ALBERT

Notes: It has become evident that the float zone crystal growth method and isothermal liquid bridges may be very sensitive to the residual acceleration environment of a spacelab. Indeed, the shape equilibria show a high degree of sensitivity and, thus, even the small steady acceleration associated with the effective low gravity environment of a spacecraft cannot be ignored. Using a slender-body approximation, the problem of determining the axisymmetric response of the shape of the free surface of a cylindrical liquid column bounded by two solid regions is modeled by a 1-D system of nonlinear equations. It is found that the sensitivity of the zone shape depends on the static Bond number, B0, aspect ratio, and viscosity, as well as the amplitude and frequency of the disturbance. The general trend is an increase in tolerable residual gravity with increasing frequency. At the eigenfrequencies of the zone, however, there are dramatic deviations from this trend. At these frequencies the tolerable residual gravity level can be two orders of magnitude lower at this frequency. For the cases considered the values of B0 were taken to be 0.002 and 0.02 and the dimensionless viscosities, C=ν(ρ/γR0)1/2, used were in the range 0.001–0.01. Aspect ratios ranging from 96.3% to 82.7% of the Rayleigh limit were examined. For these cases, the frequencies associated with the lowest tolerable acceleration have been found in the 10−2–10−1 Hz range. In terms of previously recorded and predicted residual accelerations, the sensitive frequency ranges for the cases examined are 10−2–10−1 Hz and 1–10 Hz. Maximum tolerable residual gravity levels as low as 10−6 g have been calculated. The effect of viscosity is seen to increase the tolerable acceleration level for all frequencies. The equilibrium shape, as determined by the steady background acceleration, has a pronounced effect at low frequencies. A change in slenderness of the bridge markedly changes the sensitivity to residual acceleration as the Rayleigh limit is approached.

Notes: 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 Λ (=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 SSSR, Moscow, 1968)]. The stability margin represents the height of a local potential energy barrier adjacent to the well of a given stable equilibrium. Wherever a linearly stable equilibrium is nonunique equilibrium, the stability margin corresponds to the smallest among the heights of saddle points on the potential energy surface that are adjacent to the well. The saddle point that determines the stability margin is the point of emergence from the well and leads to the energy wells corresponding to other equilibria or to infinity. Unless the total energy of perturbations exceeds the stability margin for a given stable equilibrium, the liquid bridge will return to that equilibrium state. In this work we determined the stability margin in part of the stability region where axisymmetric bridges that are already unstable to small axisymmetric perturbations coexist with stable ones. The domains of existence of a variety of unstable axisymmetric bridges are constructed using previous results concerning the bifurcation structure. This enabled us to construct contours of the dimensionless stability margin within the linear stability region not only in the vicinity of the stability boundary, but also far from it. The stability margins for bridges with fixed values of the slenderness, as well as for cylindrical and catenoidal bridges, are also calculated. © 2002 American Institute of Physics.

Notes: 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. © 1999 American Institute of Physics.

Notes: The stability problem for the axisymmetric equilibrium states of an isorotating liquid bridge between equidimensional circular disks in a constant axial gravity field is considered. In particular, we examine the stability of bridges satisfying two constraints that are typical for the floating zone method used for materials purification and single crystal growth. First we consider the constraint that the relative volume of the bridge, V, is equal to 1. Here, V is the ratio of the actual bridge volume to that of a cylinder pinned to the edges of disks. For this case, the critical values of the slenderness (Λ) (ratio of the disk separation to the diameter) and of the free surface slopes (β1,β2) at both disks have been determined for a wide range of the Bond (B) and Weber (W) numbers. The second constraint is that the surface slopeβ1 at one of the disks is prescribed. The chosen values are 90° and 75° and correspond to extremes in growth angle values encountered in floating zone crystal growth. For this case, the dependencies of critical Λ and V values B and W have been calculated. In addition, both axial gravity directions are considered separately and the values of the slope angle, β2, at the other disk are also analyzed for critical states. The solution of the stability problem for any liquid bridge is discussed in detail using the case for B=W=0.1 as an example. In particular, the relationship between the general boundary of the stability region and the stability of bridges subject to the constraints outlined above is examined. © 1997 American Institute of Physics.

Notes: The stability of equilibrium configurations of a capillary liquid in a circular cylindrical container with planar ends is investigated. The liquid is under zero gravity conditions, and its wetting angle is constant over the entire solid surface. Attention is focused on the case for which the free surface consists of two disconnected pieces (connectivity components) that bound the connected liquid domain. First we outline the method used to determine critical states with disconnected free surfaces when each connectivity component is axisymmetric. Then we examine the stability of disconnected surfaces for the simple cases that arise when each connectivity component represents a closed sphere or a part of a sphere. Ten configurations were considered that represent all possible combinations of the following connectivity components: A closed sphere (that bounds a gas bubble), a spherical cap in contact with the lateral wall of a cylinder; a spherical cap in contact with a cylinder endwall, and a portion of a sphere (that does not cross the cylinder's axis of symmetry) bounded by a cylindrical wall and a flat endwall. © 2000 American Institute of Physics.

Notes: The bifurcation of the solutions of the nonlinear equilibrium problem of a weightless liquid bridge with a free surface pinned to the edges of two coaxial equidimensional circular disks is examined. The bifurcation is studied in the neighborhood of the stability boundary for axisymmetric equilibrium states with emphasis on the boundary segment corresponding to nonaxisymmetric critical perturbations. The first approximations for the shapes of the bifurcated equilibrium surfaces are obtained. The stability of the bifurcated states is then determined from the bifurcation structure. Along the maximum volume stability limit, depending on values of the system parameters, loss of stability with respect to nonaxisymmetric perturbations results in either a jump or a continuous transition to stable nonaxisymmetric shapes. The value of the slenderness at which a change in the type of transition occurs is found to be Λs=0.4946. Experimental investigation based on a neutral buoyancy technique agrees with this prediction. It shows that, for Λ〈Λs, the jump is finite and that a critical bridge undergoes a finite deformation to a stable nonaxisymmetric state. © 1997 American Institute of Physics.

Notes: A virtual variational approach is used to deduce the interfacial conditions for thermomechanical equilibrium in two-phase crystals separated by a curved interface. The interface is modeled as a Gibbsian dividing surface and the excess quantities which include the deformation gradients, entropy, and number density of components are accounted for explicitly. Conditions necessary for equilibrium are obtained for both a coherent and incoherent interface that incorporate the effects of surface stress. An example illustrating the use of these new interfacial conditions in establishing boundary conditions is given.

Notes: A virtual variational approach for deducing the conditions for thermomechanical equilibrium is extended to solid-fluid systems with curved interfaces. A surface excess energy density is introduced which depends on excess entropy, number densities of the excess constituent components, the surface deformation gradient, the surface orientation and the principal curvatures. The coupling and roles of the surface stress and the Cahn–Hoffman ξ-vector in stressed solid-fluid systems is identified. Results are used to examine the case of a solid isotropic sphere immersed in a fluid.

Notes: The effects on water status and growth of controlled cycles of water stress applied at various stages of development were studied on a semi-dwarf spring wheat (Triticum aestivum L.). The plants were grown in controlled environment chambers of the Duke University Phytetron at 24/18°C with a 12-h photo-period at about 600 μE m−2 s−1. Groups of plants were subjected to severe water stress by withholding irrigation, beginning at the 7th leaf, early anthesis, or early dough stages of development. A second cycle started 9 to 13 days after termination of the first cycle and maintained until the flag leaf water potential reached –25 bars at each of the growth stages.The lower leaves showed sign of wilting as indicated by curling in the first drying cycle at –7 bars and in the second cycle at –9 bars of leaf water potential during all stages of growth. Although these leaves recovered completely upon rewatering, onset of senescence was accelerated by three days in stressed plants. A preliminary drying cycle did not increase the ability of the plants to withstand subsequent stress because of severity of stress. Water stress of –25 bars at all three stages of growth reduced seed yield. The reduction was greater when a second stress cycle was also applied. Stress applied during early anthesis stage produced the smallest and the least number of seeds. The lack of osmotic adjustment probably was due to very rapid and severe development of water stress.

Notes: Frankliniella fusca (Hinds)] to seedling peanut (Arachis hypogaea L.) has not been documented to reduce yield and quality. However, thrips injury may be economically important when combined with another factor, such as postemergence herbicide injury. This note reports results of a field experiment in which control of tobacco thrips during an unusually dry early season greatly increased peanut seed yield and quality. 'Florunner' peanut was grown using preplant and postemergence herbicides for weed control. Treatments consisted of an untreated control and four labeled insecticides applied at planting or soon after crop emergence. Populations of adult tobacco thrips were significantly suppressed by aldicarb [2-methyl-2-(methylthio) propionaldehyde )-(methylcarbamoyl) oxime]; all insecticides significantly suppressed immature thrips. Aldicarb, the most efficacious insecticide treatment, significantly improved peanut yield by 32% and quality as determined by percentage of total sound mature kernels. All but one of the remaining insecticide treatments significantly improved seed yield, with increases ranging from 9 to 31%. Rainfall was extremely low early in the growing season, and (based on 41 yr of records at the site) drier conditions occur 10% of the time. This is a frequency great enough to matter, but low enough to make further research difficult. The observations reported here suggest that early-season moisture stress intensifies peanut yield and quality losses associated with combined injury from thrips and postemergence herbicides.