# Theoretical and Experimental Analysis for Cleaning Ice Cores from EtisolTM 140 Drill Liquid
## 2 Theoretical Section and Calculations
### Evaluation of Ice Sublimation and Fluid Evaporation  
At the drilling site of BEOI, a ventilated container is planned for storing fresh ice cores for one week at \(-50\ ^{\circ}C\) with a suggested air flux of 40 m\({}^{3}\)/h. The aim is to remove the drilling fluid from the ice by drying. There are, however, two constraints: loss of ice should be small (the best would be nothing) and removal of drilling fluid should be large (the target would be all of it). Considering Equations (1) and (2), the main driving force for material diffusion is the difference between the vapor partial pressures. We may assume that initially the ice is covered by the drilling fluid, but after some time it may become exposed. Sublimation of exposed ice is driven by the relative humidity of the air surrounding the core. Under static conditions (no air is exchanged) an equilibrium is eventually reached, and sublimation stops when \(P_{V}=P_{ice}=P_{sat}\); RH\(\%=100\%\). In our system, the air for ventilation is taken from a deep hole in the firm pack at the temperature of \(-50\ ^{\circ}C\), which is the annual mean temperature at the site. As this air is passing through only snow and firm before entering the container, the equilibrium conditions of the air match those of the air inside the container. This condition prevents the sublimation of ice from the core: \(M=0\). Moreover, since sublimation requires heat (latent heat of sublimation is about 675 Cal/g = 2824 J/g), the surface material of the ice core will cool from any small amount of sublimation, in agreement with similar studies on liquids [17], resulting \(T_{ice}<T_{air}\). If the temperature of the ice decreases, the driving force for vapor transfer will be further diminished, according to Equations (1) and (2). The numbers simply indicate that ice sublimation is not a significant issue in a ventilated chamber.  
To establish an absolute upper limit on the maximum amount of ice loss, we assume a quasi-static condition. We also assume that ice sublimation will provide vapor to the  
Figure 1: Vapor pressure over ice and Estisol\({}^{\rm TM}\) 140 as a function of temperature. The plot is in linear-log scales, indicating a fast-growing variation.  
saturation point before the ventilated air exits and we neglect ice cooling. In each hour, 40 m\({}^{3}\) of air at \(-50\)\({}^{\circ}\)C is replaced in the ventilation chamber. Using the ideal gas law and remembering [PERSON] law in Equation (3), we can calculate the maximum ice weight loss as a function of temperature for different values of RH%, as shown in Figure 2.  
Using saturated air coming from a deep hole in the firn pack we do not expect any losses in the ice core. Anyway, at \(-50\)\({}^{\circ}\)C, even in dry air (RH = 0%), the maximum loss (257 g) is negligible, considering the typical size of an ice core (diameter \(\sim\) 10 cm, length \(\sim\) 1 m, weight \(\sim\) 7.26 kg) and that the ventilation container is planned to have space for 200 ice cores (1452 kg).  
A similar analysis can be done to calculate the evaporation of the exposed drilling fluid. Again, this is an upper limit since part of the fluid could be trapped inside the pores of the core and not exposed to the air flux. The maximum amount of Estisol\({}^{\text{TM}}\) 140 that could be removed as a function of temperature is reported in Figure 2. In particular, at the working temperature of \(-50\)\({}^{\circ}\)C, after one week in the ventilation container this value is only 2.9 g. Given the density of Estisol\({}^{\text{TM}}\) 140 as 930 Kg/m\({}^{3}\)[3], the liquid loss corresponds to a volume of only 3.2 mL of fluid for the whole ventilation chamber, which is a negligible amount, and this is even an overestimation of the real expected value.