Category Archives: fluid mechanics

From strain measurements to assessing El Niño events

Figure 11 from RSOS 201086One of the exciting aspects of leading a university research group is that you can never be quite sure where the research is going next.  We published a nice example of this unpredictability last week in Royal Society Open Science in a paper called ‘Transformation of measurement uncertainties into low-dimensional feature space‘ [1].  While the title is an accurate description of the contents, it does not give much away and certainly does not reveal that we proposed a new method for assessing the occurrence of El Niño events.  For some time we have been working with massive datasets of measurements from arrays of sensors and representing them by fitting polynomials in a process known as image decomposition [see ‘Recognising strain‘ on October 28th, 2015]. The relatively small number of coefficients from these polynomials can be collated into a feature vector which facilitates comparison with other datasets [see for example, ‘Out of the valley of death into a hype cycle‘ on February 24th, 2021].  Our recent paper provides a solution to the issue of representing the measurement uncertainty in the same space as the feature vector which is roughly what we set out to do.  We demonstrated our new method for representing the measurement uncertainty by calibrating and validating a computational model of a simple beam in bending using data from an earlier study in a EU-funded project called VANESSA [2] — so no surprises there.  However, then my co-author and PhD student, Antonis Alexiadis went looking for other interesting datasets with which to demonstrate the new method.  He found a set of spatially-varying uncertainties associated with a metamodel of soil moisture in a river basin in China [3] and global oceanographic temperature fields collected monthly over 11 years from 2002 to 2012 [4].  We used the latter set of data to develop a new technique for assessing the occurrence of El-Niño events in the Pacific Ocean.  Our technique is based on global ocean dynamics rather than on the small region in the Pacific Ocean which is usually used and has the added advantages of providing a confidence level on the assessment as well as enabling straightforward comparisons of predictions and measurements.  The comparison of predictions and measurements is a recurring theme in our current research but I did not expect it to lead into ocean dynamics.

Image is Figure 11 from [1] showing convex hulls fitted to the cloud of points representing the uncertainty intervals for the ocean temperature measurements for each month in 2002 using only the three most significant principal components . The lack of overlap between hulls can be interpreted as implying a significant difference in the temperature between months.

References:

[1] Alexiadis, A. and Ferson, S. and  Patterson, E.A., , 2021. Transformation of measurement uncertainties into low-dimensional feature vector space. Royal Society Open Science, 8(3): 201086.

[2] Lampeas G, Pasialis V, Lin X, Patterson EA. 2015.  On the validation of solid mechanics models using optical measurements and data decomposition. Simulation Modelling Practice and Theory 52, 92-107.

[3] Kang J, Jin R, Li X, Zhang Y. 2017, Block Kriging with measurement errors: a case study of the spatial prediction of soil moisture in the middle reaches of Heihe River Basin. IEEE Geoscience and Remote Sensing Letters, 14, 87-91.

[4] Gaillard F, Reynaud T, Thierry V, Kolodziejczyk N, von Schuckmann K. 2016. In situ-based reanalysis of the global ocean temperature and salinity with ISAS: variability of the heat content and steric height. J. Climate. 29, 1305-1323.

Salt increases nanoparticle diffusion

About two and half years ago, I wrote about an article we had published on the motion of nanoparticles [see ‘Slow moving nanoparticles‘ on December 13th, 2017] in which we had shown that, for very small particles at low concentrations, the motion of a particle is independent of its size and does not flow the well-known Stokes-Einstein law.  Our article presented convincing evidence from experiments to support our conclusions but was light on explanation in terms of the mechanics.  At the end of last year, we published a short article in Scientific Reports, in which we demonstrated that the motion of nanoparticles at low concentrations is dependent on the interaction of van der Waals forces and electrostatic forces.  Van der Waals forces are short-range attractive forces between uncharged molecules due to interacting dipole moments, whereas the electrostatic forces are the repulsion of electric charges.  We changed both of these forces by using salt solutions of different concentration and observing the changes in nanoparticle behaviour.  Increasing the molarity increases the diffusion of the particles until the solution is saturated, as shown in the picture for 50 nanometre diameter gold particles (that’s about half the diameter of a coronavirus particle or one thousandth of the diameter of a human hair).  Our findings have implications for understanding the behaviour of nanoparticles dispersed in biological media, which typically contain salt in solution, because the concentration of salt ions in the medium affects nanoparticle diffusion that has been shown to influence cellular uptake and toxicity.

Sources:

Coglitore D, Edwardson SP, Macko P, Patterson EA, Whelan MP, Transition from fractional to classical Stokes-Einstein behaviour in simple fluids, Royal Society Open Science, 4:170507, 2017.

Giorgi F, Coglitore D, Curran JM, Gilliland D, Macko P, Whelan M, Worth A & Patterson EA, The influence of inter-particle forces on diffusion at the nanoscale, Scientific Reports, 9:12689, 2019.

Size matters

Most of us have a sub-conscious understanding of the forces that control the interaction of objects in the size scale in which we exist, i.e. from millimetres through to metres.  In this size scale gravitational and inertial forces dominate the interactions of bodies.  However, at the size scale that we cannot see, even when we use an optical microscope, the forces that the dominate the behaviour of objects interacting with one another are different.  There was a hint of this change in behaviour observed in our studies of the diffusion of nanoparticles [see ‘Slow moving nanoparticles‘ on December 13th, 2017], when we found that the movement of nanoparticles less than 100 nanometres in diameter was independent of their size.  Last month we published another article in one of the Nature journals, Scientific Reports, on ‘The influence of inter-particle forces on diffusion at the nanoscale‘, in which we have demonstrated by experiment that Van der Waals forces and electrostatic forces are the dominant forces at the nanoscale.  These forces control the diffusion of nanoparticles as well as surface adhesion, friction and colloid stability.  This finding is significant because the ionic strength of the medium in which the particles are moving will influence the strength of these forces and hence the behaviour of the nanopartices.  Since biological fluids contain ions, this will be important in understanding and predicting the behaviour of nanoparticles in biological applications where they might be used for drug delivery, or have a toxicological impact, depending on their composition.

Van der Waals forces are weak attractive forces between uncharged molecules that are distance dependent.  They are named after a Dutch physicist, Johannes Diderik van der Waals (1837-1923).  Electrostatic forces occur between charged particles or molecules and are usually repulsive with the result that van der Waals and electrostatic forces can balance each other, or not depending on the circumstances.

Sources:

Giorgi F, Coglitore D, Curran JM, Gilliland D, Macko P, Whelan M, Worth A & Patterson EA, The influence of inter-particle forces on diffusion at the nanoscale, Scientific Reports, 9:12689, 2019.

Coglitore D, Edwardson SP, Macko P, Patterson EA, Whelan MP, Transition from fractional to classical Stokes-Einstein behaviour in simple fluids, Royal Society Open Science, 4:170507, 2017. doi: .

Patterson EA & Whelan MP, Tracking nanoparticles in an optical microscope using caustics. Nanotechnology, 19 (10): 105502, 2009.

Image: from Giorgi et al 2019, figure 1 showing a photograph of a caustic (top) generated by a 50 nm gold nanoparticle in water taken with the optical microscope adjusted for Kohler illumination and closing the condenser field aperture to its minimum following method of Patterson and Whelan with its 2d random walk over a period of 3 seconds superimposed and a plot of the same walk (bottom).

On the trustworthiness of multi-physics models

I stayed in Sheffield city centre a few weeks ago and walked past the standard measures in the photograph on my way to speak at a workshop.  In the past, when the cutlery and tool-making industry in Sheffield was focussed around small workshops, or little mesters, as they were known, these standards would have been used to check the tools being manufactured.  A few hundred years later, the range of standards in existence has extended far beyond the weights and measures where it started, and now includes standards for processes and artefacts as well as for measurements.  The process of validating computational models of engineering infrastructure is moving slowly towards establishing an internationally recognised standard [see two of my earliest posts: ‘Model validation‘ on September 18th, 2012 and ‘Setting standards‘ on January 29th, 2014].  We have guidelines that recommend approaches for different parts of the validation process [see ‘Setting standards‘ on January 29th, 2014]; however, many types of computational model present significant challenges when establishing their reliability [see ‘Spatial-temporal models of protein structures‘ on March 27th, 2019].  Under the auspices of the MOTIVATE project, we are gathering experts in Zurich on November 5th, 2019 to discuss the challenges of validating multi-physics models, establishing credibility and the future use of data from experiments.  It is the fourth in a series of workshops held previously in Shanghai, London and Munich.  For more information and to register follow this link. Come and join our discussions in one of my favourite cities where we will be following ‘In Einstein’s footprints‘ [posted on February 27th, 2019].

The MOTIVATE project has received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 754660.

The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.