An approximate mathematical model for solidification of a flowing liquid in a microchannel

Myers, T.G.; Low, J.

doi:10.1007/s10404-011-0807-4

Cited by 16 publications

(17 citation statements)

References 22 publications

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“…An expression for the annular ice growth period ( ) can be obtained by integrating Eq. Low [39] adopted a different modeling approach where they used lubrication theory to approximate the period of annular ice growth in microchannels and arrived at the same conclusion.…”

Section: Model Simplificationmentioning

confidence: 99%

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Ice formation modes during flow freezing in a small cylindrical channel

Jain

Miglani

Huang

et al. 2019

International Journal of Heat and Mass Transfer

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Freezing of water flowing through a small channel can be used as a nonintrusive flow control mechanism for microfluidic devices. However, such ice valves have longer response times compared to conventional microvalves. To control and reduce the response time, it is crucial to understand the factors that affect the flow freezing process inside the channel. This study investigates freezing in pressure-driven water flow through a glass channel of 500 m inner diameter using measurements of external channel wall temperature and flow rate synchronized with high-speed visualization. The effect of flow rate on the freezing process is investigated in terms of the external wall temperature, the growth duration of different ice modes, and the channel closing time. Freezing initiates as a thin layer of ice dendrites that grows along the inner wall and partially blocks the channel, followed by the formation and inward growth of a solid annular ice layer that leads to complete flow blockage and ultimate channel closure. A simplified analytical model is developed to determine the factors that govern the annular ice growth, and hence the channel closing time. For a given channel, the model predicts that the annular ice growth is driven purely by conduction due to the temperature difference between the outer channel wall and the equilibrium ice-water interface. The flow rate affects the initial temperature difference, and thereby has an indirect effect on the annular ice growth. Higher flow rates require a lower wall

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Section: Model Simplificationmentioning

confidence: 99%

“…D mathematical model for predicting annular ice growth in square and circular cross-section microchannels was presented by Myers and Low[39]. The channel length was assumed to be much larger than the hydraulic diameter in order to simplify the governing equations based on the lubrication theory.…”

mentioning

confidence: 99%

Ice formation modes during flow freezing in a small cylindrical channel

Jain

Miglani

Huang

et al. 2019

International Journal of Heat and Mass Transfer

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“…The problem configuration is shown on With the exception of the power law stress tensor, the above equations are identical to those describing the solidification of a Newtonian fluid studied in [11] (which in turn were adapted from the models in [12,13]). In [11] the governing equations were non-dimensionalised in the standard manner consistent with lubrication theory. Obviously we may also non-dimensionalise the above system, however, if the flow is driven by a pressure gradient (and so ∆p is fixed) then the velocity scale depends on the power law parameters.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…This means that when we compare results for different fluids, with different values of n, then the definition of the velocity scale changes and so the comparisons are not appropriate. For example in [11] the pipe closure time was plotted against the Péclet number, P e = U R 2 /(α l L). With a power law fluid, if the definition of U changes with each fluid then so will the definition of P e. For this reason we will work in dimensional form, whilst retaining the approximations suggested from the earlier non-dimensional study.…”

Section: Mathematical Modelmentioning

confidence: 99%

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Modelling the solidification of a power-law fluid flowing through a narrow pipe

Myers

Low

2013

International Journal of Thermal Sciences

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We develop a mathematical model to simulate the solidification process of a non-Newtonian power-law fluid flowing through a circular crosssection microchannel. The initial system consists of three partial differential equations, describing the fluid flow and temperature in the liquid and solid, which are solved over a domain specified by the Stefan condition. This is reduced to solving a partially coupled system consisting of a single partial differential equation and the Stefan condition. Results show qualitative differences, depending on the power law index and imposed flow conditions, between Newtonian and non-Newtonian solidification. The model behaviour is illustrated using power law models for blood and polyethylene oxide.

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