Date of Award

Spring 1-1-2012

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Y.C. Lee

Second Advisor

Ray Radebaugh

Third Advisor

Victor M. Bright

Fourth Advisor

Ronggui Yang

Fifth Advisor

John W. Daily


A number of small electronic devices benefit from micro-scale low temperature operation. Recently at the University of Colorado at Boulder and the National Institute of Standards and Technology, we have developed micro cryogenic coolers that a low-pressure, mixed-refrigerant Joule-Thomson cycle. Our devices utilize pressures that are a factor of 4 lower than the current state-of-the-art, and these low pressures allow us to use a miniature compressor. However we found that the mixed refrigerant does not perform as one would expect for larger cryocooler, due to the mini- and micro-channel flow regimes experienced by the micro cryocooler. In particular, the refrigerant experiences poor cooling with steady flow followed by enhanced cooling with pulsating flow. This dissertation covers the development of the mixed-refrigerant Joule-Thomson micro cryocooler and associated micro compressor, an analysis of the steady flow regime, an analysis of the pulsing flow regime, and the development of a model both regimes which can be used to optimize refrigerant composition and performance in micro coolers. It is found that the steady flow regime corresponds to hold-up of the liquid components of the mix along the channel wall. It can be modeled according to a solution of the Navier-Stokes equations for annular flow in a mini-channel. The pulsing flow regime corresponds to the development of liquid slugs in high-pressure mini-channels that completely fill the micro-channels. Furthermore, a model of refrigerant cooling power has been derived and verified for mixed refrigerants undergoing pulsating flow. Using this model, refrigerant mixture designs have been modified to improve cooling power and thermodynamic efficiency: a refrigerant mix designed to cool to 160 K using macro-scale mixture design rules has a specific cooling power of 237 J/mol and a thermodynamic efficiency of 8.4 % under pulsing flow, but these can be increased to 831 J/mol and 32.8 % respectively when the mix is re-designed according to the pulsating model. The steady flow model will be valid when a refrigerant mixture experiences a laminar, annular two-phase flow pattern in mini-channels. The steady flow model will fail if the liquid phase in the mini-channel fills too much of the volume, and the flow is no longer annular; in that case the pulsating flow may apply. The pulsating flow model will apply in multi-phase multi-component systems when liquid slugs form in mini-scale channels before passing into micro-channels. The limitation of this model is the assumption that 2-phase flow can be modeled as two single-phase flows, which will not be valid if volume of the liquid slugs is not greater than the volume of the micro-channels--such as in fully integrated micro-compressor/micro-cooler systems that have no mini-scale coupling channels. This pulsating flow regime represents a new flow regime to the field of cryogenics. Novel contributions from this work to the field of cryogenics include the experimental and theoretical analysis of heat and mass transport of mixed refrigerants at the interface of micro- and mini-channels. Such transport is a fundamental problem in the heat transfer community, and novel contributions of this work to that community include the study of refrigerant mixtures which experience two-phase flow over very large temperature ranges.