THRESHOLD SIZE FOR FLOWERING IN DIFFERENT HABITATS: EFFECTS OF SIZE-DEPENDENT GROWTH AND SURVIVAL

A fully passive microdroplet sorting method is presented in this paper. On the rails with dot patterns, the droplets were sorted in different ways depending on their size. However, the effect of droplet properties on the threshold size of the sorting was eliminated. The droplet positions on two railways and the Laplace pressure of the droplets on the dot patterns allowed selective droplet transfer according to size. Different gaps between the rails altered the threshold size of the transfer. However, the threshold size was independent of the droplet’s surface tension and viscosity because the droplet transfer utilized only the droplet position and Laplace pressure without lateral flow to sort targets. This feature has a high potential for bio/chemical applications requiring categorization of droplet targets consisting of various mixtures as pre- or post-elements.

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Size-Dependent Phase Transformation during Gas Atomization Process of Cu–Sn Alloy Powders

Materials ◽

10.3390/ma12020245 ◽

2019 ◽

Vol 12 (2) ◽

pp. 245 ◽

Cited By ~ 3

Author(s):

Hao Pan ◽

Hongjun Ji ◽

Meng Liang ◽

Junbo Zhou ◽

Mingyu Li

Keyword(s):

Phase Transformation ◽

Nucleation Theory ◽

Gas Atomization ◽

Atomization Process ◽

Cu6sn5 Phase ◽

Lotus Leaf ◽

Threshold Size ◽

Size Dependent ◽

Droplet Sizes ◽

Transient Nucleation

For binary element atomization, it is essential to investigate the phase transformation from liquid to solid as a functions of the droplet sizes, as well as the reaction competitiveness, during gas atomizing solidification of their nuclei. In the present work, a series of phase transformations of undercooled Cu (60.9 wt.%)/Sn droplets were analyzed when atomized by pressure gas. The results indicated that the microstructures of the obtained powders and their morphologies were highly relevant to the droplet size. According to the phase characteristics analyzed by the microstructural observations in combination with the transient nucleation theory, powders with sizes from 10 to 100 μm were divided into three categories, exhibiting lotus-leaf, island, and stripe morphologies. The competitive formation of Cu6Sn5 or Cu3Sn was also controlled by the droplet sizes, and a diameter of approximately 45 μm was identified as the threshold size. After heat treatment at 300 °C for 4 h, the powders consisted of a single η’ Cu6Sn5 phase. The obtained Cu6Sn5 phase powders can be used in the field of high-temperature applications as intermetallic balls for integrated chip interconnects.

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The expected population size in a cell-size-dependent branching process

Journal of Applied Probability ◽

10.1017/s0021900200097618 ◽

1981 ◽

Vol 18 (01) ◽

pp. 65-75 ◽

Cited By ~ 1

Author(s):

Aidan Sudbury

Keyword(s):

Cell Size ◽

Exponential Growth ◽

Branching Process ◽

Expected Number ◽

Size Dependent ◽

Daughter Cells ◽

Rate Of Increase ◽

A Cell ◽

Dependent Growth ◽

Number Of Cells

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

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