We present a fractal model for droplet Sauter mean diameter in gas-liquid mist flow, based on the droplet fractal theory and the balance relationship between total droplet surface energy and total gas turbulent kinetic energy. The present model is expressed as functions of the droplet fractal dimension, gas superficial velocity, liquid superficial velocity, and other fluid characteristics. Agreement between the present model predictions and experimental measurements is obtained. Results verify the reliability of the present model.

Droplet coalescence and breakup phenomena have obtained extensive attention in many physical and chemical process applications, that is, distillation, liquid-liquid extraction, emulsification, gas absorption, and multiphase reactions [

Shavit and Chigier [

Azzopardi [

Relationship between liquid droplet diameter and turbulent force.

It has been shown that the cumulative size distributions of liquid droplets whose sizes are greater than or equal to

Equation (

The negative variable in (

Droplet Sauter mean diameter is defined as [

The numerator term of (

In gas-liquid mist flow real situation,

Similarly, the denominator term of (

Substituting (

According to the balance between the surface energy of the dispersed liquid droplets and the turbulent kinetic energy of the continuous gas flow, the Droplet Sauter mean diameter can be derived.

In gas-liquid mist flow, the relationship between liquid velocity,

The total free surface energy of dispersed droplets in continuous gas flow is

It can be seen that the value of the droplet fractal dimension is

Substituting (

The total turbulent kinetic energy of gas-liquid mist flow can be expressed [

Total surface free energy of droplets in gas flow and the turbulent kinetic energy of gas are balanced [

Substituting (

Equation (

Based on mist flow characteristics, maximum droplet diameter can be expressed as [

Substituting (

Substituting (

Equation (

Figure

Comparison between experimental results and present model predictions.

Based on the droplet fractal theory and the balance relationship between total droplet surface energy and total gas turbulent kinetic energy, the fractal expression for droplet Sauter mean diameter in gas-liquid mist flow is derived. Agreement between the present model predictions and experimental measurements is obtained. Results verify the reliability of the present model.

Cross-sectional area of a conduit, m^{2}

Cross-sectional area occupied by liquid, m^{2}

Conduit diameter, m

Droplet fractal dimensions

Total surface free energy, W

Total turbulent kinetic energy, W

Fractal accumulative droplet number

Liquid velocity, m/s

Gas superficial velocity, m/s

Liquid superficial velocity, m/s

Droplet diameter, m

Maximum droplet diameter, m

Minimum droplet diameter, m

Droplet Sauter mean diameter

Gas density, kg/m^{3}

Liquid density, kg/m^{3}

Interfacial tension, N/m.

Gas phase

Liquid phase

Superficial

Turbulent.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors are grateful for financial support from the National Science Fund for Distinguished Young Scholars of China (51125019), the National Natural Science Foundation of China (51474181), and the 2014 Australia China Natural Gas Technology Partnership Fund Top Up Scholarship.