Modelling a phenomena has been a great interest for researchers. The question came to me, how can we model a floc growth during coagulation-flocculation process. Many studies reported floc growth using the approach of population balance model and fractal dimension, such as recent study by Moruzzi et al (Article A combined experimental and numerical approach to the assess...
). However, I haven't seen any other approach such as modelling floc as a growing sphere. Can anyone share their thoughts and expertise regarding this matter?
Dear Hans Kristianto please do recommend my answer if helpful.
Modeling floc growth during coagulation involves simulating the aggregation and growth of small suspended particles into larger flocs in a liquid. This process is commonly used in water treatment for the removal of impurities and pollutants. There are various models to describe floc growth, and one of the commonly used approaches is the population balance model. Here's a simplified guide to modeling floc growth during coagulation:
### 1. **Population Balance Model:**
- The population balance model describes the evolution of particle size distribution over time. It considers the coagulation and breakup of particles, providing a comprehensive understanding of floc dynamics.
### 2. **Basic Equations:**
- The general population balance equation is given by:
\[ \frac{\partial n(r, t)}{\partial t} = G(r, t) - B(r, t) \]
- Where:
- \( n(r, t) \) is the number concentration of particles with radius \( r \) at time \( t \).
- \( G(r, t) \) represents the growth rate due to coagulation.
- \( B(r, t) \) represents the breakup rate.
### 3. **Coagulation Kernel (Growth Rate):**
- The coagulation kernel represents the probability of two particles colliding and forming a larger floc. It depends on factors such as particle concentration, size, and water quality. Various mathematical formulations can be used for the coagulation kernel, including the Smoluchowski equation.
### 4. **Breakup Rate:**
- The breakup rate describes the probability of a floc breaking into smaller fragments. It is influenced by factors like shear forces, turbulence, and the strength of the floc. The breakup rate can be modeled using empirical relationships or detailed fluid dynamics simulations.
### 5. **Initial Conditions:**
- Set initial conditions for the particle size distribution at the start of coagulation. This could be based on the characteristics of the suspended particles in the water.
### 6. **Numerical Solution:**
- Solve the population balance equation numerically using methods such as finite difference or finite element techniques. Commercial software or programming languages like MATLAB or Python can be employed for this purpose.
### 7. **Parameter Estimation:**
- Calibrate the model by adjusting parameters like coagulation and breakup rates based on experimental data or known system behavior.
### 8. **Validation:**
- Validate the model by comparing its predictions with independent experimental data.
### 9. **Sensitivity Analysis:**
- Perform sensitivity analyses to understand the impact of variations in parameters on the model predictions.
### 10. **Application to Specific Systems:**
- Apply the model to simulate floc growth in specific coagulation systems, adjusting parameters based on the characteristics of the water to be treated.
It's important to note that modeling floc growth is a complex task, and the accuracy of the model depends on the underlying assumptions and the representativeness of the chosen coagulation and breakup models. Collaborating with experts in fluid dynamics, water treatment, and numerical modeling can enhance the reliability of the developed model.
Thank you for your response.. However the main question has not been adressed yet; that is weather we can modelled it as a spherical that grow in the radius, instead using population balance model.
PS: I found the same answer using chat gpt.
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