Indentation of ellipsoidal and cylindrical elastic shells

Thin shells are found in nature at scales ranging from viruses to hens’ eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus et al. [Phys. Rev. Lett. (submitted)] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells

The indentation of pressurized elastic shells: From polymeric capsules to yeast cells

Pressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of baker’s yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium

Wrinkling of pressurized elastic shells

We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We present scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells

The Liquid Blister Test

We consider a thin elastic sheet adhering to a stiff substrate by means of the surface tension of a thin liquid layer. Debonding is initiated by imposing a vertical displacement at the centre of the sheet and leads to the formation of a delaminated region, or `blister'. This experiment reveals that the perimeter of the blister takes one of three different forms depending on the vertical displacement imposed. As this displacement is increased, we observe first circular, then undulating and finally triangular blisters. We obtain theoretical predictions for the observed features of each of these three families of blisters. The theory is built upon the F\"{o}ppl-von K\'{a}rm\'{a}n equations for thin elastic plates and accounts for the surface energy of the liquid. We find good quantitative agreement between our theoretical predictions and experimental results, demonstrating that all three families are governed by different balances between elastic and capillary forces. Our results may bear on micrometric tapered devices and other systems where elastic and adhesive forces are in competition.Comment: 23 pages, 11 figs approx published versio

Fluctuation Spectra and Force Generation in Non-equilibrium Systems

Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The non-equilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that for a narrow, unimodal spectrum, the force exerted by a non-equilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important non-equilibrium interactions are encoded within the fluctuation spectrum. In this sense the noise becomes the signal

Indentation of a floating elastic sheet: Geometry versus applied tension

The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force--indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations the force--indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes.Comment: 24 pages, revised version submitted to Proc. R. Soc.

Unravelling Nanoconfined Films of Ionic Liquids

The confinement of an ionic liquid between charged solid surfaces is treated using an exactly solvable 1D Coulomb gas model. The theory highlights the importance of two dimensionless parameters: the fugacity of the ionic liquid, and the electrostatic interaction energy of ions at closest approach relative to thermal energy, in determining how the disjoining pressure exerted on the walls depends on the geometrical confinement. Our theory reveals that thermodynamic fluctuations play a vital role in the "squeezing out" of charged layers as the confinement is increased. The model shows good qualitative agreement with previous experimental data, with all parameters independently estimated without fitting

Morphological and genetic barcoding study confirming the first Stegastes variabilis (Castelnau, 1855) report in the Mediterranean Sea

This paper presents morphometric and genetic barcoding analyses of the first record of the Cocoa Damselfish, Stegastes variabilis in the Mediterranean Sea. A single specimen was captured from Senglea waterfront, Malta (Central Mediterranean) on the 15th of September 2013. The species is non-indigenous in the Mediterranean, as it is native to the tropical Western Atlantic. Apart from undertaking identification through meristics and morphometric measurements of the specimen, genetic analyss of the 3410 bp mtDNA genes were carried out to confirm the species' identity. The latter was useful given that the genus Stegastes is known to be composed of morphologically very similar species, with variable colour patterns

Associations of Abdominal Muscle Area and Radiodensity with Adiponectin and Leptin: The Multiethnic Study of Atherosclerosis.

ObjectiveThis study examined the associations of muscle area and radiodensity with adiponectin and leptin.MethodsA total of 1,944 participants who enrolled in the Multi-Ethnic Study of Atherosclerosis underwent computed tomography to quantify body composition and measurements of adiponectin, leptin, interleukin-6, C-reactive protein, and resistin.ResultsThe mean age and BMI of participants were 64.7 years and 28.1 kg/m2 and 49% were female. With adjustment for age, gender, race/ethnicity, traditional cardiovascular disease risk factors, inflammatory biomarkers, physical activity, and sedentary behavior, a 1-SD increment in total abdominal, stability, and locomotor muscle area was associated with a 19%, 17%, and 12% lower adiponectin level, respectively (P < 0.01 for all) but not leptin (P > 0.05). Muscle radiodensity was more robustly associated with adiponectin and leptin in the multivariable linear regression models. That is, with full adjustment for all covariates, a 1-SD increment in total abdominal, stability, and locomotor muscle radiodensity was associated with a 31%, 31%, and 18% lower adiponectin level (P < 0.01 for all) and a 6.7%, 4.6%, and 8.1% higher leptin level (P < 0.05 for all), respectively.ConclusionsThe data suggest that increases in muscle area and radiodensity may have positive impacts on chronic inflammation and, in turn, reduce the risk of cardiometabolic disease