Hello and welcome to the first post of the new year 2025! I hope you had a great Christmas break and I welcome you all back to a new exciting year of polymer engineering topics.
Let us start with a Rule of Thumb post (check out my other Rules of Thumb posts here). We are living in non-linear, exponential times, which can be seen daily by the rapid advancements in technology, from Artificial Intelligence (AI), to the stock market.
For example, if you take the compounded interest of the S&P 500, we see an exponential growth over time. Compounded interest is for Warren Buffet the key for wealth building.
For our brain it is harder to imagine exponential relations, since for us humans, linear thinking is the main "operating model"
There are lots of examples of exponential behaviour:
- Population growth
- Growth of cells
- Spread of a disease in a pandemic
- Financial - compounding interest rates
Water lily and exponential growth
A good way to represent exponential behaviour is by looking at a pond where water lilies are growing. Water lilies double in area each day, resulting in an exponential growth. Let us imagine the following: the water lilies take 30 days to cover the whole pond. When will they cover half of the lake?
Exactly, on the twenty-ninth day.
Example from polymer engineering: power-law of polymer melt viscosity
Also in the plastics industry and polymer engineering, a well known example of exponential behaviour is the viscosity of polymer melts (Figure 1).
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| Figure 1: Water Lilies and Polymer Melts - Both Show Exponential Behaviours. |
In general, the viscosity of plastics is a function of shear rate, temperature, pressure, and chemical composition.
At low shear rates, polymer melts show a linear behaviour (= Newtonian behaviour). In the lower shear rate region, the viscosity is independent of the shear rate.
The viscosity reaches a level which is referred to as zero-shear viscosity.
At higher shear rates, the Power law behaviour takes over and the viscosity decreases with increasing the shear rate following a negative slope of (n-1), where n is the Power-law index.
This quantitative relationship is represented by the Power-Law model, where n is the Power-law index and k is consistency (Pa*s); Typical n values of polymer melts are between 0.2 and 0.6.
Conclusions
Exponential behaviours are dominating not only our daily life, however also the plastics industry and polymer engineering topics. It is important to have a certain awareness about such behaviours to not be suppressed and use the exponential times in our favours.
More Rule of Thumb posts can be found under “Start here”
Latest Rule of Thumb posts:
Rule of Thumb in Polymer Injection Moulding: Fast Estimation of Cooling Time
Rule of Thumb in Polymer Engineering: How Economy of Scale Can Lower Costs
Rule of Thumb: Dealing with Weld lines in Polymer Injection Moulding
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Literature:
[1] https://www.forbes.com/sites/bill_stone/2024/08/25/warren-buffetts-secret-formula-for-wealth-creation/
[2] https://www.azom.com/article.aspx?ArticleID=19175
