Interfaces ice-pore

In order to quantify the matter transfers involved at the ice/pore interface, we can express the incoming matter flux j [mol m" s" ] on a point of the ice surface by using the Langmuir-Knudsen formula ... 

In our model, the ambient vapour pressure is considered as uniform on any horizontal plane of the snow sample (because the macroscopic TG can be supposed constant across the sample). Consequently, on such a plane, P(Ca,Tf) is given by the values of the curvature and temperature that have been averaged on the considered plane. By knowing the temperature and the curvature fields on the ice/pore interface, one can then use the equation (5) to compute the local matter fluxes occurring in each point of this interface. 

As shown in part 2, the sign of Z can predict the faceting or the rounding of the shapes. So, having a 3D image of snow offers to check the validity of our model. We tested the model on a sample submitted to a low TG of 3 K m". To compute Z, we need to estimate both the curvature and the temperature in each point of the ice/pore interface ... 

In membrane filtration, water-filled pores are frequently encountered and consequently the liquid-solid transition of water is often used for membrane pore size analysis. Other condensates can however also be used such as benzene, hexane, decane or potassium nitrate [68]. Due to the marked curvature of the solid-liquid interface within pores, a freezing (or melting) point depression of the water (or ice) occurs. Figure 4.9a illustrates schematically the freezing of a liquid (water) in a porous medium as a fimction of the pore size. Solidification within a capillary pore can occur either by a mechanism of nucleation or by a progressive penetration of the liquid-solid meniscus formed at the entrance of the pore (Figure 4.9b). 

Thermoporimetry [10,11] can reliably be used to obtain the pore-size distribution of porous particles suspended in water. The basis of the technique is that the surface area of the ice-liquid water interface increases when the ice penetrates narrow pores. As the diameter of a pore is smaller, the increase in interfacial area is larger. To freeze the water in narrower pores thus requires lower temperatures. The temperature at which the heat of solidification of water is set free thus indicates the width of the pores, and the amount of heat released indicates the pore volume. Measurement by DSC (differential scanning calorimetry) can provide the data for determination of the pore-size distribution of porous particles suspended in pure water. It has been observed that the first layer of water molecules present on the surface of oxides cannot be frozen apparently the interaction with the surface of the oxides is so high that the layer is already frozen without attaining the structure of ice. Thermoporimetry can, therefore, also provide data about the interaction of water with the surfaces of solids. Thermoporimetry with other liquids, e. g. benzene, can provide information about the interaction of surfaces with, e. g., apolar liquids. 

Microporous membranes are often used in many processes to remove impurities or contaminants through size-selective filtration. The breath figures method also finds application in this field, specially the approaches that facilitate the easy transfer to other supports. Another prerequisite is the formation of through pores that penetrate from the top of the layer to the bottom and the use of ice support favors this fact. For example, highly uniform membranes of PS-h-PDMAEMA have been prepared with pores on the micrometer scale for size-selective separation. The films were prepared by casting at an air-ice interface and easily transferred onto other supports [219]. Miktoarm star copolymers with proper water wettability and mechanical stability have been used to fabricate separation membranes also using ice substrate [131]. Moreover, the breath figures approach has been employed to build polymer membranes on structured substrates in order to obtain hierarchically structured microsieves [208]. 

In spite of the advances made in PEFC modeling, many challenges remain. First, there is a critical need to couple, in some computationally efficient way, the pore-level or particle-level submodels with the macroscopic cell-level models in order to take into account the effects of the microstmctures of CDL/MPL and CL. Second, further efforts are also needed to model the cold start, transient, and two-phase transport at the ceU level. At present, a framework of single fuel-cell modehng has been developed, but the physics is not yet completely understood. For example, ice formation within the catalyst layer and its impact on the electrochemical reaction need further study. The two-phase transport at the CL-MPL and MPL-CDL interfaces is not clearly understood at present. Third, current... 

The water distribution was then captured with the freezing method detailed above. The pictures indicate that ice formed at the interface between the CL and MPL and no ice can be observed in the MPL pores. This suggests that there is no liquid water in the pores in the MPL although there is liquid water at the interface. The capillary pressure of water in the pores can be estimated to be in the order of 300 kPa and it would appear to be difficult for water to flow into the pores in liquid form. 

An interesting theory of the interference of ice formation and growth rate and conversely the damage to porous media produced by ice formation has been described in reference [150]. By use of expressions for the forces across interfaces related to the surface tension between the various components and the tension generated in a circular gel pore by an advancing curved ice front, the reduction in melting temperature of the ice can be derived from the Clausius-Clapeyron equation according to... 

Water rises up capillary tubes. In freezing soils, numerous experiments and the frost heave phenomenon itself demonstrate that water moves towards the interfaces of ice with water in the soil pores (capillaries). Furthermore, as water leaves the soil pores. 

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