J. Iwan D. Alexander

Nano-microscale models of periosteocytic flow show differences in stresses imparted to cell body and processes.

In order to understand how local changes in mechanical environment are translated into cellular activity underlying tissue level bone adaptation, there is a need to explore fluid flow regimes at small scales such as the osteocyte. Recent developments in computational fluid dynamics (CFD) provide impetus to elucidate periosteocytic flow through development of a nano–microscale model to study local effects of fluid flow on the osteocyte cell body, which contains the cellular organelles, and on the osteocyte processes, which connect the cell to the entire cellular network distributed throughout bone tissue. For each model, fluid flow was induced via a pressure gradient and the velocity profile and wall shear stress at the cell-fluid interface were calculated using a CFD software package designed for nano/micro-electro-mechanical-systems device development. Periosteocytic flow was modeled, taking into consideration the nanoscale dimensions of the annular channels and the flow pathways of the periosteocytic flow volume, to analyze the local effects of fluid flow on the osteocyte cell body (within the lacuna) and its processes (within the canaliculi). Based on the idealized model presented in this article, the osteocyte cell body is exposed primarily to effects of hydrodynamic pressure and the cell processes (CP) are exposed primarily to fluid shear stress, with highest stress gradients at sites where the process meets the cell body and where two CP link at the gap junction. Hence, this model simulates subcellular effects of fluid flow and suggests, for the first time to our knowledge, major differences in modes of loading between the domain of the cell body and that of the cell process.

Application of the lattice Boltzmann method to two-phase Rayleigh-Benard convection with a deformable interface

The lattice Boltzmann method (LBM) is extended to include the effects of interfacial tension and its dependence on temperature and is applied to the problem of buoyancy-driven flow in a non-isothermal two-phase system. No a priori assumptions are made regarding the shape and dynamic roles of the interface. The behavior of interface is obtained as part of the solution of the lattice Boltzmann equations. A parametric study of the effects of thermally induced density change, buoyancy, surface tension variation with temperature on interface dynamics, flow regimes and heat transfer is presented.

INVESTIGATION OF VIBRATIONAL CONTROL OF CONVECTIVE FLOWS IN BRIDGMAN MELT GROWTH CONFIGURATIONS

It is generally recognized that oscillatory, or pulsatile, flow significantly alters the transfer of mass, heat and momentum in fluid systems. A numerical investigation of thermovibrational buoyancy-driven flow in differentially heated cylindrical containers is presented as part of a study of thermovibrational transport regimes in Bridgman-type systems. The formulation of a physical and mathematical model for this problem is outlined and its application to the study of investigation of thermal vibrational flows is discussed. Three types of vibration are considered: translational, circularly polarized and rotational. It is demonstrated that forced vibration can significantly affect flows that have been induced by g-jitter and selected results for the cases of longitudinal and lateral vibrations are presented.

COMBINED EFFECT OF DISK INEQUALITY AND AXIAL GRAVITY ON AXISYMMETRIC LIQUID BRIDGE STABILITY

The stability of an axisymmetric liquid bridge between unequal circular disks in an axial gravity field is examined for all possible values of the liquid volume and disk separation. The parameter defining the disk inequality is K, the ratio between the radii of the smaller and larger disks. Both axisymmetric and nonaxisymmetric perturbations are considered. The parameter space chosen to delimit the stability regions is the Λ-V plane. Here, Λ is the slenderness (ratio of the disk separation to the mean diameter, 2r0, of the two support disks), and V is the relative volume (ratio of the actual liquid volume to the volume of a cylinder with a radius equal to r0). Wide ranges of the Bond number and the ratio K are considered. Emphasis is given to previously unexplored parts of the stability boundaries. In particular, we examine the maximum volume stability limit for bridges of arbitrary Λ and the minimum volume stability limit for small Λ bridges. The maximum volume stability limit was found to have two disti...

Capillary pressure of a liquid in a layer of close-packed uniform spheres

The capillary pressure in liquid partially filling the pore space in a layer of equidimensional close-packed spheres has been calculated numerically and studied experimentally. The case of square packing when the centers of the spheres are in the same plane and lie at the corners of a square receives primary consideration for zero gravity. In the absence of gravity, the menisci shapes of a liquid that occupies some fraction of the pore space are constructed using the Surface Evolver code. The mean curvature (and, hence, the capillary pressure) of the liquid surface is calculated. The dependence of capillary pressure on the liquid volume is obtained for selected contact angles in the range 0⩽θ⩽π. The evolution of the shape of the liquid’s free surface and the capillary pressure under quasistatic infiltration and drainage can be deduced from these results. The maximum pressure difference between liquid and gas required for a meniscus passing through a pore is calculated and compared with that for hexagonal ...

Shape and stability of doubly connected axisymmetric free surfaces in a cylindrical container

The equilibrium and stability of a liquid that partially fills a cylindrical container with planar ends are examined. It is assumed that the free surface is axisymmetric and does not cross the symmetry axis of the container. Particular attention is given to the case where gravity is parallel to the cylinder’s axis, and where the free surface has one contact line on the lateral cylindrical wall and the other on one of the planar ends. The equilibrium configuration of such a surface is determined by the wetting angle, α, the Bond number, B, and the relative volume, V, of the annular region bounded by the free surface and the solid container. Shapes of stable and critical surfaces have been analyzed, and the stability regions for arbitrary Bond numbers have been obtained in the α–V plane. The shape and stability problems for a zero gravity configuration with both contact lines on the lateral wall of the cylinder are also studied. In addition, the stability of a free surface with at least one contact line coinciding with the edge formed by the lateral wall and a planar end is discussed.

Stability diagrams for disconnected capillary surfaces

Disconnected free surfaces (or interfaces) of a connected liquid volume (or liquid volumes) occur when the boundary of the liquid volume consists of two or more separate surface components Γiu200a(i=1,…,m) that correspond to liquid–gas (or liquid–liquid) interfaces. We consider disconnected surfaces for which each component Γi is axisymmetric and crosses its own symmetry axis. In most cases, the stability problem for an entire disconnected equilibrium capillary surface subject to perturbations that conserve the total liquid volume reduces to the same set of problems obtained when separately considering the stability of each Γi to perturbations that satisfy a fixed pressure constraint. For fixed pressure perturbations, the stability of a given axisymmetric Γi can be found through comparison of actual and critical values of a particular boundary parameter. For zero gravity, these critical values are found analytically. For non-zero gravity, an analytical representation of the critical values is not generally po...

The stability margin for stable weightless liquid bridges

The stability of weightless axisymmetric liquid bridge equilibrium configurations to “large” disturbances is examined by calculating the stability margin. For bridges held between coaxial equidimensional circular disks (radius R0) separated by a distance H, the stability to infinitesimal perturbations (linear stability) has been thoroughly investigated and the stability region is constructed in the (Λ,V) plane. Here, the slenderness Λu2002(=H/2R0) and the relative volume V (ratio of the actual liquid volume to that of a cylinder with radius R0 and height H) are the parameters that define the system. To assess stability with respect to finite amplitude disturbances we use a potential energy analysis based on the concepts of a potential energy well and the equilibrium stability margin introduced by Myshkis [USSR Comput. Math. Math. Phys. 5, 193 (1965); Math. Notes Acad. Sci. USSR 33, 131 (1983); Introduction to the Dynamics of a Body Containing a Liquid Under Zero-Gravity Conditions (Vychisl. Tsentr Akad. Nauk ...

Flow and distribution of fluid phases through porous plant growth media in microgravity: Progress to date

Results from plant growth experiments utilizing particulate growth media during space flight revealed difficulties associated with providing reliable reproducible gaseous and water supply to plant roots. These limitations were attributed to insufficient understanding of liquid configuration and growth media transport processes in reduced gravity. The objective of this NASA-funded research program is to develop a framework for modeling and quantitative characterization of physical processes associated with flow of wetting and non-wetting phases in particulate plant growth media in microgravity. This paper provides an overview of research plans and current status of research activities. Characterization and modeling of substrate water retention and transport properties in microgravity is key to management and control of gas and liquid fluxes within plant root zones. Modeling efforts will focus on both 1) a pore network model for describing discontinuous fluid phase transport (ganglia/blobs) and 2) a statistical distribution model describing water retention and hydraulic conductivity as functions of various pore configurations. Minimizing hydrostatic forces within porous media by using thin samples on earth may provide an approximation to microgravity conditions. In our preliminary study we have used Magnetic Resonance Imaging (MRI) to detect and track the evolution of liquid configuration and dynamics within thin slices of opaque porous media (Aquafoam with mean pore size of 50 μm). Both twoand three dimensional temporal MRI imaging has been performed in thin Aquafoam slices positioned vertically and horizontally (to simulate the effect of gravity). The wetting front exhibited percolation-type patterns and fingering. Preliminary results show that gravity dominates liquid flow even for low Bond numbers. Although the capillary forces are very strong the small hydrostatic pressure built in the initial liquid volume determines the subsequent evolution of the wetting front.

Experimental confirmation of the insensitivity of mass diffusion measurements to blockages and voids along the diffusion path

Using the real-time diffusion methodology first developed by Codastefano et al. [Rev. Sci. Instrum. 48, 1650 (1977)] we show that deviations from strictly one-dimensional transport (i.e., blockages and voids) widely cited in the literature as leading to erroneous results, have little effect on the measured diffusivity. In this methodology, radiotracer, initially located at one end of a cylindrical diffusion sample, is used as the diffusant. The sample is positioned in a concentric isothermal radiation shield with collimation bores located at defined positions along its axis. The intensity of the radiation emitted through the collimators is measured as a function of time using solid state detectors. Diffusivities are calculated from the signal difference between the detectors. These results were obtained using 114mIn radiotracer in benign indium. A 60% blockage was simulated by using a 2 mm source disk diffusing into 3 mm diameter host section. A void/bubble was simulated by inserting a 1 mm diameter by 1 ...