Engineering

Printer Design: Hydrogels

Research

During the period in which we were unable to access the lab, the hydrogel team spent time researching various different hydrogels. From this research we obtained the following key points:

Natural hydrogels are biodegradable, whereas synthetic hydrogels are generally higher in mechanical strength resulting in a slower degradation rate.
Generally, gelation is not reversible in chemical gels.
Silica gels (a type of chemical gel) are traditionally the most widely used gels for crystal growth
Physical gels are most common in biomineralization. They are often comprised of polysaccharides and proteins, often mixed together.
The physical nature of the bonding interactions in these gels can vary with temperature and time
Alginate (AMH) found to be compatible with bacteria in self-healing concrete (MICP).

From the research we did, we chose to use agarose hydrogel for two reasons:

Agarose has neutral hydroxyl groups, which are known to be relatively less interactive with calcium carbonate.
Agarose is biocompatible and has a high water content which favours cell osmosis and homeostasis.

Imagine

(This is the Imagine phase of our Engineering Design Process)

In our printer, we would want the hydrogel to have various characteristics that suit its application. These include:

Relatively high viscosity
Mechanical integrity
Biodegradability
pH resistance
UV resistance

The first two points were analysed as part of the computational modelling part of this project.

Upon modelling the mechanical properties of hydrogel, we found that the model that most accurately predicted the creep viscoelastic behaviour was the Kelvin-Voigt model. This consisted of a spring and dashpot connected in parallel. By solving the differential equation using numerical analysis, it was found that if a constant stress was applied to a hydrogel medium then the strain (the ratio between its current length to original length) would initially increase rapidly but asymptotically approach a certain value, at which it would be in steady state. This would correspond to the desired shape which is to be printed.

The rate at which the hydrogel would reach this state is dictated by the viscosity and Young's modulus of the hydrogel. More specifically, the time taken to reach equilibrium (the relaxation time) is on the order of the ratio between the two parameters. It would hence be desirable if we could have a hydrogel that hardens quickly such that it would be possible to balance production time with printing accuracy.

Because agarose is comprised of polysaccharides and polypeptides, it’s therefore very biodegradable. It degrades into agarobiose, which is a disaccharide which in itself is comprised of variants of galactose, a molecule commonly found as part of lactose. Agarose can also tolerate a large range of pH and UV extremes.

Printer Design: Nozzle

Our bacterial 3D printer must consist of a nozzle in which the bacteria diffuse into the hydrogel and the process of calcium carbonate precipitation takes place. We have been fortunate enough this year to collaborate with the Ashesi Ghana iGEM team, who helped us come up with the concept for a nozzle design for the printer. Combining this with our initial two import chamber idea when modelling diffusion, we have been able to come up with a conceptual design that is able to disperse the bacteria within the hydrogel medium while maintaining its mechanical properties.

Below discusses the process in which we implement a potential design for the printer nozzle, and how team Ashesi have aided in not only the design, but some of the mathematical modelling of the fluid dynamics which take place within the nozzle.

Initial Design Idea

Before our collaboration begun with the Ashesi Ghana iGEM team, we initially had a very conceptual idea for the design of our nozzle. The idea came from the two chamber diffusion model. The design consisted of two import tubes, one containing the hydrogel and one the bacteria. The tubes were such that they came in at an angle which created a vortex and mixing occurred within the chamber of the nozzle. This eliminated the need for a separate mixing chamber. If we did have a mixing chamber, it would build up a residue that would precipitate calcium carbonate which would mean that the nozzle would have to be regularly replaced. The importance of this is that it allows a for more sustainable and longer lasting design, if this nozzle were to be bulk produced.

We then came in contact with the team from Ghana; team Ashesi. The team consisted primarily of students with a background in engineering, which in our case was very helpful to our project because we have no engineers on our team. They helped us design a nozzle which had an increased volume per unit surface area, which allowed more mixing to take place within the same space within the chamber. The other improvement that team Ashesi made was that the design included filleting. Filleting is the process of adding an extra layer around the joints of the nozzle. This helps the nozzle to resist cracks and fractures from the increased amount of pressure applied from the fluids within the nozzle.

This design also encapsulates the key components in hydrogel printing, such as having the correct thickness for the correct amount of hydrogel to be able to flow through whilst also not creating too much viscous impedance which would cause the hydrogel to flow on a much longer timescale.

After consideration alongside team Ashesi, we decided that the best approach would be to mix the bacteria and hydrogel in the nozzle itself. A concept for such a nozzle is shown below:

The angles at which the bacteria and hydrogel enter into the nozzle create a vortex inside and hence achieves homogenous mixing.

Fluid Mechanics Theory Overview

In order to model how quickly mixing will occur in the nozzle, our team alongside team Ashesi used some of the principles of fluid mechanics to derive an approximation for the velocity field of the fluid inside the model.

All problems in fluid mechanics can be started from the famous Navier-Stokes equation, which in principle describes how any fluid flows over time. More specifically, it describes the time dependence of the velocity of every point in the fluid, also known as the velocity field.

It is given by:

Where 𝜌 is the fluid density, 𝜇 is the viscosity, 𝒖 is the velocity vector and 𝑭 is a general force term that accounts for any additional external forces that are acting on the fluid.

While it looks quite complicated, it has the same resemblance as Newton's second law with all the terms on the left being the "mass * acceleration" and the terms on the right all being different forces that act on the fluid.

It is combined with the continuity equation, which is essentially stating that mass cannot 'magically' disappear, all mass that flows into a point must flow out again.

In terms of pure mathematics, it is very hard to solve these equations analytically, and so typically it is desirable to know what flow regime the system is in. This can be quantified by what is known as the Reynold's number, which indicates whether the flow is laminar or turbulent. The equation for the Reynold's number is given by:

In a low Reynolds number regime, this viscosity term is larger than the inertial terms, and hence the flow is likely to be laminar. By contrast in a high Reynolds number regime, the inertial forces are much larger than the viscous forces and the flow is more likely to be turbulent.

In fluid dynamics it is often the case that the equation must be simplified by making various assumptions.

Fluid Mechanical Modelling

We have been working alongside team Ashesi in order to produce a simulation for how the hydrogel will flow within the nozzle.

Below is a contour colour plot of the Reynolds number inside the nozzle design:

From this, we can see that flow is mostly in the laminar regime within the central part of the nozzle, with an increasing Reynold's number towards the edges, indicating that flow is somewhat more turbulent.

In addition team Ashesi also produced a plot of the velocity vector field to show how the hydrogel would flow inside the nozzle. This is shown below:

Improving the Design Further

While team Ashesi's nozzle design consisted of many additional features, we realised that for our specific purpose of mixing the bacteria within the hydrogel for the application of 3D printing needed to still include some features from our original design. We came up with the idea to include a form of threading on the two import tubes, such that they are able to be detached from the main chamber of the nozzle.

What We've Learned

In doing our collaboration with team Ashesi, we have been able to learn a lot about the process of engineering a design which has to take into account practicality, feasibility and sustainability, whilst also being able to carry out its function as efficiently as possible.

Our Progress

Initial Design

Updated Design (after feedback and collaboration with Ashesi Ghana)

Potential Experiments

The nozzle design is such that it will allow for the mixing of the bacteria and the hydrogel wherein the angles of the outlets for each within a conical tube create a vortex which allows for mixing. In a lab environment, we would have tried different entry angles to test how well each leads to mixing. Furthermore, as already mentioned in the CO₂ modelling paper written by team member Velizar Kirkow, we determined that the best way to for the hydrogel to be spread is over a maximised surface area. Therefore, an additional component of the testing of the nozzle would be to test whether it would be better to have a smooth end or an end with ridges.

Team:Exeter/Engineering