The Physics Behind the Particle Vibration (T-PAOLA) Experiment

The Particle Vibration experiment’s aim was to explore a new contactless manipulation method for the control of particles dispersed in a fluid using vibrations. Like magnetic fields, vibrations allow contact-less control of the flow and dispersed particles.  However, unlike magnetic or electric fields, this method is a new technique that may be used more universally. Why? Because its application is not limited to electrically conductive or active liquids and/or particles. However, the vibrations on their own are not enough to control the position of particles and force them to self-organize. The system must also be subject to a temperature gradient. This temperature gradient can be generated simply by applying heat to one side on the enclosure containing the liquid and the particles. By using this method, the particles can be driven to specific regions of the container. The particles  then accumulate forming well-defined and surprisingly regular geometric items, which resemble cylinders, paraboloids, “ovoids” and conical surfaces (see the figure below).

The number of fields and practical applications that could use this method is very high. The new level of understanding provided by these experiments conducted in space is opening the way to innovative applications in chemistry, physics, and biomaterials and inorganic materials science. In the future, this technique based on the combined use of vibrations and temperature gradients will be used for the production of “new” inorganic or organic materials in space. Similarly, it will be used to conceive new nanotechnologies (in space and even on Earth). 

Computer Simulations

This space project has its roots in a theory that the PI (Prof. M. Lappa) formulated almost ten years before the effective execution of these experiments in space. Given the impossibility to conduct relevant tests on the surface of our planet (due to the gravitational effect causing the sedimentation of particles), the theory was initially developed in the framework of advanced computer simulations, by which some initial aspects could be tested (in 2014 and further elaborated and refined over subsequent years, 2016201720192020 and 2022). 

This video shows the formation of geometric particle structure in a non-isothermal liquid contained in a cubic enclosure when subjected to vibrations as predicted by computer simulations. The vibrational acceleration is approximated here as a sinusoidal wave with a non-dimensional amplitude of 10^8 and a non-dimensional angular frequency of 5*10^3. The cubic cavity contains a mixture of liquid and spherical particles. The density ratio between the fluid and the particles is 2. Moreover, the simulation in the present video is carried out by setting the vibrational Rayleigh number to 10^5. The interested reader is referred to the scientific literature cited above for the definition and meaning of these parameters. 

Some more informative and intuitive concepts (for the lay reader) to understand the physical principles at the basis of the PARTICLE VIBRATION experiments are reported in the following. 

Different Forces Present in Fluids

What are the main forces naturally present in fluids?

There are two main forces in fluids. The first is called surface tension. This force can easily be seen by observing for example water striders on a pond or a paperclip floating in a cup.  The other force is called the buoyancy force. This force is less easy to see but remains the predominant force in most fluids. Let us specify that the buoyancy force is only predominant on the earth. This is because this force is intimately connected with gravity. In space, the lack of gravity (g=0) means that the buoyancy force is no longer the predominant force and that surface tension takes on this role. This is why, in space, water can float around in a ball, because the surface tension of the water is ”keeping in together”. However, when contained in a closed box, the surface tension force does not act on the liquid as there is no ”free surface” around the liquid. This means that neither buoyancy, nor surface tension effects have a connection with the Particle Vibration (T-PAOLA) experiment. 

Why is this important for us?

Although it may not obvious, buoyancy force can be quite disruptive when it comes to making new materials on earth. Let’s take an example. When metal alloys are made here on earth, it generally starts with a liquid-liquid state and then solidifies into the material we want. As the liquid hardens, it becomes what we call a ‘two-phase’ flow. This means that there are some solid particles in the liquid due to the hardening process. These particles have been seen to either float to the top or sink to the bottom of the mixture. This is particularly disruptive when making materials where the density of the solid two materials are different. In this case one type would rise and one type would sink, making the process very difficult. This is an example of the effect of gravity on fluids, however there are many more examples of how this force effects different types of fluid systems. By using micro gravity laboratories, we can take the effect of this force away and investigate new concepts to control the behaviour of the disprsed phase.

Why are vibrations and heat used for the T-PAOLA project?

When gravity is absent, vibrations can be used to induce a specific type of fluid motion known as vibrational convection. Just as hot water tends to “rise” inside a pot put on a fire in our kitchen, thereby creating what is known as gravitational or natural convection, vibrations applied to a fluid that is being heated in microgravity can lead to another type of fluid motion that the scientists call thermovibrational flow. This is similar to the natural convection that we experience in our everyday life (the mixing of water inside a pot due to the vortices produced by the gravity-induced buoyancy force). 

Natural convection induced by gravity in a pot containing water

Unlike classical natural convection, however, the thermovibrational convection is oscillatory, that is, its vortices change their sense of rotation continuously.

When they are applied to a fluid containing solid particles, however, vibrations can have another important effect. They can cause the time-periodic (back and forth) motion of the suspended particles along the shaking direction.

In combination with the above-mentioned time-periodic fluid motion or vortices, vibrations can therefore have a complex influence on a mixture consisting of a fluid and dispersed particles, leading to fascinating particle accumulation and self-organization phenomena.    

Although a complete exposition of the complex theory underlying the Particle Vibration (T-PAOLA) project is beyond the scope of this informative discussion, one may get an idea of the ability of vibrations to create aesthetically appealing patterns and fascinating phenomena by considering the inspirational videos below. These refer to the so-called “Chladni’s experiments or figures”. For additional details about gravitational, surface-tension-driven and thermovibrational flows, the interested visitor may consider these books:

Thermal Convection: Patterns, Evolution and Stability”, 700 pages – ISBN-13: 978-0-470-69994-2, ISBN-10: 0470699949, John Wiley & Sons, Ltd (2009, Chichester, England)

Rotating Thermal Flows in Natural and Industrial Processes“, 540 pages, ISBN-13: 978-1-1199-6079-9, ISBN-10: 1119960797, John Wiley & Sons, Ltd (2012, Chichester, England).   

Inspirational Physical Phenomena

Many years ago, Ernest Chladni, a German physicist and musician, discovered that applying certain vibrations to a solid plate with a random distribution of overlying particles created different patterns. These are called Chladni figures. They are beautiful geometrical formations and their shape depends on the type of vibration applied to the plate and also the shape of the plate itself. This indicates firstly that vibrations applied to a plate can form particle structures. It also indicates that many different patters form depending on the type of vibration applied to the plate. This phenomena can be seen in the short videos below.

The  physical mechanisms underlying these behaviours and those related to the T-PAOLA experiments are quite different (as the latter also includes a liquid that moves cyclically under the effect of vibrations and an imposed temperature difference). Moreover, the particle structures formed by T-PAOLA are three-dimensional as opposed to the two-dimensional nature of the Chladni’s figures.

Nevertheless, these phenomena share an important aspect, which allows an analogy to be drawn. Both demonstrate that vibrations can be used to exert a control on a distribution of particles, forcing them to accumulate in specific regions or form well-defined patterns.