Session LJ: Bio-Fluids: General II

Recent progress on Modeling the Human Tear Film

We report on recent results in from our modeling efforts to better understand the dynamics of the human tear film. Lubrication theory is used to reduce the problem to a nonlinear one-dimensional partial differential equations governing the tear film thickness. The curvature variation of the (ellipsoidal) cornea is studied in a model problem that illustrates the influence of this aspect of the eye. Other progress will be discussed as available, including a shear thinning fluid to model tears.   

Human Tear Film Dynamics with an Overset Grid Method

We present recent progress in the understanding of the dynamics of the human tear film on the complex eye-shaped geometry. The evolution is modeled during relaxation (after a blink) using lubrication theory and the effects of viscosity, surface tension and gravity are explored. The highly nonlinear governing partial differential equation is solved on an overset grid by a method of lines coupled with finite differences. Our two-dimensional simulations, calculated in the Overture framework, recover features seen in one-dimensional simulations and mimic some experimental observations like hydraulic connectivity around the lid margins.   

The elasto-pipette: grabbing water with thin elastic sheets

Py \emph{et. al.} [1] have recently shown that the coupling between surface tension and elasticity of thin sheets can be used to induce self-assembly of flat elastic objects into three dimensional structures: \emph{capillary origami} at play. We here present the results of a combined experimental and theoretical investigation of a related system in which a thin elastic petal-shaped plate is withdrawn from the flat interface of a liquid bath. As the plate is drawn upwards, it deforms due to interfacial and hydrostatic forces, up to a point where it completely detaches from the interface. If the bending stiffness of the plate is sufficiently low, upon detachment a regime can be attained where the petal-shaped plate can fully enclose and therefore \emph{grab} a drop from the liquid bath. We propose this mechanism as a robust means by which to manipulate and transport small fluid droplets. \noindent [1] C. Py, P. Reverly, L. Doppler, J. Bico, B. Roman and C. Baroud, \emph{Phys. Rev. Lett.} \textbf{98}, 156103 (2007).   

Wetting of textured hydrophobic surfaces

Water repellency in nature and technology typically results from textured hydrophobic surfaces. The roughness elements of such surfaces typically have edges that pin the contact lines of advancing droplets. We present the results of a numerical investigation that relates the contact angle hysteresis and adhesive force to the geometrical, wetting, and elastic properties of the substrate. A number of generic surfaces are considered, including carbon nanotube forests, nano gratings, and insect cuticle. The calculated wetting properties are used to predict common observable quantities such as the critical tilt angle for drop motion.   

Flow Measurements over Embedded Cavities Modeling the Microgeometry of Bristled Shark Skin

Certain species of sharks (e.g. shortfin mako) have a skin structure that results in a bristling of their denticles (scales) during increased swimming speeds. This unique surface geometry results in the formation of a 3D array of cavities\footnote{Patent pending.} (d-type roughness geometry) within the shark skin, thus causing it to potentially act as a means of boundary layer control. In order to further understand the effectiveness of this complex geometry, ProE was used to replicate the bristled shark skin of the shortfin mako using a rapid prototyping machine. Two simplified geometries of the shark skin, including 2D transverse cavities and a 3D array of staggered cavities, were also studied. Boundary layer measurements using DPIV were obtained and compared for all three geometries. Of particular interest is the role that the riblets, on the face of the denticles, appear to play in forming an organized array of embedded vortices within the surface.   

Suppression of shocked-bubble dynamics by tissue confinement

Estimates are made of the effect of confinement by tissues on the action of small bubbles when subjected to strong pressure waves. The applications of interest are biomedical procedures involving short strong ultrasound bursts or weak shocks of the kind delivered in shock-wave lithotripsy. Confinement is anticipated to be important in suppressing mechanical injury and slowing the rate of its spread. We consider bubbles in a liquid such as blood within a small vessel in the tissue. A generalization of the Rayleigh-Plesset equation allows us to estimate the effect of the elasticity and viscosity of the surrounding tissue. Ranges of soft-tissue properties are estimated from a variety of different measurements available in the literature. Solutions suggest that elasticity is insufficient to significantly alter bubble dynamics but that viscosities from the mid-to-high range of those suggested might play a significant role in suppressing bubble action. Simulations in two space dimensions of a shocked bubble in a water-like fluid interacting with a viscous material show that the much more complicated bubble jetting dynamics in this configuration are also significantly suppressed. The dynamics of this suppression are investigated.   

Wheat field and Dominoes

Once perturbed, an alignment of identical slender elements can either oscillate around an equilibrium position and propagate waves (wheat field limit) or destabilise and propagate a shock (dominoes limit). In the wheat field limit, we show that two kinds of waves can be observed depending on the intensity of the forcing wind. In the dominoes limit we study the shape of the shock and show that its velocity only depends on the height of a domino and on the spacing between the different elements.   

Impingement of Ring Vortices on a Wall - a Comparison of Experiments and Computations

The descending disk experiments of Kubota et al. (2008) generate ring vortices that impinge upon the floor and travel outward from the disk. These vortices do not exhibit some of the complex behavior that is found in the simulations of Khalifa and Elhadidi (2007) and DeGraw and Cimbala (2006). Among the leading candidates for the differences between the simulations and the experiments is the possible presence of turbulence in the experiment that is not present in the simulations. To study this possibility, we numerically simulate the related but simpler case of an axisymmetric ring vortex impinging upon a plane wall as both a laminar and a turbulent flow. In the laminar case, the primary vortex induces separation vortices that are periodically ejected from the surface and tend to stop growth of the primary vortex. In the turbulent case, we find that while a separation vortex may develop, it tends to be smaller and no ejection takes place. We simulate a variety of cases in which we turn turbulence on or off (in the form of the $k-\epsilon$ turbulence model), and find that the ejection-type behavior is present only in the laminar solutions, while the turbulent cases typically exhibit a primary vortex that continues to grow radially. This turbulent behavior is similar to that observed by Kubota et al., and implies that their descending disk flow is at least partially turbulent.