Publications

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A bubble in an acoustic field experiences a net 'Bjerknes' force from the nonlinear coupling of its radial oscillations with the oscillating buoyancy force. It is typically assumed that the bubble's net terminal velocity can be found by considering a spherical bubble with the imposed 'Bjerknes stresses'. We have analyzed the motion of such a bubble using a rigorous perturbation approach and found that one must include a term involving an effective mass flux through the bubble that arises from the time average of the second-order nonlinear terms in the kinematic boundary condition. The importance of this term is governed by the dimensionless parameter {alpha} = R{sup 2} {phi}/R{sup 2} {phi} {nu}.-{nu}, where R is the bubble radius, {phi} is the driving frequency, and {nu} is the liquid kinematic viscosity. If {alpha} is large, this term is unimportant, but if {alpha} is small, this term is the dominant factor in determining the terminal velocity.

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Simulations are in excellent agreement with experiments: structure - Matzke, shear modulus - Princen and Kiss E = 3.30 {sigma}/R{sub 32} = 5.32/(1 + p) {sigma}/(V){sup 1/2}, G {approx} 0.155 E = 0.512 {sigma}/R{sub 32}. IPP theory captures dependence of cell geometry on V and F. Future challenges are: simulating simple shearing flow is very expensive because of frequent topological transitions. Random wet foams require very large simulations.

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A series of experiments has been performed to allow observation of the foaming process and the collection of temperature, rise rate, and microstructural data. Microfocus video is used in conjunction with particle image velocimetry (PIV) to elucidate the boundary condition at the wall. Rheology, reaction kinetics and density measurements complement the flow visualization. X-ray computed tomography (CT) is used to examine the cured foams to determine density gradients. These data provide input to a continuum level finite element model of the blowing process.

Many weapons components (e.g. firing sets) are encapsulated with blown foams. Foam is a strong lightweight material--good compromise between conflicting needs of structural stability and electronic function. Current foaming processes can lead to unacceptable voids, property variations, cracking, and slipped schedules which is a long-standing issue. Predicting the process is not currently possible because the material is polymerizing and multiphase with changing microstructure. The goals of this project is: (1) Produce uniform encapsulant consistently and improve processability; (2) Eliminate metering issues/voids; (3) Lower residual stresses, exotherm to protect electronics; and (4) Maintain desired properties--lightweight, strong, no delamination/cracking, and ease of removal. The summary of achievements in the first year are: (1) Developed patentable chemical foaming chemistry - TA; (2) Developed persistent non-curing foam for systematic evaluation of fundamental physics of foams--Initial testing of non-curing foam shows that surfactants very important; (3) Identified foam stability strategy using a stacked reaction scheme; (4) Developed foam rheology methodologies and shear apparatuses--Began testing candidates for shear stability; (5) Began development of computational model; and (6) Development of methodology and collection of property measurements/boundary conditions for input to computational model.

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The cell structure and rheology of gas-liquid foams confined between parallel plates depend on the ratio H/R, where H is the plate spacing and R is the (equivalent spherical) bubble radius. We consider ordered three-dimensional foams that consist of 1-3 layers of bubbles. In the 'dry' limit, where the gas fraction is unity, one confined layer is composed of hexagonal cylinders; two layers contain Fejes Toth cells; and three or more layers are modeled as Kelvin cells sandwiched between Fejes Toth cells. We also consider wet foams where all of the liquid is assumed to be located in either conventional Plateau borders or wall Plateau borders adjacent to the plates. The Surface Evolver is used to calculate the foam structure and stress as a function of H/R, which enables us to evaluate elastic behavior. A relationship between the two-dimensional structure at the wall and bubble size has application to foam characterization.

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This report documents the results for the FY07 ASC Integrated Codes Level 2 Milestone number 2354. The description for this milestone is, 'Demonstrate level set free surface tracking capabilities in ARIA to simulate the dynamics of the formation and time evolution of a weld pool in laser welding applications for neutron generator production'. The specialized boundary conditions and material properties for the laser welding application were implemented and verified by comparison with existing, two-dimensional applications. Analyses of stationary spot welds and traveling line welds were performed and the accuracy of the three-dimensional (3D) level set algorithm is assessed by comparison with 3D moving mesh calculations.

As part of an effort to reduce costs and improve quality control in encapsulation and potting processes the Technology Initiative Project ''Defect Free Manufacturing and Assembly'' has completed a computational modeling study of flows representative of those seen in these processes. Flow solutions are obtained using a coupled, finite-element-based, numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. In addition, two commercially available codes, ProCAST and MOLDFLOW, are also used on geometries representing encapsulation processes at the Kansas City Plant. Visual observations of the flow in several geometries are recorded in the laboratory and compared to the models. Wetting properties for the materials in these experiments are measured using a unique flowthrough goniometer.

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The properties of solid foams depend on their structure, which usually evolves in the fluid state as gas bubbles expand to form polyhedral cells. The characteristic feature of foam structure-randomly packed cells of different sizes and shapes-is examined in this article by considering soap froth. This material can be modeled as a network of minimal surfaces that divide space into polyhedral cells. The cell-level geometry of random soap froth is calculated with Brakke's Surface Evolver software. The distribution of cell volumes ranges from monodisperse to highly polydisperse. Topological and geometric properties, such as surface area and edge length, of the entire foam and individual cells, are discussed. The shape of struts in solid foams is related to Plateau borders in liquid foams and calculated for different volume fractions of material. The models of soap froth are used as templates to produce finite element models of open-cell foams. Three-dimensional images of open-cell foams obtained with x-ray microtomography allow virtual reconstruction of skeletal structures that compare well with the Surface Evolver simulations of soap-froth geometry.

The microrheology of dry soap foams subjected to large, quasistatic, simple shearing deformations is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by calculating foam structures that minimize total surface area at each value of strain. The minimal surfaces are computed with the Surface Evolver program developed by Brakke. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V{sup 1/3} where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new foam topology associated with each stable solution branch results from a cascade of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization.