Axisymmetric Free Vibration of Layered Cylindrical Shell Filled with Fluid

The aim of the study is to analyse the axisymmetric free vibration of layered cylindrical shells filled with a quiescent fluid. The fluid is assumed to be incompressible and inviscid. The equations of axisymmetric vibrations of layered cylindrical shell filled with fluid, on the longitudinal and transverse displacement components are obtained using Love’s first approximation theory. The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for a frequency parameter and an associated eigenvector of spline coefficients. Two layered shells with three different types of materials under clamped-clamped boundary conditions are considered. Parametric studies are made on the variation of the frequency parameter with respect to length-to-radius ratio and length-to-thickness ratio.

Natural Frequency Analysis of Multilayer Truncated Conical Shells Containing Quiescent Fluid on Elastic Foundation with Different Boundary Conditions

In this paper, natural frequency of a multilayer truncated conical composite shell conveying quiescent fluid on elastic foundation with different boundary conditions is investigated and analyzed. The governing equations are presented based on the first-order shear deformation theory. Bernoulli’s equation and velocity potential have been used in the shell-fluid interface to obtain the fluid pressure. The fluid used in this study is considered non-compressible and non-viscous. The beam functions and the Galerkin weight functions method are used to describe and solve the coupled system of differential equations. Three types of boundary conditions are considered to investigate the natural frequency of the conical shells. The results show that the presence of the fluid in the conical shell reduces the fundamental natural frequency values. Also, by changing the semi-vertex conical angle from [Formula: see text] to [Formula: see text] for the simply support boundary conditions, the fundamental natural frequency value for the composite conical shell without and with fluid increases, and the presence of the elastic foundation increases the frequencies of the empty and full-fluid composite conical shells.

Ciliary chemosensitivity is enhanced by cilium geometry and motility

Cilia are hairlike organelles involved in both sensory functions and motility. We discuss the question of whether the location of chemical receptors on cilia provides an advantage in terms of sensitivity and whether motile sensory cilia have a further advantage. Using a simple advection-diffusion model, we compute the capture rates of diffusive molecules on a cilium. Because of its geometry, a non-motile cilium in a quiescent fluid has a capture rate equivalent to a circular absorbing region with ~4x its surface area. When the cilium is exposed to an external shear flow, the equivalent surface area increases to ~6x. Alternatively, if the cilium beats in a non-reciprocal way in an otherwise quiescent fluid, its capture rate increases with the beating frequency to the power of 1/3. Altogether, our results show that the protruding geometry of a cilium could be one of the reasons why so many receptors are located on cilia. They also point to the advantage of combining motility with chemical reception.

Quantification of Brownian motion under presence of flow using particle diffusometry

Particle diffusometry (PD), a quantification method for the Brownian motion, is performed by recording temporally sequential images and using correlation analysis to obtain an ensemble diffusion coefficient for all particles captured in the imaging region (Clayton et al., 2017). PD is proven to be successful in the detection of the waterborne pathogen V. cholerae in environmental samples using different imaging techniques, including an inverted fluorescence microscope as well as a handheld hardware device operated with a smartphone (Clayton et al., 2019; Moehling et al., 2020). Although we intend to use PD to calculate diffusion coefficients in quiescent fluid, oftentimes unintentional fluid flows occur, creating measurement error when calculating the diffusion coefficient. In previous work, recordings under the presence of flow were discarded to avoid incorrect measurements of the sample.

Effect of particle inertia on the alignment of small ice crystals in turbulent clouds

Small non-spherical particles settling in a quiescent fluid tend to orient so that their broad side faces down, because this is a stable fixed point of their angular dynamics at small particle Reynolds number. Turbulence randomises the orientations to some extent, and this affects the reflection patterns of polarised light from turbulent clouds containing ice crystals. An overdamped theory predicts that turbulence-induced fluctuations of the orientation are very small when the settling number Sv (a dimensionless measure of the settling speed) is large. At small Sv, by contrast, the overdamped theory predicts that turbulence randomises the orientations. This overdamped theory neglects the effect of particle inertia. Therefore we consider here how particle inertia affects the orientation of small crystals settling in turbulent air. We find that it can significantly increase the orientation variance, even when the Stokes number St (a dimensionless measure of particle inertia) is quite small. We identify different asymptotic parameter regimes where the tilt-angle variance is proportional to different inverse powers of Sv. We estimate parameter values for ice crystals in turbulent clouds and show that they cover several of the identified regimes. The theory predicts how the degree of alignment depends on particle size, shape and turbulence intensity, and that the strong horizontal alignment of small crystals is only possible when the turbulent energy dissipation is weak, of the order of 1cm2/s3 or less.

Effect of Chemical Reaction and Thermo-Diffusion in an Electrically Conducting Walters’ B Fluid over a Vertical Stretching Surface

In this article, the significance of chemical reaction and thermo-diffusion in Walters’ B fluid is examined with medium porosity under the influence of non-uniform heat generation\absorption. The nonlinear ordinary differential equations describing the flow are obtained via similarity variables and tackled by Homotopy Analysis Method. The results show among others that involvement of chemical reaction contributes to the shrinking of concentration buoyancy effect while dimensionless temperature overshoot with large values of convective heat parameter and heat generation\absorption which enable thermal potency to gain entrance to the quiescent-fluid, indicating that the two parameters can be used for drying of the components.

Instabilities of a freely moving spherical particle in a Newtonian fluid: Direct Numerical Simulation

Direct Numerical Simulations (DNS) were carried out for a freely falling/rising rigid particle in an otherwise quiescent fluid, using a non-Lagrangian multiplier based fictitious domain (FD) method. Validation studies showed that the proposed FD based DNS are in good agreement with the existing experimental results in the transition regime of falling/rising spheres. Simulations done in the transitional regime (50 < Reynolds number (Re) < 1800 and solid-to-fluid density ratios Γ = ρ p / ρ f ${\Gamma}={\rho }_{p}/{\rho }_{f}$ from 0.08 to 4), confirmed that (i) a falling spherical particle (Γ = 4) exhibits a helical trajectory in the range 270 < Re < 320, and (ii) a rising particle (Γ = 0.5) shows a zig-zagging trajectory in the same range of Re. This finding closes the uncertainty to the question as to whether or not rising/falling particles exhibit a helical and a zig-zagging trajectory. In addition to this, a total of seven distinctive flow regimes were identified, which are as follows: (I) vertical straight path (II) steady oblique path (III) Wavy oblique path (IV) zig-zagging path (for 0.08 < Γ < 1) (V) helical path (for 1 < Γ < 4) (VI) early transition to chaos and (VII) chaotic regime. Regime IV occurs only for light particles (Γ < 1), whereas Regime V occurs only for heavy particles (Γ > 1). Fast Fourier Transform (FFT) analysis characterized the presence of a bimodal frequency similar to that exhibited by flow past an isolated stationary bluff body.