2-D Model for the Description of Thermal Diffusion Cloud Chambers:  Description and First Results

Abstract

In thermal diffusion cloud chambers (TDCCs), a decrease of nucleation rate with increasing total pressure was observed repeatedly, both near atmospheric pressures and at elevated pressures. Because this pressure effect was observed almost only using TDCCs, there have been some concerns inside the nucleation community whether it is not an experimental artifact. One questionable point in this context is that, to calculate the profiles of temperature and saturation ratio in TDCCs it is assumed that if the chamber is sufficiently “flat”, a 1-d model can be used for the description of the transport processes in the central part of the chamber. The major concern in this context is that the heated chamber wall may cause a buoyancy driven convection that can propagate toward the center of the chamber and cause a slow motion of the gas mixture. To investigate this effect, a 2-d model of coupled mass, heat, and momentum transport in TDCCs has been developed. In the paper this model is described, and its predictive force is shown in comparison with a state-of-the-art 1-d model and with experimental data from the system n-propanol−He. Furthermore, results concerning the effects of wall heating, total chamber pressure, carrier gas, and chamber geometry on nucleation rates are presented. The influence of wall heating on the nucleation rate was found to be significant when transport processes inside TDCC are dominated by buoyant convection. Using the 2-d model made it possible to partly (but not completely) explain the pressure effect observed in TDDCs. It was also shown that including the process of thermal diffusion in the model may have a significant influence on the resulting profiles of nucleation rate. It was confirmed that the choice of the carrier gas in the chamber can strongly influence stability of chamber operation. With respect to the optimal chamber geometry it was shown that TDCCs should have a diameter as small and a diameter-to-height ratio as large as possible to minimize the 2-d effects. All in all, it was proven that application of 1-d models to describe the heat and mass transfer in TDCC may lead to an erroneous determination of temperature, saturation ratio, and nucleation rate profiles.

Homogeneous nucleation rate measurements of 1-propanol in helium: The effect of carrier gas pressure

“…29 The method used for the data evaluation in the TDCC has been also described in detail elsewhere ͓Brus et al ͑2005͔͒. 28 The resulting dependence J exp ͑T , S͒ can be directly compared to the theoretical prediction of any nucleation theory. The local values of nucleation rate are related to the corresponding local values of temperature and supersaturation calculated using either a traditional 1D model of mass and heat transport ͓Katz and Ostermier 31 ͑1967͒ and Smolík and Ždímal 32 ͑1994͔͒ or a more recent 2D model of mass, heat, and momentum transfer in the TDCC ͓e.g., Stratmann et al ͑2001͔͒.…”

Laser filamentation induced air-flow motion in a diffusion cloud chamber

“…The spatial distribution of air-flow velocity is the result of the coupled mass-heat transfer and flow processes, which are mathematically described by (a) the continuity, (b) the energy, (c) momentum equations of the gas. The continuity equation is described by the equation [24][25][26] ( )…”

Buoyancy-driven convective motion in a thermal diffusion cloud chamber using a water/helium mixture

“…4a) have a sinusoidal shape. Indeed the chamber wall overheating affects the temperature profile in the center portion of the cloud chamber [19] and causes a buoyancy driven convection that can propagate towards the center of the chamber leading to the motion of the gas mixture [13]: roll-shaped cells can be observed in the TDCC and the inert gas is then mixed (Fig. 4d).…”

“…We address these open questions using numerical resolution of two sets of equations, a simplified one based on a 2D model of mass and heat transport (pure diffusion simulation, not detailed in the present work), similar to this used by Stratmann et al [13], and the Navier-Stokes equations in order to describe the mass, momentum and heat transfers in the TDCC. In the latter case, the continuity, momentum and energy equations as well as the conservation of vapor mass are written assuming steady state and thermodynamic equilibrium.…”

“…Quite recently, Ferguson et al [12] performed a similar analysis with lower molecular weight gases and with an emphasis on the effect of the total pressure on the TDCC operation. Another 2D model of coupled mass, heat and momentum transport in TDCC has been developed by Stratmann et al [13] taking into account the effects of wall heating, total chamber pressure, carrier gas and chamber geometry on nucleation rates.…”