scholarly journals A nonlinear small-deformation theory for transient droplet electrohydrodynamics

2016 ◽  
Vol 810 ◽  
pp. 225-253 ◽  
Author(s):  
Debasish Das ◽  
David Saintillan
Keyword(s):  
Deformation Theory ◽  
Evolution Equations ◽  
Liquid Droplet ◽  
Small Deformation ◽  
Theoretical Models ◽  
Element Formulation ◽  
Charge Relaxation ◽  
Surface Charge Distribution ◽  
Leaky Dielectric Model ◽  
Electric Multipoles

The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher–Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of Taylor (Proc. R. Soc. Lond. A, vol. 291, 1966, pp. 159–166), there have been numerous computational and theoretical studies to predict the deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel small-deformation theory accurate to second order in electric capillary number $O(Ca_{E}^{2})$ for the complete Melcher–Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary element formulation and with existing experimental data in the small-deformation regime.

scholarly journals Mechanics of moving defects in growing sheets: 3-d, small deformation theory

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Amit Acharya ◽  
Shankar C. Venkataramani
Keyword(s):  
Deformation Theory ◽  
Small Deformation

Dynamic Analysis of Plates with Cut-Out Carrying Concentrated and Distributed Mass

2020 ◽  
Vol 162 (A3) ◽  
Author(s):  
S Pal ◽  
S Haldar ◽  
K Kalita
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Formulation ◽  
Plate Bending ◽  
Mass Lumping ◽  
First Order ◽  
Side Ratio ◽  
Isotropic Plates

An isoparametric plate bending element with nine nodes is used in this paper for dynamic analysis of isotropic cut-out plate having concentrated and uniformly distributed mass on the plate. The Mindlin’s first-order shear deformation theory (FSDT) is used in the present finite element formulation. Two proportionate mass lumping schemes are used. The effect of rotary inertia is included in one of the mass lumping schemes in the present element formulation. Dynamic analysis of rectangular isotropic plates with cut-out having different side ratio, thickness ratio and boundary condition is analysed using a finite element method. The present results are compared with the published results. Some new results on isotropic plates with cut-out having different side ratio, ratio of side-to-thickness of the plate, different position and size of cut-out in plates subjected to transversely concentrated and distributed mass are presented.

scholarly journals Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations

2017 ◽  
Vol 829 ◽  
pp. 127-152 ◽  
Author(s):  
Debasish Das ◽  
David Saintillan
Keyword(s):  
Numerical Simulations ◽  
Electric Fields ◽  
Small Deformation ◽  
Dielectric Liquid ◽  
Uniform Electric Field ◽  
Liquid Drops ◽  
Wide Range ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric

Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviours contingent on field strength and material properties. These phenomena are best described by the Melcher–Taylor leaky dielectric model, which hypothesizes charge accumulation on the drop–fluid interface and prescribes a balance between charge relaxation, the jump in ohmic currents from the bulk and charge convection by the interfacial fluid flow. Most previous numerical simulations based on this model have either neglected interfacial charge convection or restricted themselves to axisymmetric drops. In this work, we develop a three-dimensional boundary element method for the complete leaky dielectric model to systematically study the deformation and dynamics of liquid drops in electric fields. The inclusion of charge convection in our simulations permits us to investigate drops in the Quincke regime, in which experiments have demonstrated a symmetry-breaking bifurcation leading to steady electrorotation. Our simulation results show excellent agreement with existing experimental data and small-deformation theories.

Constitutive Modeling of Polymer Films From Viscoelasticity to Viscoplasticity

1998 ◽  
Vol 120 (2) ◽  
pp. 145-149 ◽  
Author(s):  
Z. Qian ◽  
M. Lu ◽  
S. Liu
Keyword(s):  
Polymer Films ◽  
Constitutive Modeling ◽  
Evolution Equations ◽  
Small Deformation ◽  
Back Stress ◽  
Deformation Mechanisms ◽  
Master Curves ◽  
Model Predictions ◽  
Polycarbonate Film ◽  
Good Agreement

A unified constitutive model for polymer films is proposed with viscoelastic characterization at small deformation and viscoplastic characterization at large deformation based on molecular chain deformation mechanisms. The evolution equations and the temperature dependence of drag stress and back stress are established from molecular network theories in this paper. The material constants are then determined by master curves and a consistent procedure. A good agreement between the experimental data of polycarbonate film tests and model predictions is achieved.

Modeling Damage Evolution in Friction Stir Welding Process

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Youliang He ◽  
Paul R. Dawson ◽  
Donald E. Boyce
Keyword(s):  
Friction Stir Welding ◽  
Void Growth ◽  
Evolution Equations ◽  
Volume Fraction ◽  
Welding Process ◽  
Three Dimensions ◽  
Element Formulation ◽  
Operational Parameters ◽  
Friction Stir ◽  
Welding Processes

The evolution of voids (damage) in friction stir welding processes was simulated using a void growth model that incorporates viscoplastic flow and strain hardening of incompressible materials during plastic deformation. The void growth rate is expressed as a function of the void volume fraction, the effective deformation rate, and the ratio of the mean stress to the strength of the material. A steady-state Eulerian finite element formulation was employed to calculate the flow and thermal fields in three dimensions, and the evolution of the strength and damage was evaluated by integrating the evolution equations along the streamlines obtained in the Eulerian configuration. The distribution of internal voids within the material was qualitatively compared with experimental results, and a good agreement was observed in terms of the spatial location of voids. The effects of pin geometry and operational parameters such as tool rotational and travel speeds on the evolution of damage were also examined.

Droplet deformation in dispersions with unequal viscosities and zero interfacial tension

2001 ◽  
Vol 426 ◽  
pp. 199-228 ◽  
Author(s):  
ERIC D. WETZEL ◽  
CHARLES L. TUCKER
Keyword(s):  
Experimental Data ◽  
Velocity Field ◽  
Interfacial Tension ◽  
Deformation Theory ◽  
Small Deformation ◽  
Droplet Deformation ◽  
Special Cases ◽  
Linear Velocity Field ◽  
Small Deformations ◽  
Jeffery’S Equation

An analytical model is presented for the deformation of an ellipsoidal Newtonian droplet, suspended in another Newtonian fluid with different viscosity and zero interfacial tension. The theory is exact for any linear velocity field, and is not limited to small deformations. It encompasses some well-known special cases, such as Jeffery's equation for solid axisymmetric particles and Taylor's small-deformation theory for droplets. Example calculations exhibit droplet stretching, reorientation, and tumbling, and provide a reasonable match to available experimental data on transient and steady droplet shapes. The corresponding rheological theory for dilute dispersions is also derived, in a form that explicitly includes the effects of microstructure on dispersion rheology.

Small deformation theory for two leaky dielectric drops in a uniform electric field

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190517
Author(s):  
Michael Zabarankin
Keyword(s):  
Electric Field ◽  
Deformation Theory ◽  
Small Deformation ◽  
Dielectric Constants ◽  
Dynamics Simulation ◽  
Uniform Electric Field ◽  
Fluid Viscosity ◽  
Ambient Fluid ◽  
Drop Dynamics ◽  
Leaky Dielectric

A small deformation theory for two non-identical spherical drops freely suspended in an ambient fluid and subjected to a uniform electric field is presented. The three phases are assumed to be leaky dielectric (slightly conducting) viscous incompressible fluids and the nonlinear effects of inertia and surface charge convection are neglected. The deformed shapes of the drops are linearized with respect to the electric capillary number that characterizes the balance between the electric stress and the surface tension. When the two drops are sufficiently far apart, their deformed shapes are predicted by Taylor’s small deformation theory—depending on Taylor’s discriminating function, the drops may become prolate, oblate or remain spherical. When the two drops get closer to each other, in addition to becoming prolate/oblate, they start translating and developing an egg shape. (Since there is no net charge, the centre of mass of the two drops remains stationary.) The extent of each of these ‘modes’ of deformation depends on the distance between the drops’ centres and on drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities. The predictions of the small deformation theory for two drops perfectly agree with the existing results of two-drop dynamics simulation based on a boundary-integral equation approach. Moreover, while previous works observed only three types of behaviour for two identical drops—the drops may either become prolate or oblate and move towards each other or become prolate and move away from each other—the small deformation theory predicts that non-identical drops may, in fact, become oblate and move away from each other when the drop-to-ambient fluid conductivity ratios are reciprocal and the drop-to-ambient fluid viscosity ratios are sufficiently large. The presented theory also readily yields an analytical insight into the interplay among different modes of drop deformation and can be used to guide the selection of the phases’ electromechanical properties for two-drop dynamics simulations.

DYNAMIC ANALYSIS OF PLATES WITH CUT-OUT CARRYING CONCENTRATED AND DISTRIBUTED MASS

2021 ◽  
Vol 162 (A3) ◽  
Author(s):  
S Pal ◽  
S Haldar ◽  
K Kalita
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Formulation ◽  
Plate Bending ◽  
Mass Lumping ◽  
First Order ◽  
Side Ratio ◽  
Isotropic Plates

An isoparametric plate bending element with nine nodes is used in this paper for dynamic analysis of isotropic cut-out plate having concentrated and uniformly distributed mass on the plate. The Mindlin’s first-order shear deformation theory (FSDT) is used in the present finite element formulation. Two proportionate mass lumping schemes are used. The effect of rotary inertia is included in one of the mass lumping schemes in the present element formulation. Dynamic analysis of rectangular isotropic plates with cut-out having different side ratio, thickness ratio and boundary condition is analysed using a finite element method. The present results are compared with the published results. Some new results on isotropic plates with cut-out having different side ratio, ratio of side-to-thickness of the plate, different position and size of cut-out in plates subjected to transversely concentrated and distributed mass are presented.

scholarly journals A new approach for the fracture grouting pressure in soil mass

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878643
Author(s):  
Zhi-bin Wang ◽  
Jin-feng Zou ◽  
Hai Yang
Keyword(s):  
Large Deformation ◽  
Failure Criterion ◽  
Deformation Theory ◽  
Small Deformation ◽  
Soil Mass ◽  
Parameter Analysis ◽  
Strength Failure ◽  
Grouting Pressure ◽  
Fracture Grouting ◽  
Coulomb Failure Criterion

This study focuses on analytical solutions of the fracture grouting pressure. Based on the cavity expansion and fracture grouting mechanism, the small deformation in the elastic zone, large deformation in the plastic zone, and non-associated flow rules are assumed. The solutions of the fracture grouting pressure based on the Unified Strength failure criterion, spatial mobilized plane criterion, Mohr–Coulomb failure criterion, and modified Cambridge model (MMC) are proposed for the large-deformation and small-deformation assumptions, respectively. A parameter analysis was conducted to analyze the differences between large-deformation and small-deformation theories. A comparison of the local test data with theoretical results reveals that the Cambridge model is more suitable for weakly consolidated soil and that the Mohr–Coulomb theory is suitable for over-consolidated soil. For all yield criteria in the study, the analysis indicates that the large-deformation theory has more reliable results than the small-deformation theory. The results in this study can direct the design and operation of fracture grouting.

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