Droplet Evaporation
Use the Droplet Evaporation node to predict how liquid droplets will evaporate in the surrounding gas. Because this feature defines the rate of change of particle mass, it can only be used when the particle mass or diameter is solved for, so either Specify particle mass or Specify particle diameter must be selected from the Particle size distribution list in the physics interface Additional Variables section.
In addition, after adding the Droplet Evaporation node to a model, you must select it from the Accretion or evaporation rate specification list in the settings for the Particle Properties node.
Model Input
The model inputs for the Temperature T (SI unit: K) and the Absolute pressure pA (SI unit: Pa) are always shown in the settings window for this feature, even if there are no material properties that depend on them.
Evaporation Model
Select an option from the Evaporation model list:
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The simple Maxwell model (the default) treats droplet evaporation as a purely diffusive phenomenon at the droplet surface.
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The Stefan-Fuchs model also considers the advective transport of the vapor-gas mixture away from the droplet surface during evaporation. If the droplets are well below their boiling point, this usually gives only slightly faster evaporation than the Maxwell model.
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Select Specify evaporation constant to enter a value or expression for the Evaporation constant κ (SI unit: m2/s) directly. The default is 1 mm2/s. This is the time derivative of the square of the droplet diameter. The square of the diameter has been observed to decrease at a constant rate when the droplet is at a steady-state temperature, a phenomenon sometimes called the d2 law.
The Maxwell and Stefan-Fuchs evaporation models require a value or expression for the surface temperature of the droplet. If the Compute particle temperature check box has been selected in the physics interface Additional Variables section, a dependent variable for temperature is defined on every model particle. Otherwise, enter the Droplet surface temperature Ts (SI unit: K) directly. The default is 293.15 K.
If the Stefan-Fuchs evaporation model is used and the Compute particle temperature check box is selected, you can also select the Include droplet heating check box to model the heat-up of evaporating droplets in a hot gas environment. This check box is cleared by default.
If you select Include droplet heating, it is recommended not to add a Convective Heat Losses node to the model since this would effectively double-count the heating of the droplet by the surrounding fluid
Vapor Pressure
This section is shown when the Maxwell or Stefan-Fuchs evaporation model is selected.
Choose an option from the Saturation vapor pressure at droplet surface list: Clausius-Clapeyron equation or User defined (the default). For User defined the default value is pv,s = 10 mmHg or 10 Torr. For Clausius-Clapeyron equation enter the Reference temperature Tref (SI unit: K, default 100°C) and the Saturation vapor pressure at reference temperature pv,ref (SI unit: Pa, default 1 atm).
Enter a value or expression for the Ambient vapor pressure pv,a (SI unit: Pa). The default is 0.
Diffusion Coefficient
This section is shown when the Maxwell or Stefan-Fuchs evaporation model is selected.
If a Material node has been added to the model to define the material properties of the droplet vapor, select it from the Droplet vapor properties list. The default is None, which means the material properties must be specified directly.
Select an option from the Vapor diffusion coefficient list: From thermal properties or User defined (the default). For User defined the default value is Dv = 1 mm2/s. If From thermal properties is selected, the following material properties can be taken From material, or values or expressions can be entered directly:
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Heat capacity at constant pressure Cp (SI unit: J/(kg K)) of the gas surrounding the droplet. The default is 1 kJ/(kg K).
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Thermal conductivity k (SI unit: W/(m K)) of the gas surrounding the droplet. The default is 0.025 W/(m K).
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Particle vapor specific heat capacity Cp,v (SI unit: J/(kg K)). The default value is 1 kJ/(kg K).
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Particle vapor thermal conductivity kv (SI unit: W/(m K)). The default value is 0.025 W/(m K).
If From material is selected, the Material node used to define these properties is the one selected from the Droplet vapor properties list (for Cp,v and kv). If the specific heat capacity and conductivity of the vapor and gas are temperature-dependent, they are evaluated at a reference temperature Tr, defined as
This method of averaging is sometimes called the two-thirds rule.
Molar Mass
This section is shown when the Maxwell or Stefan-Fuchs evaporation model is selected.
Enter a value or expression for the Droplet vapor molar mass Mv (SI unit: kg/mol). The default is 18.02 g/mol. Then enter a value or expression for the Fluid molar mass Mf (SI unit: kg/mol). The default is 28.97 g/mol.
Handling of Small Droplets
The equations of motion used by the Particle Tracing for Fluid Flow interface depend on the particle mass and particle diameter being positive. If they become negative, the time-dependent solver might return an error message. It is therefore recommended to make particles disappear if they become extremely small due to evaporation. To do so, select an option from the Removal of small droplets list:
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For Never, the droplets will not disappear.
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For Specify cutoff particle mass (the default), enter a value or expression for the Cutoff particle mass mp,c (SI unit: kg). The default is 10-14 kg.
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For Specify cutoff particle diameter, enter a value or expression for the Cutoff particle diameter dp,c (SI unit: m). The default is 1 μm.
Specifying a cutoff of zero (either mass or diameter) can still result in error messages due to the discrete nature of the time steps taken by the solver, which still allows it to overshoot the specified value slightly. It is recommended to give a sufficiently large cutoff mass or diameter so that the particle size cannot decrease from this value to zero in a single time step.
Droplet Evaporation Theory