quart. Rev. Biophys.

137

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Ice formation in aqueous solutions and suspensions involves a number of significant changes and processes in the residual liquid. The resulting effects were described concerning the redistribution of dissolved salts, the behaviour of gaseous solutes and bubble formation, the rejection and entrapment of second-phase particles. This set of conditions is also experienced by biological cells subjected to freezing. The influences of ice formation in that respect and their relevance for cryopreservation were considered as well. A model of transient heat conduction and solute diffusion with a planar ice front, propagating through a system of finite length was found to be in good agreement with measured salt concentration profiles. The spacing of the subsequently developing columnar solidification pattern was of the same order of magnitude as the pertubation wavelengths predicted from the stability criterion. Non-planar solidification of binary salt solutions was described by a pure heat transfer model under the assumption of local thermodynamic equilibrium. The rejection of gaseous solutes and the resulting gas concentration profile ahead of a planar ice front has been estimated by means of a test bubble method, yielding a distribution coefficient of 0.05 for oxygen. The nucleation of gas bubbles has been observed to occur at slightly less than 20-fold supersaturation. The subsequent radial growth of the bubbles obeys a square-root time dependence as expected from a diffusion controlled model until the still expanding bubbles become engulfed by the advancing ice-liquid interface. The maximum bubble radii decrease for increasing ice front velocities. The transition between repulsion and entrapment of spherical latex particles by an advancing planar ice-front has been characterized by a critical value of the velocity of the solidification interface. The critical velocity is inversely proportional to the particle radius as suggested by models assuming an undisturbed ice front. The increase of the critical velocity for increasing thermal gradients shows good agreement with a theoretically predicted square-root type of dependence. Critical velocities have also been measured for yeast and red blood cells. The effect of freezing on biological cells has been analyzed for human lymphocytes and erythrocytes. The reduction of cell volume observed during non-planar freezing agrees reasonably well with shrinkage curves calculated from a water transport model. The probability of intracellular ice formation has been characterized by threshold cooling rates above which the amount of water remaining within the cell is sufficient for crystallization.(ABSTRACT TRUNCATED AT 400 WORDS)

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“…The occurrence of sidebranches can be attributed to the diffusive (Mullins and Sekerka) instability. According to Mullins and Sekerka [10], a planar solid-liquid interface is morphologically unstable against infinitesimal small perturbation if the wavelength of the perturbation l is larger than the characteristic stability length l s of system defined as l s ¼ 2pðd 0 lÞ 1=2 , where l is the diffusion length, which is given by l ¼ 2Du À1 for planar interface advancing with the growth velocity u. Kotler and Tiller [11] have performed one of the first analytic investigations of the dendrite sidebranch evolution. They applied the Mullins and Sekerka-type perturbation analysis to steady-state paraboloid of revolution, and showed that such a body is unstable against evolution of repetitive rings.…”

Section: Introductionmentioning

confidence: 99%