Sublimation Flux Research Articles

Determination of bolometric albedo based on spectroscopic measurements for selected dust analogues and its impact on the change of cometary brightness during its outburst

The paper presents the results of spectroscopic measurements for selected dust analogues, based on which change in cometary brightness was determined. In the first part of the article, we present the results of laboratory measurements of hemispherical albedo for selected dust analogues using a Cary 5000 spectrometer with an integrating sphere. In the case of this system and the tested samples, the obtained hemispherical albedo values ranged from 0.35 ± 0.07% to 41.58 ± 0.07%. The obtained measurement results were used to determine the bolometric albedo and geometric albedo. For the analogue consisting of charcoal, the Bond albedo was equal to AB(charcoal) = 2.15%, whereas the geometric albedo was equal to pv(charcoal) = 6.76%. The second part of the paper presents an analytical method allowing us to calculate the amplitude of the change of cometary brightness during the outburst. The calculations show that the upper value of the amplitude is 6.5 magnitudes, which is within the medium range amplitude of the outburst. Calculations have shown that as the bolometric albedo increases for a given agglomerate porosity, the temperature decreases, which determines a smaller sublimation flux, which translates into a larger change in the cometary brightness.

New measurements of the hemispherical albedo of cometary analogues: Influence on the amplitude of the change of cometary brightness during its outburst

The paper presents new experimental results of measurements of the hemispherical albedo of a potential comet analogue and an analysis of its influence on the change in the cometary brightness. Measurements of the spectral properties of the tested analogues were performed using a Cary 5000 spectrometer in the wavelength range from 200 to 2500 nm. Two samples were used as a dust analogue: a mixture of sand and ash (sample A) and a mixture of sand and charcoal (sample B), respectively. The obtained hemispherical albedo values for the tested samples ranged from 1.20% to 32.25%. In particular, for sample B, the obtained hemispherical albedo values are comparable to the actual reflectance for comet 67P. Based on the obtained spectral properties of the tested samples, a thermodynamic model of cometary activity was developed and used, among others, to calculate the power absorbed by the tested analogue and the sublimation flux occurring through the porous structure of the fine-grained dust present on the cometary surface. The obtained results were used to calculate the change in the cometary brightness during its outburst, the upper limit of which was equal to 5.36 magnitude.

Hydrological regimes and evaporative flux partitioning at the climatic ends of high mountain Asia

Abstract High elevation headwater catchments are complex hydrological systems that seasonally buffer water and release it in the form of snow and ice melt, modulating downstream runoff regimes and water availability. In High Mountain Asia (HMA), where a wide range of climates from semi-arid to monsoonal exist, the importance of the cryospheric contributions to the water budget varies with the amount and seasonal distribution of precipitation. Losses due to evapotranspiration and sublimation are to date largely unquantified components of the water budget in such catchments, although they can be comparable in magnitude to glacier melt contributions to streamflow. Here, we simulate the hydrology of three high elevation headwater catchments in distinct climates in HMA over 10 years using an ecohydrological model geared towards high-mountain areas including snow and glaciers, forced with reanalysis data. Our results show that evapotranspiration and sublimation together are most important at the semi-arid site, Kyzylsu, on the northernmost slopes of the Pamir mountain range. Here, the evaporative loss amounts to 28% of the water throughput, which we define as the total water added to, or removed from the water balance within a year. In comparison, evaporative losses are 19% at the Central Himalayan site Langtang and 13% at the wettest site, 24 K, on the Southeastern Tibetan Plateau. At the three sites, respectively, sublimation removes 15%, 13% and 6% of snowfall, while evapotranspiration removes the equivalent of 76%, 28% and 19% of rainfall. In absolute terms, and across a comparable elevation range, the highest ET flux is 413 mm yr−1 at 24 K, while the highest sublimation flux is 91 mm yr−1 at Kyzylsu. During warm and dry years, glacier melt was found to only partially compensate for the annual supply deficit.

On the importance of the humidity flux for the surface mass balance in the accumulation zone of the Greenland Ice Sheet

Abstract. It is highly uncertain how the humidity flux between the snow surface and the atmosphere contributes to the surface mass balance (SMB) of the interior Greenland Ice Sheet (GrIS). Due to sparse observations, evaluations of the simulated humidity flux are limited. Model-based estimates of the humidity flux contribution to the SMB are, therefore, unconstrained and even disagree in magnitude and sign. In this study, we evaluate the regional climate model MAR at the EGRIP (East Greenland Ice-Core Project) site in the accumulation zone of the GrIS. We use a combined dataset of continuous one-level bulk estimates of the humidity flux covering the period of May 2016–August 2019 and eddy-resolving eddy-covariance humidity flux measurements from all four summer seasons. In summer, we document a bias of too little sublimation (−1.3 W m−2, −1.65 mm w.e.) caused by a cold bias in both air and surface temperature, leading to a reduced humidity gradient. In winter, MAR overestimates vapor deposition by about 1 order of magnitude. This is a consequence of an overestimated temperature gradient in too stable atmospheric conditions compared to observations. Both systematic errors cause a large discrepancy in the annual net humidity flux between the model and observations of −9 mm w.e. yr−1. Remarkably, the simulated net annual humidity flux contributes positively to the SMB, contrary to observations documenting a net sublimation flux. We correct the systematic errors by applying a simple but effective correction function to the simulated latent heat flux. Using this correction, we find that 5.1 % of the annual mass gain at the EGRIP site sublimates again, and 4.3 % of the total mass gain is deposited vapor from the near-surface air. The estimated net humidity flux contribution to the annual SMB is about −1 % (net sublimation) compared to +5.6 % for the uncorrected simulation. In summer, the corrected MAR simulation shows that vapor deposition accounts for 9.6 % of the total mass gain and that 31 % of the total mass gain at the EGRIP site sublimates again. The net fluxes contribute to −32 % of the summer SMB. These results demonstrate that the humidity flux is a major driver of the summer SMB in the accumulation zone of the GrIS and highlight that even small changes could increase its importance for the annual SMB in a warming climate.

Ejection of porous dust–ice agglomerates from the surface of the cometary nucleus

This paper presents two problems related to the ejection of particles from the surface of the cometary nucleus. The first problem is related to the phase of quiet sublimation. This part of the paper discusses the influence of the water ice sublimation flux on the size of particles that are lifted into the coma. In these considerations, three formulas were used to describe the water ice sublimation flux. The calculations show that the size of the particle lifted into the coma depends on its density and the sublimation flux of water ice. The second mechanism is related to the cometary outburst phase. In this part of the paper, it was proposed that the cometary outburst as a high-energy process may significantly contribute to explaining the presence of small particles in the coma. Based on the calculations performed, it was shown that the dimensions of these particles depend on the adopted value of the power index in the power law. Based on the considerations presented in this paper, the presence of both large and fine dust particles observed in the coma during the Rosetta mission can be explained.

The influence of hemispherical albedo on the dynamics of cometary particles

ABSTRACT This paper presents a new approach to determining the dimensions of particles that can be lifted to a coma by the sublimation flux of water ice. Due to the diverse colour of the cometary surfaces, in the presented calculations we take into account the influence of the reflectance coefficient (hemispherical albedo) on the size of particles lifted from the surface of the nucleus. A Cary 5000 spectrometer was used to measure hemispherical albedo. Spectroscopic measurements used dust particles that consisted of pure silicate or were a mixture of pure silicate and organic compounds such as charcoal, soot, and ash. In addition, these admixtures acted as a means of darkening the tested sample. Depending on the colour of the sample and the wavelength, the measured value of hemispherical albedo oscillated in the range from 4.93 per cent to 48.65 per cent. A thermodynamic model of cometary matter emission was developed based on the results of hemispherical albedo measurements. The performed numerical simulations show that the temperature decreases with the increase of the hemispherical albedo, which translates into the sublimation flux and the dynamics of the dust-ice particles present on the surface of the cometary nucleus. Taking into account the extreme values of the hemispherical albedo, the differences in the size of particles carried away from the surface of the nucleus are in the order of centimeters.

Laboratory measurement of volatile ice vapor pressures with a quartz crystal microbalance

Nitrogen, carbon monoxide, and methane are key materials in the far outer Solar System where their high volatility enables them to sublimate, potentially driving activity at very low temperatures. Knowledge of their vapor pressures and latent heats of sublimation at relevant temperatures is needed to model the processes involved. We describe a method for using a quartz crystal microbalance to measure the sublimation flux of these volatile ices in the free molecular flow regime, accounting for the simultaneous sublimation from and condensation onto the quartz crystal to derive vapor pressures and latent heats of sublimation. We find vapor pressures to be somewhat lower than previous estimates in literature, with carbon monoxide being the most discrepant of the three species, almost an order of magnitude lower than had been thought. These results have important implications across a variety of astrophysical and planetary environments.

A Case Study on Drivers of the Isotopic Composition of Water Vapor at the Coast of East Antarctica

AbstractStable water isotopes (SWIs) contain valuable information on the past climate and phase changes in the hydrologic cycle. Recently, vapor measurements in the polar regions have provided new insights into the effects of snow‐related and atmospheric processes on SWIs. The purpose of this study is to elucidate the drivers of the particularly depleted vapor isotopic composition measured on a ship close to the East Antarctic coast during the Antarctic Circumnavigation Expedition in 2017. Reanalysis data and backward trajectories are used to model the isotopic composition of air parcels arriving in the atmospheric boundary layer (ABL) above the ship. A simple model is developed to account for moisture exchanges with the snow surface. The model generally reproduces the observed trend with strongly depleted vapor δ18O values in the middle of the 6‐day study period. This depletion is caused by direct air mass advection from the ice sheet where the vapor is more depleted in heavy SWIs due to distillation during cloud formation. The time spent by the air masses in the marine ABL shortly before arrival at the ship is crucial as ocean evaporation typically leads to an abrupt change in the isotopic signature. Snow sublimation is another important driver when the isotopic composition of the sublimation flux differs substantially from that of the advected air mass, for example, marine air arriving at the coast or free‐tropospheric air descending from high altitudes. Despite strong simplifications, our model is a useful and computationally efficient method for understanding SWI dynamics at polar sites.

Callisto's Atmosphere: First Evidence for H2 and Constraints on H2O

AbstractWe explore the parameter space for the contribution to Callisto's H corona observed by the Hubble Space Telescope from sublimated H2O and radiolytically produced H2 using the Direct Simulation Monte Carlo method. The spatial morphology of this corona produced via photoelectron and magnetospheric electron‐impact‐induced dissociation is described by tracking the motion of and simulating collisions between the hot H atoms and thermal molecules including a near‐surface O2 component. Our results indicate that sublimated H2O produced from the surface ice, whether assumed to be intimately mixed with or distinctly segregated from the dark nonice or ice‐poor regolith, cannot explain the observed structure of the H corona. On the other hand, a global H2 component can reproduce the observation, and is also capable of producing the enhanced electron densities observed at high altitudes by Galileo's plasma‐wave instrument, providing the first evidence of H2 in Callisto's atmosphere. The range of H2 surface densities explored, under a variety of conditions, that are consistent with these observations is ∼(0.4–1) × 108 cm−3. The simulated H2 escape rates and estimated lifetimes suggest that Callisto has a neutral H2 torus. We also place a rough upper limit on the peak H2O number density (≲108 cm−3), column density (≲1015 cm−2), and sublimation flux (≲1012 cm−2 s−1), all of which are 1–2 orders of magnitude less than that assumed in previous models. Finally, we discuss the implications of these results, as well as how they compare to Europa and Ganymede.

Quantifying the Stable Water Isotopologue Exchange Between the Snow Surface and Lower Atmosphere by Direct Flux Measurements

AbstractSurface processes in high latitudes play an important role in global climate and thus understanding the physics of these systems is critical for improving climate projections. The characterization of the stable water isotopologue flux between the surface and the atmosphere offers the potential to constrain parameterizations of these physical surface exchange processes in numerical models. In addition, observations of isotopologue surface fluxes allow the evaluation of surface fluxes as a process influencing the formation of the climate signal retrieved from ice core isotopologue records. Here, we present a record of stable water isotopologue surface fluxes measured in‐situ in the accumulation zone of the Greenland Ice Sheet at the East Greenland Ice Core Project site. We measured isotopologue fluxes above the snow surface directly by combining high‐frequency eddy covariance measurements with low‐frequency isotopologue measurements from a cavity ring‐down spectrometer (CRDS). We developed a method to correct for the high‐frequency loss of the CRDS by combining humidity measurements from both the CRDS and eddy covariance instruments. Using this approach our measurements provide the first direct observations of water isotopologue fluxes in polar areas. We observed a clear diurnal cycle in the fluxes of the different water isotopologues. The isotopic composition of the sublimation and deposition flux showed to be dependent on the snow and vapor isotopic composition, respectively. To a first order, the isotopic composition of the sublimation flux could be derived assuming equilibrium fractionation during sublimation.

Process analytical technology for monitoring pharmaceuticals freeze-drying – A comprehensive review

ABSTRACTThe goal of this paper is to review the available process analytical technology tools for monitoring the batch freeze-drying process for pharmaceuticals. These systems aim evaluating in-line product temperature, sublimation flow rate, and values of some model parameters in such a way that it can be used for in-line or off-line process optimization. A detailed survey of the systems proposed in the literature is presented, grouping them on the basis of monitored variable, namely, product temperature, heat flux to the product, sublimation flux, and, finally, other variables. The advantages and drawbacks of the techniques are critically assessed, taking into account the possibility of using them not only at lab-scale but also at production scale, beside, obviously, the possibility of getting reliable measurements of the desired variables.

Model-Based PAT for Quality Management in Pharmaceuticals Freeze-Drying: State of the Art.

Model-based process analytical technologies can be used for the in-line control and optimization of a pharmaceuticals freeze-drying process, as well as for the off-line design of the process, i.e., the identification of the optimal operating conditions. This paper aims at presenting the state of the art in this field, focusing, particularly, on three groups of systems, namely, those based on the temperature measurement (i.e., the soft sensor), on the chamber pressure measurement (i.e., the systems based on the test of pressure rise and of pressure decrease), and on the sublimation flux estimate (i.e., the tunable diode laser absorption spectroscopy and the valveless monitoring system). The application of these systems for in-line process optimization (e.g., using a model predictive control algorithm) and to get a true quality by design (e.g., through the off-line calculation of the design space of the process) is presented and discussed.

On the Design of a Fuzzy Logic–Based Control System for Freeze-Drying Processes

This article is focused on the design of a fuzzy logic–based control system to optimize a drug freeze-drying process. The goal of the system is to keep product temperature as close as possible to the threshold value of the formulation being processed, without trespassing it, in such a way that product quality is not jeopardized and the sublimation flux is maximized. The method involves the measurement of product temperature and a set of rules that have been obtained through process simulation with the goal to obtain a unique set of rules for products with very different characteristics. Input variables are the difference between the temperature of the product and the threshold value, the difference between the temperature of the heating fluid and that of the product, and the rate of change of product temperature. The output variables are the variation of the temperature of the heating fluid and the pressure in the drying chamber. The effect of the starting value of the input variables and of the control interval has been investigated, thus resulting in the optimal configuration of the control system. Experimental investigation carried out in a pilot-scale freeze-dryer has been carried out to validate the proposed system.

Spatial Variation of Pressure in the Lyophilization Product Chamber Part 2: Experimental Measurements and Implications for Scale-up and Batch Uniformity.

Product temperature during the primary drying step of freeze-drying is controlled by a set point chamber pressure and shelf temperature. However, recent computational modeling suggests a possible variation in local chamber pressure. The current work presents an experimental verification of the local chamber pressure gradients in a lab-scale freeze-dryer. Pressure differences between the center and the edges of a lab-scale freeze-dryer shelf were measured as a function of sublimation flux and clearance between the sublimation front and the shelf above. A modest 3-mTorr difference in pressure was observed as the sublimation flux was doubled from 0.5 to 1.0 kg·h-1·m-2 at a clearance of 2.6 cm. Further, at a constant sublimation flux of 1.0 kg·h-1·m-2, an 8-fold increase in the pressure drop was observed across the shelf as the clearance was decreased from 4 to 1.6 cm. Scale-up of the pressure variation from lab- to a manufacturing-scale freeze-dryer predicted an increased uniformity in drying rates across the batch for two frequently used pharmaceutical excipients (mannitol and sucrose at 5% w/w). However, at an atypical condition of shelf temperature of +10°C and chamber pressure of 50 mTorr, the product temperature in the center vials was calculated to be a degree higher than the edge vial for a low resistance product, thus reversing the typical edge and center vial behavior. Thus, the effect of local pressure variation is more significant at the manufacturing-scale than at a lab-scale and accounting for the contribution of variations in the local chamber pressures can improve success in scale-up.

A Binary Gas Transport Model Improves the Prediction of Mass Transfer in Freeze Drying

Monitoring partial vapor pressure in the freeze-drying chamber is a cheap, global, and non-intrusive way to assess the end of the primary drying stage. Most existing dynamic freeze-drying models which predict this partial pressure describe mass transfer between the product and the condenser via a mass transfer resistance or a mass transfer coefficient. Experimental evidence suggests that such models can be significantly in error for some values of the sublimation flux, leading to physically inconsistent predictions and possibly incorrect assessment of primary drying termination, with potential risk of product damage if moving to secondary drying and increasing shelf temperature while some ice is still present. Assuming a binary gas transport model for vapor and inert gas leads to improved and consistent predictions and explains the apparent variation of the mass transfer resistance with total pressure, shelf temperature, and product sublimation area.

Formula for determining the surface temperature of the fullerite consisting of a C60-C70 mixture from a mass spectrum

A calculation is used to show that the kinetic energy of particles in the sublimation flux of the fullerite consisting of a mixture of C60 and C70 that is caused by a pulsed laser beam is significantly higher than the interparticle interaction energy, i.e., kT ≫ E. This finding is used to deduce a formula to determine the fullerite surface temperature from mass spectrum data on the basis of gas-kinetic equations and the data obtained by the Knudsen method for a fullerene effusion flux. The calculated and experimental results are compared. Specific features are noted for the procedure of measuring the temperature. Examples for calculating the surface temperature for other heating methods are given.

Fast freeze-drying cycle design and optimization using a PAT based on the measurement of product temperature

This paper is focused on the use of an innovative Process Analytical Technology for the fast design and optimization of freeze-drying cycles for pharmaceuticals.The tool is based on a soft-sensor, a device that uses the experimental measure of product temperature during freeze-drying, a mathematical model of the process, and the Extended Kalman Filter algorithm to estimate the sublimation flux, the residual amount of ice in the vial, and some model parameters (heat and mass transfer coefficients).The accuracy of the estimations provided by the soft-sensor has been shown using as test case aqueous solutions containing different excipients (sucrose, polyvinylpyrrolidone), processed at various operating conditions, pointing out that the soft-sensor allows a fast estimation of model parameters and product dynamics without involving expensive hardware or time consuming analysis.The possibility of using the soft-sensor to calculate in-line (or off-line) the design space of the primary drying phase is here presented and discussed. Results evidences that by this way, it is possible to identify the values of the heating fluid temperature that maintain product temperature below the limit value, as well as the operating conditions that maximize the sublimation flux. Various experiments have been carried out to test the effectiveness of the proposed approach for a fast design of the cycle, evidencing that drying time can be significantly reduced, without impairing product quality.

On the Use of Artificial Neural Networks to Monitor a Pharmaceutical Freeze-Drying Process

This paper is focused on the use of artificial neural networks to monitor a pharmaceutical freeze-drying process. A detailed phenomenological model of the process is used to provide the dataset for the learning phase of the neural network development. Then, a methodology based on a self-adaptive differential evolution scheme is combined with a back-propagation algorithm, as local search method, for the simultaneous structural and parametric optimization of the neural network which models the freeze-drying process. Using some experimentally available measurements at a generic time t, the neural network is able to estimate the temperature of the product and the thickness of the dried cake (the amount of residual ice, as well as the sublimation flux, can be easily calculated from the cake thickness) at a future time t + Δt, for the given operating conditions (the temperature of the heating shelf and the pressure in the drying chamber). Also, the duration of the primary drying phase and the maximum product temperature in the future are predicted, in case the operating conditions are not modified. In this way it is possible to understand if it is necessary to modify the operating conditions, in case the product temperature should trespass the limit value before the ending point of the primary drying. Despite the fact that the artificial neural network is obtained using a learning set determined for specific values of heat transfer coefficient (between the heating shelf and the product at the bottom of the container) and of mass transfer resistance (of the dried cake to vapor flow), reliable and accurate estimations are also obtained in case the sensor is used to monitor a process characterized by different values of heat and mass transfer coefficients.

Advanced approach to build the design space for the primary drying of a pharmaceutical freeze‐drying process

This paper deals with the design space of a pharmaceutical freeze-drying process. Mathematical modeling is used to investigate the effect of the operating conditions [shelf temperature (T(shelf)) and chamber pressure (P(c))] on product temperature (that has to remain below a limit value) and sublimation flux (that has to be lower than a level that would cause choked flow). The algorithm takes into account the variation of the design space with time due to the increase in the dried layer thickness. Besides T(shelf) and P(c), the dried layer thickness is used as the third coordinate of the diagram, thus resulting in just one graph that can be used to build recipes with variable operating conditions, as well as to analyze the effect of process failures. Such results are compared with those obtained when the variation of the design space with time is not accounted for; in this case, the design space comprises those operating conditions that fulfill the operation constraints throughout primary drying, thus giving a much more conservative recipe when designing the process or potentially misleading results when analyzing process failures. Finally, the proposed method has been used to design, and experimentally validate, a recipe for a pharmaceutical formulation.

On the Use of Mathematical Models to Build the Design Space for the Primary Drying Phase of a Pharmaceutical Lyophilization Process

The aim of this article is to show a procedure to build the design space for the primary drying of a pharmaceuticals lyophilization process. Mathematical simulation of the process is used to identify the operating conditions that allow preserving product quality and meeting operating constraints posed by the equipment. In fact, product temperature has to be maintained below a limit value throughout the operation, and the sublimation flux has to be lower than the maximum value allowed by the capacity of the condenser, besides avoiding choking flow in the duct connecting the drying chamber to the condenser. Few experimental runs are required to get the values of the parameters of the model: the dynamic parameters estimation algorithm, an advanced tool based on the pressure rise test, is used to this purpose. A simple procedure is proposed to take into account parameters uncertainty and, thus, it is possible to find the recipes that allow fulfilling the process constraints within the required uncertainty range. The same approach can be effective to take into account the heterogeneity of the batch when designing the freeze-drying recipe.