Bubble rise in molten glasses and silicate melts during heating and cooling cycles

The Hadamard-Rybczynski equation describes the steady-state buoyant rise velocity of an unconfined spherical bubble in a viscous liquid. This solution has been experimentally validated for the case where the liquid viscosity is held constant. Here, we extend this result for non-isothermal conditions, by developing a solution for bubble position in which we account for the time-dependent liquid viscosity, liquid and gas densities, and bubble radius. We validate this solution using experiments in which spherical bubbles are created in a molten silicate liquid by cutting gas cavities into glass sheets, which are stacked, then heated through the glass transition interval. The bubble-bearing liquid, which has a strongly temperature-dependent viscosity, is subjected to various heating and cooling programs such that the bubble rise velocity varies through the experiment. We find that our predictions match the final observed position of the bubble measured in blocks of cooled glass to within the experimental uncertainty, even after the application of a complex temperature-time pathway. We explore applications of this solution for industrial, artistic, and natural volcanological applied problems.

A Bayesian Framework to Estimate Fluid and Material Parameters in Micro-swimmer Models

To advance our understanding of the movement of elastic microstructures in a viscous fluid, techniques that utilize available data to estimate model parameters are necessary. Here, we describe a Bayesian uncertainty quantification framework that is highly parallelizable, making parameter estimation tractable for complex fluid-structure interaction models. Using noisy in silico data for swimmers, we demonstrate the methodology's robustness in estimating fluid and elastic swimmer parameters, along with their uncertainties. We identify correlations between model parameters and gain insight into emergent swimming trajectories of a single swimmer or a pair of swimmers. Our proposed framework can handle data with a spatiotemporal resolution representative of experiments, showing that this framework can be used to aid in the development of artificial micro-swimmers for biomedical applications, as well as gain a fundamental understanding of the range of parameters that allow for certain motility patterns.

Stokes' mathematical education

George Gabriel Stokes won the coveted title of Senior Wrangler in 1841, a year in which the examination papers for the Cambridge Mathematical Tripos were notoriously difficult. Coming top in the Mathematical Tripos was a notable achievement, but for Stokes it was a prize hard won after several years of preparation, and not only years spent at Cambridge. When Stokes arrived at Pembroke College, he had spent the previous two years at Bristol College, a school which prided itself on its success in preparing students for Oxford and Cambridge. This article follows Stokes' path to the senior wranglership, tracing his mathematical journey from his arrival in Bristol to the end of his final year of undergraduate study at Cambridge. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Sir George Gabriel Stokes, Bart (1819-1903): his impact on science and scientists

Lucasian Professor Sir George Gabriel Stokes was appointed joint-Secretary of the Royal Society in 1854, a post he held for the unprecedented period of 31 years, relinquishing the role when he succeeded T.H. Huxley as President in 1885. An eminent scientist of the Victorian era, Stokes explained fluorescence (he also coined the word) and his hydrodynamical formulae (the 'Navier-Stokes equations') remain ubiquitous today in the physics of any phenomenon involving fluid flows, from pipelines to glaciers to large-scale atmospheric perturbations. He also made seminal advances in optics and mathematics, and formulae that bear his name remain widely used today. The historiography however appears to understate Stokes's significant impact on science as unacknowledged collaborator on a wide range of scientific developments. His scientific peers regarded him as a mentor, advisor, designer of crucial experiments and, as editor of the Royal Society's scientific journals, arbiter of the standards of excellence in scientific communication to be attained before publication would be considered. Three brief case studies on Stokes's correspondence with Lord Kelvin, Sir William Crookes and the chemist Arthur Smithells exemplify how his impact was conveyed through the work of other scientists. This paper also begins consideration of why the character and worldview of Stokes led him to eschew personal reputation and profit for the sake of science and the Royal Society, and of how the development of the discipline of history of science has impacted on historiography relating to Stokes and others. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Stokes, Tyndall, Ruskin and the nineteenth-century beginnings of climate science

Although we humans have known since the first smokey campfires of prehistory that our activities might alter our local surroundings, the nineteenth century saw the first indications that humankind might alter the global environment; what we currently know as anthropogenic climate change. We are now celebrating the bicentenaries of three figures with a hand in the birth of climate science. George Stokes, John Tyndall and John Ruskin were born in August 1819, August 1820 and February 1819, respectively. We look back from the perspective of two centuries following their births. We outline their contributions to climate science: understanding the equations of fluid motion and the recognition of the need to collect global weather data together with comprehending the role in regulating terrestrial temperature played by gases in the atmosphere. This knowledge was accompanied by fears of the Earth's regression to another ice age, together with others that industrialization was ruining humankind's health, morals and creativity. The former fears of global cooling were justified but seem strange now that the balance has tipped so far the other way towards global warming; the latter, on the other hand, today seem very prescient. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Estimation of Temperature and Associated Uncertainty from Fiber-Optic Raman-Spectrum Distributed Temperature Sensing

Distributed temperature sensing (DTS) systems can be used to estimate the temperature along optic fibers of several kilometers at a sub-meter interval. DTS systems function by shooting laser pulses through a fiber and measuring its backscatter intensity at two distinct wavelengths in the Raman spectrum. The scattering-loss coefficients for these wavelengths are temperature-dependent, so that the temperature along the fiber can be estimated using calibration to fiber sections with a known temperature. A new calibration approach is developed that allows for an estimate of the uncertainty of the estimated temperature, which varies along the fiber and with time. The uncertainty is a result of the noise from the detectors and the uncertainty in the calibrated parameters that relate the backscatter intensity to temperature. Estimation of the confidence interval of the temperature requires an estimate of the distribution of the noise from the detectors and an estimate of the multi-variate distribution of the parameters. Both distributions are propagated with Monte Carlo sampling to approximate the probability density function of the estimated temperature, which is different at each point along the fiber and varies over time. Various summarizing statistics are computed from the approximate probability density function, such as the confidence intervals and the standard uncertainty (the estimated standard deviation) of the estimated temperature. An example is presented to demonstrate the approach and to assess the reasonableness of the estimated confidence intervals. The approach is implemented in the open-source Python package "dtscalibration".

Thermal Shock Response of Yeast Cells Characterised by Dielectrophoresis Force Measurement

Dielectrophoresis is an electric force experienced by particles subjected to non-uniform electric fields. Recently, several technologies have been developed focused on the use of dielectrophoretic force (DEP) to manipulate and detect cells. On the other hand, there is no such great development in the field of DEP-based cell discrimination methods. Despite the demand for methods to differentiate biological cell states, most DEP developed methods have been focused on differentiation through geometric parameters. The novelty of the present work relies upon the point that a DEP force cell measurement is used as a discrimination method, capable of detecting heat killed yeast cells from the alive ones. Thermal treatment is used as an example of different biological state of cells. It comes from the fact that biological properties have their reflection in the electric properties of the particle, in this case a yeast cell. To demonstrate such capability of the method, 279 heat-killed cells were measured and compared with alive cells data from the literature. For each cell, six speeds were taken at different points in its trajectory inside a variable non-uniform electric field. The electric parameters in cell wall conductivity, cell membrane conductivity, cell membrane permittivity of the yeast cell from bibliography explains the DEP experimental force measured. Finally, alive and heat-treated cells were distinguished based on that measure. Our results can be explained through the well-known damage of cell structure characteristics of heat-killed cells.

Micro-Raman Spectroscopy for the Determination of Local Temperature Increases in TiO2 Thin Films due to the Effect of Radiation

This study applied a classic method involving Raman spectroscopy and the use of Stokes and anti-Stokes peaks to measure the temperature of TiO2 thin films found in dye-sensitized solar cells (DSSCs). In addition, three mathematical formulae were used and analyzed to estimate the increase in temperature generated solely by the effect of the radiation. The tests and calculations performed showed an increase in the temperature of the TiO2 film. That is, the films were heated by the radiation they were exposed to. A temperature increase of up to 30 K was detected for the sample with a single layer of TiO2, and over 40 K for the sample with three layers for the highest radiation powers used, and greater increases in temperature were observed in the thicker films.

Stokes trap for multiplexed particle manipulation and assembly using fluidics

The ability to confine and manipulate single particles and molecules has revolutionized several fields of science. Hydrodynamic trapping offers an attractive method for particle manipulation in free solution without the need for optical, electric, acoustic, or magnetic fields. Here, we develop and demonstrate the Stokes trap, which is a new method for trapping multiple particles using only fluid flow. We demonstrate simultaneous manipulation of two particles in a simple microfluidic device using model predictive control. We further show that this approach can be used for fluidic-directed assembly of multiple particles in solution. Overall, this technique opens new vistas for fundamental studies of particle-particle interactions and provides a new method for the directed assembly of colloidal particles.