Wednesday 10 September 2025 16:30 - 17:30 | Promotie Rick Spijkers | Physics of absorption and evaporation of cryogens in a porous medium

Physics of absorption and evaporation of cryogens in a porous medium

The PhD defence of Rick Spijkers will take place in the Waaier building of the University of Twente and can be followed by a live stream

Live stream

Rick Spijkers is a PhD student in the department Energy, Materials and Systems. (Co)Promotors are prof.dr.ir. S. Vanapalli and prof.dr.ir. H.J.M. ter Brake from the faculty Science & Technology (TNW), University of Twente.

Dry-shippers are used to transport biomedical samples at temperatures below -150 °C, maintained by liquid nitrogen absorbed into a porous lining material. The material retains the liquid nitrogen, thereby preventing accidental spills and ensures compliance aviation safety regulations. Despite their widespread adoption, the porous materials present several challenges affecting their performance. These limitation include cleanability, structural integrity, liquid retention and wicking speed. The materials liquid nitrogen retention directly impacts the cold storage time of precious medication, as the heat ingress is counteracted by evaporation of liquid nitrogen. Cleaning is a challenge because traditional liquid cleaning agents would be absorbed into the porous lining, damaging the material on cool down. These challenges necessitate the selection or engineering of new porous media with improved properties. In addition to the traditional dynamics governing the liquid absorption process, evaporation may significantly influence the wicking process within the often superheated porous material of the dry-shipper. While the impact of evaporation on wicking performance is of crucial importance, comprehensive studies addressing this phenomenon are still lacking. This thesis provides a systematic analysis to advance the understanding of evaporation effects on wicking into porous media. The investigation addresses multiple scales, namely the dry-shipper scale, the porous media scale, and the microscale.

On the dry-shipper scale, the focus lays on the behavior of the whole system, in particular the cold storage time, evaporation rate, and temperature profile. The evaluation of dry-shippers is separated into two parts: a review of commercial dry-shippers based on reported performance, and an  experimental examination of a dry-shippers evaporation rate and temperature profile under simulated conditions.

The performance of thirty-two commercial dry-shippers is evaluated to establish a benchmark for future design improvements and to assess the dominant heat leak mechanisms. A predictive model is fitted to the reported cold storage times, estimating storage performance as a function of absorbed liquid nitrogen volume, neck diameter, and a cylindrical approximation of the external surface area. The analysis reveals that heat transfer through the neck is the dominant loss mechanism, contributing at least twice as much as the vacuum insulation. The resulting model provides a reference for optimizing dry-shipper designs by accounting for geometric corrections. These findings suggest that design improvements should primarily target reducing heat leakage through the neck region.

The thermal behavior of a dry-shipper is experimentally investigated and compared to a standard cryostat. Unlike standard cryostats, where liquid nitrogen is stored in a pool at the bottom, dry-shippers retain the liquid within a porous lining, resulting in the absence of stratification. The thermal characteristic is studied by subjecting an instrumented dry-shipper to various simulated conditions, including variations in ambient temperature and placement angle relative to the upright position. The experiments show that, for a fixed ambient temperature, the evaporation rate in the dry-shipper remains constant over time, while in the liquid cryostat it decreases as the liquid level drops. Furthermore, a linear relationship is observed between the evaporation rate and ambient temperature in the dry-shipper, consistent with conductive heat transfer through the neck region. Based on this relationship, a simplified model is developed to predict the evaporation rate as a function of ambient temperature, enabling indirect estimation of the remaining liquid nitrogen charge. This model can assist shipping organizations in planning transport and may be integrated into smart monitoring systems.

The behavior of a dry-shipper is substantially influenced by the porous material retaining the liquid nitrogen. The absorbed liquid volume determines the cold storage time and can be significantly reduced due to vapor trapping. The wicking dynamics are governed by factors such as flow conductivity, capillary pressure, and evaporation rate. These considerations motivate a detailed investigation of the wicking dynamics at the porous scale.

The porous material may trap vapor during dry-shipper filling, particularly when evaporation occurs, which reduces transport and storage time. The conditions leading to vapor formation are investigated by immersing porous samples into liquid nitrogen and measuring the absorbed liquid volume. For saturated liquid nitrogen, materials with small pores (∼0.45 μm) do not retain a vapor phase, whereas materials with larger pores (1–100 μm) are observed to contain a vapor phase. However, after immersion into subcooled liquid nitrogen, no vapor phase is observed in either material, which is attributed to condensation. These findings identify two methods to suppress the formation of a residual vapor phase: using materials with small pores, or condensing the vapor phase by subcooling the liquid nitrogen.

The permeability is investigated as it governs the flow through porous materials. In dry-shippers, the gas permeability is particularly important due to the volumetric expansion upon evaporation, which exceeds a factor of 175. The permeability of the porous lining material was experimentally characterized by measuring the pressure drop over a sample while varying the gas flow rates. At reduced pressures, rarefaction effects were observed, consistent with the Knudsen number, and described by the Klinkenberg correction. At higher flow velocities, form drag effects were observed and described by the Forchheimer correction, even though these were not predicted by Reynolds-number-based criteria. The results show that the Forchheimer number provides a more reliable onset criterion than the Reynolds number, which is primarily applicable to packed particle beds described by the Ergun equation. This underlines the need for careful evaluation of form drag effects in porous materials with unconventional microstructures.

For optimal material selection, it is essential to understand evaporation-affected wicking into superheated porous materials. The mass of both a long porous sample and a liquid nitrogen bath were measured simultaneously after contact, enabling determination of the imbibed liquid mass and the evaporation rate. The wicking behavior of two porous materials showed good agreement with a Lucas-Washburn type model balancing capillary pressure with viscous drag and gravitational forces, although the accuracy depends on the chosen effective pore radius. To examine the generality of the Lucas-Washburn framework, a bonded fibrous material was also characterized. Its permeability and capillary pressure were estimated using a literature model based on fiber diameter and porosity, showing reasonable agreement with observations, considering the limited model inputs. The wicking of both saturated and subcooled liquid nitrogen was also examined to investigate potential reductions in evaporation, but no difference was observed. This behavior was explained by evaluating the vapor recoil pressure and evaporation-induced vapor viscous drag within the Lucas-Washburn framework, showing both effects to be negligible for the small samples examined. Nevertheless, the Lucas-Washburn framework is demonstrated to effectively describe the wicking behavior, particularly when appropriate permeability models and triple-line density models for capillary pressure are applied, which may also provide a valid description of evaporation effects.

The impact of evaporation on capillary-driven imbibition into superheated microchannels is investigated to provide a fundamental understanding of wicking at the pore scale in porous materials. The meniscus movement of ethanol and isopropanol is optically tracked in wide 50 μm deep microchannels that allow for precise temperature control. For microchannels preheated to temperatures below the liquid’s saturation temperature, the meniscus motion agrees well with the Lucas-Washburn equation. At microchannel temperatures exceeding the saturation temperature, imbibition persists up to 6.8 K above the saturation point, accompanied by a gradual velocity reduction until imbibition is fully suppressed. For the liquids used, the volumetric expansion upon evaporation, by at least a factor of 347, leads to a substantial increase in vapor velocity. This effect is incorporated into the Lucas-Washburn equation by accounting for the increased vapor viscosity and the vapor recoil effect resulting from the momentum increase upon evaporation. The experimental results are used to estimate the magnitude of these two effects, together with the evaporation mass flux. The analysis shows that vapor recoil is negligible compared to vapor viscosity, consistent with observations from the porous material wicking experiments. Lastly, a simplified numerical model demonstrates local cooling to the liquid’s saturation temperature near the triple line, thereby preventing the heat flux from approaching infinity as the liquid wedge becomes progressively thinner near the contact line. While the model captures the general dynamics, a discrepancy remains between the predicted and measured evaporation fluxes, indicating the need for a more refined model incorporating the thin film near the triple line and dynamic contact angle variations, which is beyond the scope of the present thesis. These findings establish a solid experimental basis for validating advanced theoretical models of evaporation-driven imbibition and contribute to a fundamental understanding of wicking in porous media affected by evaporation.

Finally, the findings across the investigated scales are summarized and translated into recommendations for dry-shipper design and porous material selection. The Lucas-Washburn framework is briefly reviewed, with particular attention to the commonalities observed across the different scales. Methods to determine the required material properties, based on capillary pressure, viscous drag, and gravitational effects, are discussed. In addition, the influence of evaporation and subcooling is briefly reviewed. These aspects are combined to formulate design guidelines for dry-shippers and porous materials.