Filtration forms a vital part of our everyday lives, from the vacuum cleaners and air purifiers that we use to keep our homes clean to filters that are used in the pharmaceutical industry to remove viruses from liquids such as blood. If you've ever replaced the filter in your vacuum cleaner you will have seen that it is composed of a nonwoven medium – a fluffy material comprising many fibres laid down in a mat. These fibres trap dust particles as contaminated air passes through, protecting the motor from becoming damaged and clogged by the dust. A key question that we ask when designing these filters is, how does the arrangement of the fibres in the filter affect its ability to remove dust?
One way in which we could answer this question is to manufacture many different types of filters, with different fibre sizes and arrangements, and then test the performance of each filter. However, this is time consuming and expensive. Moreover, while we would be able to determine which filter is best out of those that we manufactured, we would not know if we could have made an even better one. By developing a mathematical model, we can quickly and easily assess the performance of any type of filter, and determine the optimal design for a specific filtration task, such as a vacuum cleaner or a virus filter. This work is in collaboration with leading British household device manufacturer Dyson.
As contaminants stick onto the surface of the filter fibres they will grow in size and we must capture this in our mathematical model to predict the filter performance. For a filter composed of periodically spaced and uniformly sized fibres, eventually all the fibres will become so loaded with contaminants that they will touch each other. At this point the filter blocks and we can terminate our simulation. However, for a filter with randomly arranged fibres, we may find ourselves in a scenario in which two fibres start off quite close to one another and so touch after trapping only a small amount of contaminant on their surface. At this point the majority of the rest of the filter is still able to trap contaminants and so we do not want to stop our filtration simulation yet. To compare the performance of filters with periodic and random fibre arrangements we therefore introduce an agglomeration algorithm. This provides a way for us to model two touching fibres as a single entity that also traps contaminants, and allows us to continue our simulation.
Filter devices operate in one of two regimes:
We divide our filters into three types, comprising: (i) uniformly sized periodically arranged fibres; (ii) uniformly sized randomly arranged fibres; or (iii) randomly sized and randomly arranged fibres. We compare the performance of each of these three filter types through four different metrics:
Our studies show that:
Thus, we find that the randomness in the fibres that we see in the filters in everyday processes can actually offer an advantage to the filtration performance. Since different filtration challenges will place different emphasis on the importance on the four performance metrics, our mathematical model can quickly and easily predict the optimum filter design for a given requirement.