scholarly journals Faraday instability on a sphere: numerical simulation

2019 ◽  
Vol 870 ◽  
pp. 433-459 ◽  
Author(s):  
A. Ebo-Adou ◽  
L. S. Tuckerman ◽  
S. Shin ◽  
J. Chergui ◽  
D. Juric
Keyword(s):  
Body Force ◽  
Three Dimensional ◽  
Capillary Waves ◽  
Platonic Solids ◽  
Interface Motion ◽  
Spherical Drop ◽  
Low Viscosity ◽  
Faraday Instability ◽  
Viscous Drop ◽  
Time Periodic

We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the interface motion of the parametrically forced oscillating viscous drop, as well as the velocity field inside and outside the drop. Forcing frequencies are chosen so as to excite spherical harmonic wavenumbers ranging from 1 to 6. We excite gravity waves for wavenumbers 1 and 2 and observe translational and oblate–prolate oscillation, respectively. For wavenumbers 3 to 6, we excite capillary waves and observe patterns analogous to the Platonic solids. For low viscosity, both subharmonic and harmonic responses are accessible. The patterns arising in each case are interpreted in the context of the theory of pattern formation with spherical symmetry.

Faraday waves on a cylindrical fluid filament – generalised equation and simulations

2018 ◽  
Vol 857 ◽  
pp. 80-110 ◽  
Author(s):  
Sagar Patankar ◽  
Palas Kumar Farsoiya ◽  
Ratul Dasgupta
Keyword(s):  
Linear Theory ◽  
Body Force ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mathieu Equation ◽  
Faraday Waves ◽  
Stability Chart ◽  
Fluid Filament ◽  
The Stability ◽  
Time Periodic

We perform linear stability analysis of an interface separating two immiscible, inviscid, quiescent fluids subject to a time-periodic body force. In a generalised, orthogonal coordinate system, the time-dependent amplitude of interfacial perturbations, in the form of standing waves, is shown to be governed by a generalised Mathieu equation. For zero forcing, the Mathieu equation reduces to a (generalised) simple harmonic oscillator equation. The generalised Mathieu equation is shown to govern Faraday waves on four time-periodic base states. We use this equation to demonstrate that Faraday waves and instabilities can arise on an axially unbounded, cylindrical capillary fluid filament subject to radial, time-periodic body force. The stability chart for solutions to the Mathieu equation is obtained through numerical Floquet analysis. For small values of perturbation and forcing amplitude, results obtained from direct numerical simulations (DNS) of the incompressible Euler equation (with surface tension) show very good agreement with theoretical predictions. Linear theory predicts that unstable Rayleigh–Plateau modes can be stabilised through forcing. This prediction is borne out by DNS results at early times. Nonlinearity produces higher wavenumbers, some of which can be linearly unstable due to forcing and thus eventually destabilise the filament. We study axisymmetric as well as three-dimensional perturbations through DNS. For large forcing amplitude, localised sheet-like structures emanate from the filament, suffering subsequent fragmentation and breakup. Systematic parametric studies are conducted in a non-dimensional space of five parameters and comparison with linear theory is provided in each case. Our generalised analysis provides a framework for understanding free and (parametrically) forced capillary oscillations on quiescent base states of varying geometrical configurations.

Some quantitative applications of vascular corrosion casting

1992 ◽  
Vol 50 (1) ◽  
pp. 738-739
Author(s):  
Fred E. Hossler
Keyword(s):  
Blood Vessels ◽  
Nuclear Orientation ◽  
Three Dimensional ◽  
Surrounding Tissue ◽  
Confocal Laser ◽  
Corrosion Casting ◽  
Venous Valve ◽  
Casting Technique ◽  
Low Viscosity ◽  
Quantitative Measurements

Preparation of replicas of the complex arrangement of blood vessels in various organs and tissues has been accomplished by infusing low viscosity resins into the vasculature. Subsequent removal of the surrounding tissue by maceration leaves a model of the intricate three-dimensional anatomy of the blood vessels of the tissue not obtainable by any other procedure. When applied with care, the vascular corrosion casting technique can reveal fine details of the microvasculature including endothelial nuclear orientation and distribution (Fig. 1), locations of arteriolar sphincters (Fig. 2), venous valve anatomy (Fig. 3), and vessel size, density, and branching patterns. Because casts faithfully replicate tissue vasculature, they can be used for quantitative measurements of that vasculature. The purpose of this report is to summarize and highlight some quantitative applications of vascular corrosion casting. In each example, casts were prepared by infusing Mercox, a methyl-methacrylate resin, and macerating the tissue with 20% KOH. Casts were either mounted for conventional scanning electron microscopy, or sliced for viewing with a confocal laser microscope.

An isotropic elasto-damage-plastic micromechanical framework of innovative pothole patching materials featuring high-toughness, low-viscosity nanomolecular resin

2021 ◽  
pp. 105678952110286
Author(s):  
H Zhang ◽  
J Woody Ju ◽  
WL Zhu ◽  
KY Yuan
Keyword(s):  
Strain Energy ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Companion Paper ◽  
Computational Algorithms ◽  
Mechanical Behaviors ◽  
High Toughness ◽  
Low Viscosity ◽  
Innovative Materials ◽  
Continuum Thermodynamic

In a recent companion paper, a three-dimensional isotropic elastic micromechanical framework was developed to predict the mechanical behaviors of the innovative asphalt patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD), under the splitting tension test (ASTM D6931). By taking advantage of the previously proposed isotropic elastic-damage framework and considering the plastic behaviors of asphalt mastic, a class of elasto-damage-plastic model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation to predict the behaviors of the innovative materials more accurately. Specifically, the governing damage evolution is characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence; the plastic flow is introduced by means of an additive split of the stress tensor. Corresponding computational algorithms are implemented into three-dimensional finite elements numerical simulations, and the outcomes are systemically compared with suitably designed experimental results.

scholarly journals Thermomechanical modelling of the Scandinavian ice sheet: implications for ice-stream formation

1999 ◽  
Vol 28 ◽  
pp. 83-89 ◽  
Author(s):  
A. J. Payne ◽  
D.J. Baldwin
Keyword(s):  
Three Dimensional ◽  
Ice Sheet ◽  
Ice Streams ◽  
Ice Flow ◽  
Low Viscosity ◽  
Ice Stream ◽  
Scandinavian Ice Sheet ◽  
The Baltic ◽  
Stream Formation ◽  
Initial Results

AbstractThis work attempts to explain the fan-like landform assemblages observed in satellite images of the area covered by the former Scandinavian ice sheet (SIS). These assemblages have been interpreted as evidence of large ice streams within the SIS. If this interpretation is correct, then it calls into doubt current theories on the formation of ice streams. These theories regard soft sediment and topographic troughs as being the key determinants of ice-stream location. Neither can be used to explain the existence of ice streams on the flat, hard-rock area of the Baltic Shield. Initial results from a three-dimensional, thermomechanical ice-sheet model indicate that interactions between ice flow, form and temperature can create patterns similar to those mentioned above. The model uses a realistic, 20 km resolution gridded topography and a simple parameterization of accumulation and ablation. It produces patterns of maximum ice-sheet extent, which are similar to those reconstructed from the area’s glacial geomorphology. Flow in the maximum, equilibrium ice sheet is dominated by wedges of warm, low-viscosity, fast-flowing ice. These are separated by areas of cold, slow-flowing ice. This patterning appears to develop spontaneously as the modelled ice sheet grows.

Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm

1999 ◽  
Vol 391 ◽  
pp. 249-292 ◽  
Author(s):  
ALEXANDER Z. ZINCHENKO ◽  
MICHAEL A. ROTHER ◽  
ROBERT H. DAVIS
Keyword(s):  
Three Dimensional ◽  
Adaptive Mesh ◽  
Boundary Integral ◽  
Small Surface ◽  
Low Viscosity ◽  
Primary Breakup ◽  
Dimensional Boundary ◽  
Normal Vectors ◽  
Passive Technique ◽  
Line Singularities

A three-dimensional boundary-integral algorithm for interacting deformable drops in Stokes flow is developed. The algorithm is applicable to very large deformations and extreme cases, including cusped interfaces and drops closely approaching breakup. A new, curvatureless boundary-integral formulation is used, containing only the normal vectors, which are usually much less sensitive than is the curvature to discretization errors. A proper regularization makes the method applicable to small surface separations and arbitrary λ, where λ is the ratio of the viscosities of the drop and medium. The curvatureless form eliminates the difficulty with the concentrated capillary force inherent in two-dimensional cusps and allows simulation of three-dimensional drop/bubble motions with point and line singularities, while the conventional form can only handle point singularities. A combination of the curvatureless form and a special, passive technique for adaptive mesh stabilization allows three-dimensional simulations for high aspect ratio drops closely approaching breakup, using highly stretched triangulations with fixed topology. The code is applied to study relative motion of two bubbles or drops under gravity for moderately high Bond numbers [Bscr ], when cusping and breakup are typical. The deformation-induced capture efficiency of bubbles and low-viscosity drops is calculated and found to be in reasonable agreement with available experiments of Manga & Stone (1993, 1995b). Three-dimensional breakup of the smaller drop due to the interaction with a larger one for λ=O(1) is also considered, and the algorithm is shown to accurately simulate both the primary breakup moment and the volume partition by extrapolation for moderately supercritical conditions. Calculations of the breakup efficiency suggest that breakup due to interactions is significant in a sedimenting emulsion with narrow size distribution at λ=O(1) and [Bscr ][ges ]5–10. A combined capture and breakup phenomenon, when the smaller drop starts breaking without being released from the dimple formed on the larger one, is also observed in the simulations. A general classification of possible modes of two-drop interactions for λ=O(1) is made.

The development of asymmetry and period doubling for oscillatory flow in baffled channels

1996 ◽  
Vol 328 ◽  
pp. 19-48 ◽  
Author(s):  
E. P. L. Roberts ◽  
M. R. Mackley
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Period Doubling ◽  
Progressive Increase ◽  
Newtonian Flow ◽  
Chaotic Flow ◽  
Spatially Periodic ◽  
Dimensional Simulation ◽  
Time Periodic

We report experimental and numerical observations on the way initially symmetric and time-periodic fluid oscillations in baffled channels develop in complexity. Experiments are carried out in a spatially periodic baffled channel with a sinusoidal oscillatory flow. At modest Reynolds number the observed vortex structure is symmetric and time periodic. At higher values the flow progressively becomes three-dimensional, asymmetric and aperiodic. A two-dimensional simulation of incompressible Newtonian flow is able to follow the flow pattern at modest oscillatory Reynolds number. At higher values we report the development of both asymmetry and a period-doubling cascade leading to a chaotic flow regime. A bifurcation diagram is constructed that can describe the progressive increase in complexity of the flow.

Entrainment and Transport in Idealized Three-Dimensional Gravity Current Simulation

2006 ◽  
Vol 23 (9) ◽  
pp. 1249-1269 ◽  
Author(s):  
Yu-Heng Tseng ◽  
David E. Dietrich
Keyword(s):  
Gravity Current ◽  
Vertical Mixing ◽  
Three Dimensional ◽  
Ocean Model ◽  
Numerical Dissipation ◽  
Good Convergence ◽  
Low Viscosity ◽  
Denmark Strait ◽  
Dimensional Gravity ◽  
Fine Resolution

Abstract A purely z-coordinate Dietrich/Center for Air Sea Technology (DieCAST) ocean model is applied to the Dynamics of Overflow Mixing and Entrainment (DOME) idealized bottom density current problem that is patterned after the Denmark Strait. The numerical results show that the background viscosity plays a more important role than the chosen coordinate system in the entrainment and mixing if the background viscosity is not small enough. Both higher horizontal viscosity and coarser resolution leads to slower along-slope propagation. Reducing vertical mixing parameterization also leads to slower along-slope propagation with thicker plume size vertically. The simulation gives consistent results for the moderate- and fine-resolution runs. At a very coarse grid the dense water descends more slowly and is mainly dominated by diffusion. Time-averaged downstream transport and entrainment are not very sensitive to viscosity after the flow reaches its quasi-steady status. However, more realistic eddies and flow structures are found in low-viscosity runs. The results show good convergence of the resolved flow as expected and clarify the effects of numerical dissipation/mixing on overflow modeling. Larger numerical dissipation is not required nor recommended in z-coordinate models.

scholarly journals Comparison of the internal fit of metal crowns fabricated by traditional casting, computer numerical control milling, and three-dimensional printing

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257158
Author(s):  
Wei-Ting Chou ◽  
Chuan-Chung Chuang ◽  
Yi-Bing Wang ◽  
Hsien-Chung Chiu
Keyword(s):  
3D Printing ◽  
Minimum Distance ◽  
Statistical Significance ◽  
Three Dimensional ◽  
Reference Points ◽  
Numerical Control ◽  
Maximum Distance ◽  
Cnc Milling ◽  
Low Viscosity ◽  
Internal Fit

This experimental study aimed to compare the internal fit (marginal fit and internal discrepancy) of metal crowns fabricated by traditional casting and digital methods (computer numerically controlled (CNC) milling and three-dimensional [3D] printing). Thirty standard master abutment models were fabricated using a 3D printing technique with digital software. Metal crowns were fabricated by traditional casting, CNC milling, and 3D printing. The silicon replica method was used to measure the marginal and internal fit. A thin layer of low-viscosity polyvinyl siloxane material was placed inside each crown and on the die (like a seat) until the material was set. Replicas were examined at four reference points under a microscope: the central pit (M1), cusp tip (M2), axial wall (M3), and margin (M4). The measured data were analyzed using a one-way analysis of variance (ANOVA) to verify statistical significance, which was set at p < 0.05. In the traditional casting group, the minimum distance measured was at M3 (90.68 ± 14.4 μm) and the maximum distance measured was at M1 (145.12 ± 22 μm). In the milling group, the minimum distance measured was at M3 (71.85 ± 23.69 μm) and the maximum distance measured was at M1 (108.68 ± 10.52 μm). In the 3D printing group, the minimum distance measured was at M3 (100.59 ± 9.26 μm) and the maximum distance measured was at M1 (122.33 ± 7.66 μm). The mean discrepancy for the traditional casting, CNC milling, and 3D printing groups was 120.20, 92.15, and 111.85 μm, respectively, showing significant differences (P < 0.05). All three methods of metal crown fabrication, that is, traditional casting, CNC milling, and 3D printing, had values within the clinically acceptable range. The marginal and internal fit of the crown was far superior in the CNC milling method.

Dispersion of solids in fracturing flows of yield stress fluids

2017 ◽  
Vol 830 ◽  
pp. 93-137 ◽  
Author(s):  
S. Hormozi ◽  
I. A. Frigaard
Keyword(s):  
Yield Stress ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Process Variations ◽  
Model Framework ◽  
Shear Rates ◽  
Low Viscosity ◽  
High Shear Rates ◽  
Solids Concentration

Solids dispersion is an important part of hydraulic fracturing, both in helping to understand phenomena such as tip screen-out and spreading of the pad, and in new process variations such as cyclic pumping of proppant. Whereas many frac fluids have low viscosity, e.g. slickwater, others transport proppant through increased viscosity. In this context, one method for influencing both dispersion and solids-carrying capacity is to use a yield stress fluid as the frac fluid. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able to include this range of flows, while still representing a significant simplification over fully three-dimensional computations. In relatively straight fractures and for fluids of moderate rheology, this simplifies into a one-dimensional model that predicts the solids concentration along a streamline within the fracture. We use this model to make estimates of the streamwise dispersion in various relevant scenarios. This model framework also predicts the transverse distributions of the solid volume fraction and velocity profiles as well as their evolutions along the flow part.

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