Post Mortem: Measureing Permeability of Microfluidic Porous Media

When you read a scientific publication, in particular papers in natural science, if you are not familiar with the circumstances of scientific reality (I mean what typically happens vs what idealy happens), you might come to the conclusion that the authors had a very specific idea of what they wanted to investigate, before performing the research. However, my experience is, that this is often not true and the outcome of the research, for whatever reason is was performed, largely determines the scientific question that a paper tries to answer.

By this I absolutely don’t want to suggest that the majority of publications do not significantly contribute to our scientific understanding of the world. In fact, I would argue that it is quite the contrary. I would argue that most oft the time we might be unable to ask the right question, if we do not have, at least, some idea of the answer. But in science we’re always trying to search and explain the unknown, so is it even possible to ask a good and non-trivial question before performing the research? There is a famous quote by Johann Wolfgang von Goethe “You only see what you know.”, which points to this problem and reminds us of the danger of sticking to closely to what we already know. Of course, there is always a trade-off. We need to have an idea of what is already known and what is not known (or let’s say, how ‘well’ we know something) in order to understand the relevance of a new observation. Most publications make it quite clear, as a motivation, why a specific question is worth to ask or why a specific system is interesting to investigate. However, the history of how events unfolded and how the authors eventually arrived at the paper that they published, is typically lost.

I believe that for some of my publications this history is actually quite interesting and worth telling. First, because it can sometimes be quite entertaining. Second, because others might learn something useful from it. And third, because there is always a chance that after a long time, some aspects of your research turn out to be really really relevant for mankind in some way or the other in this unlikely case, it would be nice to have some honest documentation about how you ended up doing what you actually did.

So therefore, I am writing this post mortem, about some of my papers. I call it post mortem in analogy to the practice in some industries, where a post mortem refers to a retrospective project wrap-up, typically written for other people familiar with the art.

The very first entry in this series will be about my publication:

Christian Scholz, Frank Wirner, Yujie Li, and Clemens Bechinger
Measurement of flow properties in microfluidic porous media with finite-sized colloidal tracers, Experiments in Fluids 53, 1327 – 1333 (2012) 

This is the very first publication of my academic career. At this moment in time I had already spend about 1.5 years of work on the subject and my impression was that I was far away from discovering anything relevant in the field (this turned out to be not true at all). It was also quite a challenge to manufacture microfluidic samples robustly in our lab. In the beginning, I had a success rate of about 10% and it was not uncommon to hear people shouting in the laboratories behind closed doors, when a sample turned out to be unusable. We regularly suffered from leaking microcluidic cells, collapsing structures, unstable sticking colloidal suspensions as well as contamination (I think this was the first time in my life, where I actually saw some kind of microorganism moving in real time). While this improved in the later stage of my PhD, thanks to the experience that builds up after crafting hundreds of samples, at this point, I was actually thinking: Well, at least we should put together an article about the technical challenges that we had overcome so far.

As the title says the article deals with the measurement of flow in microfluidic porous media using colloidal tracer particles. Typically flow properties such as the permeability in macroscopic porous media are measured by the the external factors around the porous core, such as flow rate and the applied pressure gradient. This is only possible when the flow rates are large enough so that they can be reliably measured.

Permeability is a quantification of the ability of a porous medium to conduct flow of a liquid or gas. The concept is equivalent to the electric conductivity (inverse of the resistance) of a material, which most people are more familiar with.

In this project, however, we wanted to investigate the permeability of microfluidic porous media models. The flow rates in such samples were so small that direct measurement of it seemed far out of scope with conventional laboratory equipment. One solution to, at least, visualize flow in such structures is via the injection of colloidal tracer particles. These particle follow the streamlines of the fluid and can therefore be used to trace the fluid flow. However, even though colloidal particles are relatively small (1 – 5 µm) they were still comparable to the size of the microfluidic structures that we wanted to investigate. In such a situation the speed of the particles does not trace the speed of the fluid at a single infinitesimal point. Instead, particles disturb the flow and also start to rotate. Additionally under a conventional microscope only a 2D projection of the particle motion can be seen, therefore information about the z-Position of each particle is not directly available. Due to the finite size, particles can also not come arbitrarily close to walls, therefore the fluid boundary layer near the wall cannot be accurately resolved and some of the fluid space is ‘shadowed’ of from the particle flow.

Because of this, we had to find a different method to determine permeability in our microfluidic models. We identified two options. First, a constant head method, were the pressure applied to the sample is kept constant as good as possible and the flow rate is measured relative to a reference channel, where we know estimate the flow accuratly from first principles. Second, a falling head method, where the hydrostatic pressure applied to the sample is allowed to slowly relax due to the flow. Since the flow rates are very small, this takes several hours, even for reservoirs with a tiny cross-section.

The first method appeared to work relatively robust, as long as there is no leakage or structure collapse in the samples. However, we wanted to apply a second method as well, in order to have a reference measurement by which we can compare the two different methods, such that we can be confident that we do not have missed systematic effects. For the falling head method, however, it turned out that we had to spend an enormous amount of work to get a working sample. Most samples would suffer from tiny leakage or abundance of tracer particles after some time of measurement. After several months my colleague Frank Wirner finally succeeded in manufacturing one golden sample that was stable enough for an entire measurement. Unfortunately, even for this ideal case, it turned out that the uncertainty of the fit to the measured data did result in a rather large uncertainty of the corrected permeability of the structure. So, while technically we achieved our goal of demonstrating two methods of measuring the permeability in microfluidic samples with extremely small flow rates, we decided that the constant head method was far more trustworthy and robust.

The usefulness of this technique is, in my opinion, surprisingly underestimated. We even had trouble publishing the manuscript in its initial form, since a referee was not convinced that such methods are required at all. I believe, it is easy to underestimated the difficulties of an accurate permeability measurement in thin microfluidic porous channels with ultra low flow rates. Determining the pressure applied to the sample with a differential sensor, while applying a pre-defined constant flow rate might be an alternative, but this will require very expensive ultra accurate syringe pumps and even there parasitic forces might build up in the flexible hoses and joints, such that the flow-rate needs a surprisingly long time to relax (be prepared to wait for an hour or two in between each datapoint). Or solution, I believe, is much more robust and definitely more cost-efficient.

These results are of course also the technical basis of all our later publications in Physical Review and EPL. My feeling is, that this paper shows some very interesting aspects of measuring flow in microfluidic structures, were tracers are really comparable to the typical structure size and recommend it to anyone who would like to attempt doing similar experiments.