scholarly journals Generalisation of Levine's prediction for the distribution of freezing temperatures of droplets: a general singular model for ice nucleation

2013 ◽  
Vol 13 (14) ◽  
pp. 7215-7223 ◽  
Author(s):  
R. P. Sear

Abstract. Models without an explicit time dependence, called singular models, are widely used for fitting the distribution of temperatures at which water droplets freeze. In 1950 Levine developed the original singular model. His key assumption was that each droplet contained many nucleation sites, and that freezing occurred due to the nucleation site with the highest freezing temperature. The fact that freezing occurs due to the maximum value out of a large number of nucleation temperatures, means that we can apply the results of what is called extreme-value statistics. This is the statistics of the extreme, i.e. maximum or minimum, value of a large number of random variables. Here we use the results of extreme-value statistics to show that we can generalise Levine's model to produce the most general singular model possible. We show that when a singular model is a good approximation, the distribution of freezing temperatures should always be given by what is called the generalised extreme-value distribution. In addition, we also show that the distribution of freezing temperatures for droplets of one size, can be used to make predictions for the scaling of the median nucleation temperature with droplet size, and vice versa.

2013 ◽  
Vol 13 (4) ◽  
pp. 10499-10520 ◽  
Author(s):  
R. P. Sear

Abstract. Models without an explicit time dependence, called singular models, are widely used for fitting the distribution of temperatures at which water droplets freeze. In 1950 Levine developed the original singular model. His key assumption was that each droplet contained many nucleation sites, and that freezing occurred due to the nucleation site with the highest freezing temperature. The fact that freezing occurs due to the maximum value out of large number of nucleation temperatures, means that we can apply the results of what is called extreme-value statistics. This is the statistics of the extreme, i.e., maximum or minimum, value of a large number of random variables. Here we use the results of extreme-value statistics to show that we can generalise Levine's model to produce the most general singular model possible. We show that when a singular model is a good approximation, the distribution of freezing temperatures should always be given by what is called the generalised extreme-value distribution. In addition, we also show that the distribution of freezing temperatures for droplets of one size, can be used to make predictions for the scaling of the median nucleation temperature with droplet size, and vice versa.


2012 ◽  
Vol 12 (1) ◽  
pp. 3213-3261 ◽  
Author(s):  
V. Pinti ◽  
C. Marcolli ◽  
B. Zobrist ◽  
C. R. Hoyle ◽  
T. Peter

Abstract. Emulsion and bulk freezing experiments were performed to investigate immersion ice nucleation on clay minerals in pure water, using various kaolinites, montmorillonites, illites as well as natural dust from the Hoggar Mountains in the Saharan region. DSC (differential scanning calorimeter) measurements were performed on the kaolinites KGa-1b and KGa-2 from the Clay Mineral Society and kaolinite from Sigma-Aldrich; the montmorillonites SWy-2 and STx-1b from the Clay Mineral Society and the acid treated montmorillonites KSF and K-10 from Sigma Aldrich; the illites NX and SE from Arginotec. The emulsion experiments provide information on the average freezing behaviour characterized by the average nucleation sites. These experiments revealed one to two distinct heterogeneous freezing peaks, which suggest the presence of a low number of qualitatively distinct average nucleation site classes. We refer to the peak at the lowest temperature as "standard peak" and to the one at higher temperatures as "special peak". Conversely, freezing in bulk samples is not initiated by the average nucleation sites, but by a very low number of "best sites". The kaolinites showed quite narrow standard peaks with onset temperatures 239 K < Tonstd < 242 K and best sites with averaged median freezing temperature Tmedbest = 257 K. Only the kaolinite from Sigma Aldrich featured a special peak with freezing onset at 248 K. The illites showed broad standard peaks with freezing onsets at 244 K < Tonstd < 246 K and best sites with averaged median freezing temperature Tmedbest = 262 K. Montmorillonites had standard peaks with onsets 238 K < Tonstd < 240 K and best sites with Tmedbest=257 K. SWy-2, M K10, and KSF featured special peaks with onsets at Tonspcl=247, 240, and 242 K, respectively. M K10 and KSF both from Sigma Aldrich had less intense standard peaks compared to the ones from the Clay Mineral Society suggesting that a fraction of the standard sites are lost by the acid treatment. The acid treatment had however, no evident effect on best sites. Our investigations demonstrate that immersion freezing temperatures of clay minerals strongly depend on the amount of clay mineral present per droplet and on the exact type (location of collection and pre-treatment) of the clay mineral. We suggest that apparently contradictory results obtained by different groups with different setups can indeed be brought into good agreement when only clay minerals of the same type and amount per droplet are compared. The natural sample from the Hoggar Mountains, a region whose dusts have been shown to be composed mainly of illite, showed very similar freezing characteristics to the illites with freezing peak onsets 247 K < Tonstd < 248 K for the average and Tmedbest = 261 K for the best sites. Relating the concentration of best IN to the dust concentration in the atmosphere suggested that the best IN in the Hoggar sample would be common enough downwind of their source region to account for ambient IN number densities in the temperature range of 250–260 K at least during dust events.


2012 ◽  
Vol 12 (13) ◽  
pp. 5859-5878 ◽  
Author(s):  
V. Pinti ◽  
C. Marcolli ◽  
B. Zobrist ◽  
C. R. Hoyle ◽  
T. Peter

Abstract. Emulsion and bulk freezing experiments were performed to investigate immersion ice nucleation on clay minerals in pure water, using various kaolinites, montmorillonites, illites as well as natural dust from the Hoggar Mountains in the Saharan region. Differential scanning calorimeter measurements were performed on three different kaolinites (KGa-1b, KGa-2 and K-SA), two illites (Illite NX and Illite SE) and four natural and acid-treated montmorillonites (SWy-2, STx-1b, KSF and K-10). The emulsion experiments provide information on the average freezing behaviour characterized by the average nucleation sites. These experiments revealed one to sometimes two distinct heterogeneous freezing peaks, which suggest the presence of a low number of qualitatively distinct average nucleation site classes. We refer to the peak at the lowest temperature as "standard peak" and to the one occurring in only some clay mineral types at higher temperatures as "special peak". Conversely, freezing in bulk samples is not initiated by the average nucleation sites, but by a very low number of "best sites". The kaolinites and montmorillonites showed quite narrow standard peaks with onset temperatures 238 K


2016 ◽  
Vol 16 (14) ◽  
pp. 8915-8937 ◽  
Author(s):  
Claudia Marcolli ◽  
Baban Nagare ◽  
André Welti ◽  
Ulrike Lohmann

Abstract. AgI is one of the best-investigated ice-nucleating substances. It has relevance for the atmosphere since it is used for glaciogenic cloud seeding. Theoretical and experimental studies over the last 60 years provide a complex picture of silver iodide as an ice-nucleating agent with conflicting and inconsistent results. This review compares experimental ice nucleation studies in order to analyze the factors that influence the ice nucleation ability of AgI. The following picture emerges from this analysis: the ice nucleation ability of AgI seems to be enhanced when the AgI particle is on the surface of a droplet, which is indeed the position that a particle takes when it can freely move in a droplet. The ice nucleation by particles with surfaces exposed to air depends on water adsorption. AgI surfaces seem to be most efficient at nucleating ice when they are exposed to relative humidity at or even above water saturation. For AgI particles that are completely immersed in water, the freezing temperature increases with increasing AgI surface area. Higher threshold freezing temperatures seem to correlate with improved lattice matches as can be seen for AgI–AgCl solid solutions and 3AgI·NH4I·6H2O, which have slightly better lattice matches with ice than AgI and also higher threshold freezing temperatures. However, the effect of a good lattice match is annihilated when the surfaces have charges. Also, the ice nucleation ability seems to decrease during dissolution of AgI particles. This introduces an additional history and time dependence for ice nucleation in cloud chambers with short residence times.


2015 ◽  
Vol 15 (21) ◽  
pp. 31867-31889
Author(s):  
K.-T. O ◽  
R. Wood

Abstract. In this work, based on the well-known formulae of classical nucleation theory (CNT), the temperature TNc = 1 at which the mean number of critical embryos inside a droplet is unity is derived and proposed as a new approximation for homogeneous freezing temperature of water droplets. Without consideration of time dependence and stochastic nature of the ice nucleation process, the approximation TNc = 1 is able to reproduce the dependence of homogeneous freezing temperature on drop size and water activity of aqueous drops observed in a wide range of experimental studies. We use the TNc = 1 approximation to argue that the distribution of homogeneous freezing temperatures observed in the experiments may largely be explained by the spread in the size distribution of droplets used in the particular experiment. It thus appears that this approximation is useful for predicting homogeneous freezing temperatures of water droplets in the atmosphere.


Author(s):  
Arvid Naess ◽  
Oleh Karpa

In the reliability engineering and design of offshore structures, probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as, e.g., wave heights and wind speeds (WS), application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the average conditional exceedance rate (ACER) method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method, it is possible to provide an accurate estimate of the extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the true extreme value distribution. When it has been ascertained that this cascade has converged, an estimate of the extreme value distribution has been obtained. In this paper, it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will be demonstrated for measured coupled WS and wave height data.


Author(s):  
A. Naess ◽  
O. Gaidai

Air gap statistics for offshore platforms is directly related to the extreme value statistics of the random ocean wave field. The present paper describes a new method for predicting the extreme values of a random wave field in both space and time. The method relies on the use of data provided by measurements or Monte Carlo simulation combined with a technique for estimating the extreme value distribution of a recorded time series. The time series in question represents the spatial extremes of the random field at each point in time. The time series is constructed by sampling the available realization of the random field over a suitable grid defining the domain in question and extracting the extreme value. This is done for each time point of a suitable time grid. Thus, a time series of spatial extremes is produced. This time series provides the basis for estimating the extreme value distribution using recently developed techniques for time series, which results in an accurate practical procedure for solving a very difficult problem. This procedure is applied to the prediction of air gap statistics for a jacket structure.


2021 ◽  
Vol 105 ◽  
pp. 125-133
Author(s):  
Jin Zhe Chen ◽  
Ge Ping Bi

Gumbel extreme value distribution is used to predict the maximum depth of decarburization of piston rod. The results show that: 1) The prediction maximum depth of decarburization of piston rod should include four steps: data collection, parameter estimation, distribution test and maximum value prediction. 2) The maximum depth of decarburization of piston rod consistent with Gumbel minimum distribution. 3) When the return period is 1000, the predicted maximum depth of decarburization is (0.12 ± 0.01) mm, (k = 2).


Author(s):  
A. Naess ◽  
C. T. Stansberg ◽  
O. Batsevych

The paper presents a study of the extreme value statistics related to measurements on a scale model of a large tension leg platform (TLP) subjected to random waves in a wave basin. Extensive model tests were carried out in three irregular sea states. Time series of the motion responses and tether tension were recorded for a total of 18 three hour tests (full scale). In this paper we discuss the statistics of the measured tether tension. The focus is on a comparison of two alternative methods for the prediction of extreme tether tension from finite time series records. One method is based on expressing the extreme value distribution in terms of the average upcrossing rate. The other is a novel method that can account for statistical dependence in the recorded time series by utilizing a cascade of conditioning approximations. Both methods rely on introducing a specific parametric form for the tail part of the extreme value distribution. This is combined with an optimization procedure to determine the parameters involved, which allows prediction of various extreme response levels.


1968 ◽  
Vol 46 (3) ◽  
pp. 329-333 ◽  
Author(s):  
R. W. Salt

Gut contents are the source of ice nucleation in feeding insects; in those non-feeding forms where it has been possible to observe nucleation, residual food within the gut has been the source. When freezing is confined to tissues with no digestive elements, such as excised appendages, preferred nucleation sites may be observed but the tissues or structures involved have not been identified. Haemolymph and intracellular matter are improbable as functional nucleating sites, reducing the anatomical possibilities greatly.Isolated appendages were also used to demonstrate that the relation between freezing temperature and mass in aqueous systems is more accurately defined by the numbers or other quantitative aspects of nucleators than by the mass of water.


Sign in / Sign up

Export Citation Format

Share Document