Viscoacoustic squeeze-film force on a rigid disk undergoing small axial oscillations

This paper investigates the air flow induced by a rigid circular disk or piston vibrating harmonically along its axis of symmetry in the immediate vicinity of a parallel surface. Previous attempts to characterize these so-called ‘squeeze-film’ systems largely relied on simplifications afforded by neglecting either fluid acceleration or viscous forces inside the thin enclosed gas layer. The present viscoacoustic analysis employs the asymptotic limit of small vibration amplitudes to investigate the flow by systematic reduction of the Navier–Stokes equations in two distinct flow regions, namely, the inner gaseous film where streamlines are nearly parallel to the confining walls and the near-edge region of non-slender flow that features gas exchange with the surrounding stagnant atmosphere. The flow in the gaseous film depends on the relevant Stokes number, defined as the ratio of the characteristic viscous time across the film to the characteristic oscillation time, and on a compressibility parameter, defined as the square of the ratio of the acoustic time for radial pressure equilibration to the oscillation time. A Strouhal number based on the local residence time emerges as an additional governing parameter for the near-edge region, which is incompressible at leading order. The method of matched asymptotic expansions is used to describe the solution in both regions, across which the time-averaged pressure exhibits comparable variations that give opposing contributions to the resulting time-averaged force experienced by the disk or piston. A diagram structured with the Stokes number and compressibility parameter as coordinates reveals that this steady squeeze-film force, typically repulsive for small values of the Stokes number, alternates to attraction across a critical separation contour in the parametric domain that exists for all Strouhal numbers. This analysis provides, for the first time, a unifying viscoacoustic theory of axisymmetric squeeze films, which yields a reduced parametric description for the time-averaged repulsion/attraction force that is potentially useful in applications including non-contact fluid bearings and robot locomotion.

Using VOF Slip Velocity to Improve Productivity of Planing Hull CFD Simulations

Use of Computational fluid dynamics (CFD) tools is becoming common practice in the analysis of high speed craft. These numerical tools are of great value, since they can provide high-fidelity insight into performance of various designs by modelling non-linear effects due to viscous forces and turbulence. However, CFD tools are often seen as computationally expensive and prohibitive in a design environment. One of the main issues that impacts the use of CFD tools is numerical ventilation, when air is artificially entrained beneath the hull while using the Volume of Fluid (VOF) scheme to model the free surface. To overcome this issue, traditionally, very fine grids are requested near the surface of the hull to resolve the flow. In this paper, it will be illustrated how the use of an algebraic VOF slip velocity, in conjunction with a tight overset model and adaptive mesh refinement prevent the issue of numerical ventilation while simultaneously using a more computationally efficient mesh that produces accurate results in calm water resistance calculations. A verification and validation process comparing the VOF slip velocity method against experimental data for a known hull was conducted. Computational cost and accuracy associated with VOF slip velocity is discussed. The methodology is then applied to a stepped hull and comparisons between towing tank experiments and simulation results are looked at.

Kinematics of the viscous filament during the droplet breakup in air

The dripping regime in the vicinity of droplet breakup is analyzed concerning the evolution of the filament’s neck and its corresponding thinning velocity. Three flow regimes are observed as the relative time decreases: (i) a monotonous increase of the neck’s thinning velocity, where inertia and capillarity are balanced, (ii) a transition region characterized by the equilibrium between inertia, capillarity, and viscous forces, where the thinning velocity varies non-monotonically with the relative time and (iii) the final pinch-off regime, where velocity decreases or oscillates around a constant value. Based on the correlation between experimental data and numerics, the distribution of the zeta - coefficient (defined as the non-dimensional second invariant of the velocity gradient) on the droplet’s profile is used to quantify the ratio between elongation and rotation of the fluid at the interface. The regions dominated by extension, where pure elongation is located at zeta = 1 , are determined. One main result of this study is the confirmation that distribution of the zeta - coefficient is a relevant parameter to analyze and to quantify the breakup process. This result has the potential of developing novel techniques and more precise procedures in determining the interfacial rheology of viscous and complex fluids.

Stability effect of an axial magnetic field on fluid flow bifurcation between coaxial cylinders

Numerical simulations aim to investigate the bifurcation caused by swirling flow between two coaxial vertical cylinders, and the fluid layers produced by the thermal gradient. The stability of both bifurcation and fluid layers by an axial magnetic field is analyzed. The finite-volume method is used to solve the governing Navier–Stokes, temperature and potential equations. A conducting viscous fluid characterized by a small Prandtl number [Formula: see text] is placed in the gap between two coaxial cylinders. The combination of aspect ratio, [Formula: see text] and Reynolds number, [Formula: see text] for three annular gaps ([Formula: see text] and [Formula: see text]) is compared in terms of flow stability, and heat transfer rates. Without a magnetic field, the vortex breakdown takes place near the inner cylinder due to the increased pumping action of the Ekman boundary layer. Fluid layered structures are developed by the competition between buoyancy and viscous forces. The increase in the magnitude of the magnetic field retarders the onset of the oscillatory instability caused by the disappearance of the vortex breakdown and reduces the number of fluid layers. The limits in which a vortex breakdown bubble manifests and the limits of transition from the multiple fluid layers to the single fluid layer are established.

Parabolic velocity profile causes shape-selective drift of inertial ellipsoids

Understanding particle drift in suspension flows is of the highest importance in numerous engineering applications where particles need to be separated and filtered out from the suspending fluid. Commonly known drift mechanisms such as the Magnus force, Saffman force and Segré–Silberberg effect all arise only due to inertia of the fluid, with similar effects on all non-spherical particle shapes. In this work, we present a new shape-selective lateral drift mechanism, arising from particle inertia rather than fluid inertia, for ellipsoidal particles in a parabolic velocity profile. We show that the new drift is caused by an intermittent tumbling rotational motion in the local shear flow together with translational inertia of the particle, while rotational inertia is negligible. We find that the drift is maximal when particle inertial forces are of approximately the same order of magnitude as viscous forces, and that both extremely light and extremely heavy particles have negligible drift. Furthermore, since tumbling motion is not a stable rotational state for inertial oblate spheroids (nor for spheres), this new drift only applies to prolate spheroids or tri-axial ellipsoids. Finally, the drift is compared with the effect of gravity acting in the directions parallel and normal to the flow. The new drift mechanism is stronger than gravitational effects as long as gravity is less than a critical value. The critical gravity is highest (i.e. the new drift mechanism dominates over gravitationally induced drift mechanisms) when gravity acts parallel to the flow and the particles are small.

Highly motile nanoscale magnetic artificial cilia

Among the many complex bioactuators functioning at different scales, the organelle cilium represents a fundamental actuating unit in cellular biology. Producing motions at submicrometer scales, dominated by viscous forces, cilia drive a number of crucial bioprocesses in all vertebrate and many invertebrate organisms before and after their birth. Artificially mimicking motile cilia has been a long-standing challenge while inspiring the development of new materials and methods. The use of magnetic materials has been an effective approach for realizing microscopic artificial cilia; however, the physical and magnetic properties of the magnetic material constituents and fabrication processes utilized have almost exclusively only enabled the realization of highly motile artificial cilia with dimensions orders of magnitude larger than their biological counterparts. This has hindered the development and study of model systems and devices with inherent size-dependent aspects, as well as their application at submicrometer scales. In this work, we report a magnetic elastomer preparation process coupled with a tailored molding process for the successful fabrication of artificial cilia with submicrometer dimensions showing unprecedented deflection capabilities, enabling the design of artificial cilia with high motility and at sizes equal to those of their smallest biological counterparts. The reported work crosses the barrier of nanoscale motile cilia fabrication, paving the way for maximum control and manipulation of structures and processes at micro- and nanoscales.

Evolutionary divergence of anaphase spindle mechanics in nematode embryos constrained by antagnonistic pulling and viscous forces

Cells are the basic unit of biological organization, and their division is remarkably conserved across phyla. However from an evolutionary perspective, it remains unclear how much cellular parameters can diverge, without altering the basic function they sustain. We address the mechanics of asymmetric mitotic spindle positioning during the first embryonic division of six nematode species. We propose a viscoelastic model of spindle positioning and mobility that can provide a physical explanation of why in C. elegans it undergoes oscillations during elongation, whereas most others lack oscillations. To test this model, we measured the pulling forces and opposing cytoplasmic drag by a combination of laser ablation of the anaphase spindle and tracking of intracellular granules. While centrosomes of all species recoil on spindle cutting, quantitative differences correlate with the cytoplasmic viscosity. In fact, increased viscosity correlates with decreased oscillation speeds of intact spindles across species. However, the absence of oscillations despite low viscosity in some species, can only be explained by smaller pulling forces. Consequently, we find that spindle mobility across the species analyzed here is characterized by a tradeoff between cytoplasmic viscosity and pulling forces. Our work provides a framework for understanding mechanical constraints on evolutionary diversification of spindle mobility.

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

Immiscible two-phase flow of Newtonian fluids in porous media exhibits a power law relationship between flow rate and pressure drop when the pressure drop is such that the viscous forces compete with the capillary forces. When the pressure drop is large enough for the viscous forces to dominate, there is a crossover to a linear relation between flow rate and pressure drop. Different values for the exponent relating the flow rate and pressure drop in the regime where the two forces compete have been reported in different experimental and numerical studies. We investigate the power law and its exponent in immiscible steady-state two-phase flow for different pore size distributions. We measure the values of the exponent and the crossover pressure drop for different fluid saturations while changing the shape and the span of the distribution. We consider two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. In case of the capillary bundle when the pores do not interact to each other, we find that the exponent is always equal to 3/2 irrespective of the distribution type. For the dynamical pore network model on the other hand, the exponent varies continuously within a range when changing the shape of the distribution whereas the width of the distribution controls the crossover point.

Flowering in bursting bubbles with viscoelastic interfaces

The lifetime of bubbles, from formation to rupture, attracts attention because bubbles are often present in natural and industrial processes, and their geometry, drainage, coarsening, and rupture strongly affect those operations. Bubble rupture happens rapidly, and it may generate a cascade of small droplets or bubbles. Once a hole is nucleated within a bubble, it opens up with a variety of shapes and velocities depending on the liquid properties. A range of bubble rupture modes are reported in literature in which the reduction of a surface energy drives the rupture against inertial and viscous forces. The role of surface viscoelasticity of the liquid film in this colorful scenario is, however, still unknown. We found that the presence of interfacial viscoelasticity has a profound effect in the bubble bursting dynamics. Indeed, we observed different bubble bursting mechanisms upon the transition from viscous-controlled to surface viscoelasticity-controlled rupture. When this transition occurs, a bursting bubble resembling the blooming of a flower is observed. A simple modeling argument is proposed, leading to the prediction of the characteristic length scales and the number and shape of the bubble flower petals, thus paving the way for the control of liquid formulations with surface viscoelasticity as a key ingredient. These findings can have important implications in the study of bubble dynamics, with consequences for the numerous processes involving bubble rupture. Bubble flowering can indeed impact phenomena such as the spreading of nutrients in nature or the life of cells in bioreactors.