Inertial effects on the dynamics, streamline topology and interfacial stresses due to a drop in shear

2011 ◽  
Vol 683 ◽  
pp. 149-171 ◽  
Author(s):  
Rajesh Kumar Singh ◽  
Kausik Sarkar
Keyword(s):  
Reynolds Number ◽  
Viscosity Ratio ◽  
Shear Plane ◽  
Interfacial Stress ◽  
Rigid Sphere ◽  
Interfacial Stresses ◽  
Drop Shape ◽  
Flow Axis ◽  
Viscous Drop ◽  
Varying Viscosity

AbstractDeformation of a viscous drop in shear at finite inertia and the streamlines around it are numerically investigated. Inertia destroys the closed streamlines found in Stokes flow. It creates reversed streamlines and streamlines spiralling around the vorticity axis. Spiralling streamlines spiral either towards the central shear plane or away from it depending on the viscosity ratio and the inertia. The zones of open or reversed streamlines as well as streamlines spiralling towards or away from the central shear plane are delineated for varying viscosity ratio and Reynolds number. In contrast to the infinite extent of the closed Stokes streamlines around a rigid sphere in shear, the region of the spiralling streamlines in the vorticity direction both for a rigid sphere and a drop shrinks with inertia. Inertia increases deformation, and introduces oscillations in drop shape. An approximate analysis explains the scaling of oscillation frequency and damping with Reynolds and capillary numbers. The steady-state drop inclination angle with the flow axis increases with increasing Reynolds number for small Reynolds number. But it decreases at higher Reynolds number, especially for larger capillary numbers. For smaller capillary numbers, drop inclination reaches higher than $4{5}^{\ensuremath{\circ} } $ (the direction of maximum extension), critically affecting the interfacial stresses due to the drop. It changes the sign of first and second normal interfacial stress differences (and thereby these components of the effective stresses of an emulsion of such drops). Increasing viscosity ratio orients the drop towards the flow axis, which increases the critical Reynolds number above which the drop inclination reaches more than $4{5}^{\ensuremath{\circ} } $.

On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface

1990 ◽  
Vol 217 ◽  
pp. 547-573 ◽  
Author(s):  
Stergios G. Yiantsios ◽  
Robert H. Davis
Keyword(s):  
Solid Surface ◽  
Viscosity Ratio ◽  
Bond Number ◽  
Boundary Integral ◽  
Fractional Powers ◽  
Drop Shape ◽  
Wide Range ◽  
Deformable Interface ◽  
Long Time ◽  
Viscous Drop

The deformation of a viscous drop, driven by buoyancy towards a solid surface or a deformable interface, is analysed in the asymptotic limit of small Bond number, for which the deformation becomes important only when the drop is close to the solid surface or interface. Lubrication theory is used to describe the flow in the thin gap between the drop and the solid surface or interface, and boundary-integral theory is used in the fluid phases on either side of the gap. The evolution of the drop shape is traced from a relatively undeformed state until a dimple is formed and a long-time quasi-steady-state pattern is established. A wide range of drop to suspending phase viscosity ratios is examined. It is shown that a dimple is always formed, independently of the viscosity ratio, and that the long-time thinning rates take simple forms as inverse fractional powers of time.

A numerical study of the deformation and burst of a viscous drop in general shear flows

1981 ◽  
Vol 109 ◽  
pp. 465-482 ◽  
Author(s):  
J. M. Rallison
Keyword(s):  
Reynolds Number ◽  
Numerical Scheme ◽  
Numerical Study ◽  
Time Dependent ◽  
Critical Flow ◽  
Two Dimensional ◽  
Flow Rates ◽  
Drop Shape ◽  
Viscous Drop ◽  
Orthogonal Rheometer

The time-dependent deformation and burst of a viscous drop in an arbitrary shear flow at zero Reynolds number is studied. The viscosities of the drop and the suspending fluid are assumed to be equal. A numerical scheme to track the (non-axisymmetric) drop shape in time is presented, and used to investigate the deformation induced by two-dimensional shear and orthogonal rheometer flows. Steady deformations, critical flow rates and burst modes are determined, and compared with asymptotic (small and large) deformation theories, and with experiment.

Dynamics of a non-spherical microcapsule with incompressible interface in shear flow

2011 ◽  
Vol 678 ◽  
pp. 221-247 ◽  
Author(s):  
P. M. VLAHOVSKA ◽  
Y.-N. YOUNG ◽  
G. DANKER ◽  
C. MISBAH
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Viscosity Ratio ◽  
Perturbation Expansion ◽  
Shear Plane ◽  
Creeping Flow ◽  
Regular Perturbation ◽  
Cell Dynamics ◽  
Initial Shape ◽  
Flow Equations

We study the motion and deformation of a liquid capsule enclosed by a surface-incompressible membrane as a model of red blood cell dynamics in shear flow. Considering a slightly ellipsoidal initial shape, an analytical solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, area-incompressibility and resistance to bending. The theory captures the observed transition from tumbling to swinging as the shear rate increases and clarifies the effect of capsule deformability. Near the transition, intermittent behaviour (swinging periodically interrupted by a tumble) is found only if the capsule deforms in the shear plane and does not undergo stretching or compression along the vorticity direction; the intermittency disappears if deformation along the vorticity direction occurs, i.e. if the capsule ‘breathes’. We report the phase diagram of capsule motions as a function of viscosity ratio, non-sphericity and dimensionless shear rate.

Stability of Viscoelastic Channel Flow

2007 ◽  
Author(s):  
Nariman Ashrafi
Keyword(s):  
Reynolds Number ◽  
Viscosity Ratio ◽  
Weissenberg Number ◽  
Base Flow ◽  
Galerkin Projection ◽  
Large Reynolds Number ◽  
One Dimensional ◽  
Stress Effects ◽  
The Stability ◽  
The One

The nonlinear stability and bifurcation of the one-dimensional channel (Poiseuille) flow is examined for a Johnson-Segalman fluid. The velocity and stress are represented by orthonormal functions in the transverse direction to the flow. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. The stability picture is dramatically influenced by the viscosity ratio. The range of shear rate or Weissenberg number for which the base flow is unstable increases from zero as the fluid deviates from the Newtonian limit as decreases. Typically, two turning points are observed near the critical Weissenberg numbers. The transient response is heavily influenced by the level of inertia. It is found that the flow responds oscillatorily. When the Reynolds number is small, and monotonically at large Reynolds number when elastic effects are dominated by inertia.

Stable equilibrium configurations of an oblate capsule in simple shear flow

2016 ◽  
Vol 791 ◽  
pp. 738-757 ◽  
Author(s):  
C. Dupont ◽  
F. Delahaye ◽  
D. Barthès-Biesel ◽  
A.-V. Salsac
Keyword(s):  
Aspect Ratio ◽  
Shear Flow ◽  
Simple Shear ◽  
Capillary Number ◽  
Stable Equilibrium ◽  
Viscosity Ratio ◽  
Shear Plane ◽  
Initial Orientation ◽  
Simple Shear Flow ◽  
Mechanical Equilibrium

The objective of the paper is to determine the stable mechanical equilibrium states of an oblate capsule subjected to a simple shear flow, by positioning its revolution axis initially off the shear plane. We consider an oblate capsule with a strain-hardening membrane and investigate the influence of the initial orientation, capsule aspect ratio$a/b$, viscosity ratio${\it\lambda}$between the internal and external fluids and the capillary number$Ca$which compares the viscous to the elastic forces. A numerical model coupling the finite element and boundary integral methods is used to solve the three-dimensional fluid–structure interaction problem. For any initial orientation, the capsule converges towards the same mechanical equilibrium state, which is only a function of the capillary number and viscosity ratio. For$a/b=0.5$, only four regimes are stable when${\it\lambda}=1$: tumbling and swinging in the low and medium$Ca$range ($Ca\lesssim 1$), regimes for which the capsule revolution axis is contained within the shear plane; then wobbling during which the capsule experiences precession around the vorticity axis; and finally rolling along the vorticity axis at high capillary numbers. When${\it\lambda}$is increased, the tumbling-to-swinging transition occurs for higher$Ca$; the wobbling regime takes place at lower$Ca$values and within a narrower$Ca$range. For${\it\lambda}\gtrsim 3$, the swinging regime completely disappears, which indicates that the stable equilibrium states are mainly the tumbling and rolling regimes at higher viscosity ratios. We finally show that the$Ca$–${\it\lambda}$phase diagram is qualitatively similar for higher aspect ratio. Only the$Ca$-range over which wobbling is stable increases with$a/b$, restricting the stability ranges of in- and out-of-plane motions, although this phenomenon is mainly visible for viscosity ratios larger than 1.

Bi-Layered Model of Interfacial Thermal Stresses with the Effect of Different Temperatures in the Layers

2011 ◽  
Vol 87 ◽  
pp. 63-70 ◽  
Author(s):  
Sujan Debnath ◽  
Muhammad Ekhlasur Rahman ◽  
Woldemichael Dereje Engida ◽  
M. V. V. Murthy ◽  
K.N. Seetharamu
Keyword(s):  
Thermal Stresses ◽  
Physical Design ◽  
Temperature Gradients ◽  
Interfacial Stress ◽  
Stress Model ◽  
Interfacial Stresses ◽  
Linear Temperature ◽  
Layered Model ◽  
Die Attach ◽  
Different Temperatures

An interfacial shearing and peeling stress model is proposed to account for different uniform temperatures and thickness wise linear temperature gradients in the layers. This upgraded model can be viewed as a more generic form to determine interfacial stresses under different temperature conditions in a bi-layered assembly. The selected shearing and peeling stress results are presented for the case of die and die attach as commonly seen in electronic packaging. The obtained results can be useful in interfacial stress evaluations and physical design of bi-material assemblies, which are used in microelectronics and photonic applications.

Interfacial Stresses of a Coated Square Hole Induced by a Remote Uniform Heat Flow

2020 ◽  
Vol 12 (06) ◽  
pp. 2050063
Author(s):  
S. C. Tseng ◽  
C. K. Chao ◽  
F. M. Chen
Keyword(s):  
Heat Flow ◽  
Shape Factor ◽  
Coating Layer ◽  
Infinite Plate ◽  
Interfacial Stress ◽  
Graphical Form ◽  
Shear Stresses ◽  
Interfacial Stresses ◽  
Uniform Heat ◽  
Square Hole

This paper presents an analytical solution of a coated square hole embedded in an isotropic infinite plate under a remote uniform heat flow. Based on conformal mapping, analytic continuation theorem and the alternation technique, temperature and stress functions are derived in a compact series form. Results of temperature contours and interfacial stresses are validated using the finite element method. The comparison indicates the high accuracy of the proposed method. Numerical results of both the interfacial normal and shear stresses for different properties and geometric parameters of a coated layer are provided in a graphical form. The results indicate that the interfacial stresses are highly dependent on the thermal expansion coefficient, thickness of the coating layer and shape factor of the coated square hole. In conclusion, the interfacial shear stresses exhibit a significant increase at the corners with abrupt geometrical changes, which would cause the delamination of the coating layer system. Furthermore, increasing the thickness of the coating layer and the shape factor results in a higher interfacial stress.

Interfacial stresses in reinforced concrete cantilever members strengthened with fibre-reinforced polymer laminates

2019 ◽  
Vol 23 (2) ◽  
pp. 277-288 ◽  
Author(s):  
Xue-jun He ◽  
Chao-Yang Zhou ◽  
Yi Wang
Keyword(s):  
Reinforced Concrete ◽  
Interfacial Stress ◽  
Design Parameters ◽  
Stress Concentrations ◽  
Concentrated Load ◽  
Interfacial Stresses ◽  
Simply Supported ◽  
Reinforced Polymer ◽  
Fibre Reinforced Polymer ◽  
Polymer Laminates

Fibre-reinforced polymers have been increasingly used to strengthen reinforced concrete structures. However, premature brittle debonding failures may occur at the ends of externally bonded fibre-reinforced polymer laminates due to interfacial stress concentrations caused by stiffness imbalances. Although many studies exist on fibre-reinforced polymer-strengthened simply supported beams and slabs, the interfacial stress distributions in fibre-reinforced polymer-strengthened cantilever members are very different from those in simply supported members. Based on the assumptions of linear elasticity, deformation compatibility and static equilibrium conditions, the interfacial stresses in fibre-reinforced polymer-strengthened reinforced concrete cantilever members under arbitrary linear distributed loads were analysed. In particular, closed-form solutions were obtained to calculate the interfacial stresses under either a uniformly distributed load or a single concentrated load located at the overhanging end of the cantilever member. Existing test results on cantilever slabs strengthened by carbon fibre–reinforced polymer sheets were used to verify the model. According to the parametric analysis, the maximum interfacial stresses can be reduced by decreasing the fibre-reinforced polymer thickness, increasing the fibre-reinforced polymer bonding length and increasing the adhesive layer thickness, and by using less rigid fibre-reinforced polymer laminates with high tensile strengths. These results are useful for engineers seeking to optimize strengthening design parameters and implement reliable debonding prevention measures.

Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion

1994 ◽  
Vol 277 ◽  
pp. 347-379 ◽  
Author(s):  
Eugene J. Chang ◽  
Martin R. Maxey
Keyword(s):  
Reynolds Number ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Oscillatory Flow ◽  
Reynolds Numbers ◽  
Oscillatory Motion ◽  
Rigid Sphere ◽  
Flow Conditions ◽  
Steady Streaming ◽  
Moderate Reynolds Number

A direct numerical simulation, based on spectral methods, has been used to compute the time-dependent, axisymmetric viscous flow past a rigid sphere. An investigation has been made for oscillatory flow about a zero mean for different Reynolds numbers and frequencies. The simulation has been verified for steady flow conditions, and for unsteady flow there is excellent agreement with Stokes flow theory at very low Reynolds numbers. At moderate Reynolds numbers, around 20, there is good general agreement with available experimental data for oscillatory motion. Under steady flow conditions no separation occurs at Reynolds number below 20; however in an oscillatory flow a separation bubble forms on the decelerating portion of each cycle at Reynolds numbers well below this. As the flow accelerates again the bubble detaches and decays, while the formation of a new bubble is inhibited till the flow again decelerates. Steady streaming, observed for high frequencies, is also observed at low frequencies due to the flow separation. The contribution of the pressure to the resultant force on the sphere includes a component that is well described by the usual added-mass term even when there is separation. In a companion paper the flow characteristics for constant acceleration or deceleration are reported.

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