A numerical study of the deformation and burst of a viscous drop in an extensional flow

1978 ◽  
Vol 89 (1) ◽  
pp. 191-200 ◽  
Author(s):  
J. M. Rallison ◽  
A. Acrivos
Keyword(s):  
Numerical Study ◽  
Extensional Flow ◽  
Small Deformation ◽  
Surface Velocity ◽  
Deformation Analysis ◽  
Slender Body Theory ◽  
Spherical Drop ◽  
Viscous Drop ◽  
Freely Suspended ◽  
Body Theory

We study the deformation and conditions for breakup of a liquid drop of viscosity λμ freely suspended in another liquid of viscosity μ with which it is immiscible and which is being sheared. The problem at zero Reynolds number is formulated exactly as an integral equation for the unknown surface velocity, which is shown to reduce to a particularly simple form when Δ = 1. This equation is then solved numerically, for the case in which the impressed shear is a radially symmetric extensional flow, by an improved version of the technique used, for Δ = 0, by Youngren & Acrivos (1976) so that we model the time-dependent distortion of an initially spherical drop. It is shown that, for a given Δ, a steady shape is attained only if the dimensionless group Ω ≡4πGμa/γ lies below a critical value Ωc(Δ), where G refers to the strength of the shear field, a is the radius of the initial spherical drop and γ is the interfacial tension. On the other hand, when Ω > Ωc the drop extends indefinitely along its long axis. The numerical results for Δ = 0·3, 0·5, 1, 2, 10 and 100 are in good agreement with the predictions of the small deformation analysis by Taylor (1932) and Barthès-Biesel & Acrivos (1973) and, at the smaller Δ, with those of slender-body theory (Taylor 1964; Acrivos & Lo 1978).

Tip streaming from slender drops in a nonlinear extensional flow

1984 ◽  
Vol 144 ◽  
pp. 281-295 ◽  
Author(s):  
J. D. Sherwood
Keyword(s):  
Steady State ◽  
Extensional Flow ◽  
Axisymmetric Flow ◽  
Rayleigh Instability ◽  
Slender Body Theory ◽  
Viscous Drops ◽  
Roll Mill ◽  
Viscous Drop ◽  
Axis Of Symmetry ◽  
Body Theory

The deformation of inviscid and slightly viscous drops is studied using slender-body theory. The imposed axisymmetric flow is a combination of a linear extensional flow, with velocity uz = G1 z along the axis of symmetry, together with a cubic flow uz = G3z3. When G3/G1 is sufficiently small the viscous drop breaks in a manner similar to that described by Acrivos & Lo (1978). For larger G3 > 0 the drop breaks by a rapid growth at its end. Steady-state experiments in a 4-roll mill show the ejection of a column of liquid from the tip of the drop, though this is probably caused by a change in the pressure gradient rather than the mechanism described above. The ejected column then breaks into droplets via the Rayleigh instability. It is hypothesized that one or other of these mechanisms corresponds to tip streaming as observed by Taylor (1934).

The constitutive equation for a dilute emulsion

1970 ◽  
Vol 44 (1) ◽  
pp. 65-78 ◽  
Author(s):  
N. A. Frankel ◽  
Andreas Acrivos
Keyword(s):  
Constitutive Equation ◽  
Numerical Solutions ◽  
Extensional Flow ◽  
Small Deformation ◽  
Order Theory ◽  
Droplet Surface ◽  
Time Dependent ◽  
Deformation Analysis ◽  
First Order Theory ◽  
Freely Suspended

A constitutive equation for dilute emulsions is developed by considering the deformations, assumed infinitesimal, of a small droplet freely suspended in a time-dependent shearing flow. This equation is non-linear in the kinematic variables and gives rise to ‘fluid memory’ effects attributable to the droplet surface dynamics. Furthermore, it has the same form as the corresponding expression for a dilute suspension of Hookean elastic spheres (Goddard & Miller 1967), and reduces to a relation previously proposed by Schowalter, Chaffey & Brenner (1968) when time-dependent effects become small.Numerical solutions are also presented for the case of a small bubble in a steady extensional flow for the purpose of estimating the range of validity of the small deformation analysis. It is shown that, unlike the drag of a bubble which, in creeping motion, is known to be relatively insensitive to its exact shape, the macroscopic stress field in an emulsion is not well described by the present analysis unless the shapes of the deformed bubbles agree closely with those given by the first-order theory. Thus, the present rheological equation should prove of value in a qualitative rather than a quantitative sense.

A numerical study of the rheological properties of suspensions of rigid, non-Brownian fibres

1996 ◽  
Vol 329 ◽  
pp. 155-186 ◽  
Author(s):  
Michael B. Mackaplow ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Integral Equations ◽  
Numerical Study ◽  
Problem Formulation ◽  
Viscosity Data ◽  
Slender Body Theory ◽  
Aspect Ratios ◽  
Wide Range ◽  
Orientation Distributions ◽  
Theological Properties ◽  
Body Theory

Using techniques developed in our previous publication (Mackaplow et al. 1994), we complete a comprehensive set of numerical simulations of the volume-averaged stress tensor in a suspension of rigid, non-Brownian slender fibres at zero Reynolds number. In our problem formulation, we use slender-body theory to develop a set of integral equations to describe the interfibre hydrodynamic interactions at all orders. These integral equations are solved for a large number of interacting fibres in a periodically extended box. The simulations thus developed are an accurate representation of the suspensions at concentrations up to and including the semidilute regime. Thus, large changes in the suspensions properties can be obtained. The Theological properties of suspensions with concentrations ranging from the dilute regime, through the dilute/semi-dilute transition, and into the semi-dilute regime, are surprisingly well predicted by a dilute theory that takes into account two-body interactions. The accuracy of our simulations is verified by their ability to reproduce published suspension extensional and shear viscosity data for a variety of fibre aspect ratios and orientation distributions, as well as a wide range of suspension concentrations.

Ambient Supercavities of Slender Bodies of Revolution

1986 ◽  
Vol 30 (03) ◽  
pp. 215-219
Author(s):  
William S. Vorus
Keyword(s):  
Cavitation Number ◽  
Slender Body ◽  
Surface Velocity ◽  
Body Of Revolution ◽  
Cavity Pressure ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Specific Analysis ◽  
Slender Bodies ◽  
Body Theory

Slender-body theory is applied in an analysis of the flow about the general supercavitating streamlined body of revolution. The formulation is specialized to the case of ambient cavity pressure (zero cavitation number) for the specific analysis conducted. Numerical procedures are outlined. The methodology is demonstrated in calculating the cavity shapes, surface velocity distributions, and cavity form drag coefficients for three idealized bodies. These are the convex paraboloid, the conical frustrum, and the concave paraboloid. Characteristic differences in the flows in each of the cases are discussed.

A Numerical Study on Squat of a Wigley Hull

2011 ◽  
Author(s):  
Mahmoud Alidadi ◽  
Sander Calisal
Keyword(s):  
Boundary Element Method ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Study ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Slender Body Theory ◽  
Flow Potential ◽  
Wigley Hull ◽  
Body Theory

A numerical study is conducted to calculate the squat for a wigley hull. An approach based on slender body theory is used to convert the three dimensional ship problem into a series of two dimensional problems in cross sections from bow to stern (solved sequentially in time). A boundary element method is used to compute the flow potential at every cross section. The ship squat is calculated from the pressure integration over the hull. Numerical results for the Wigley hull is presented and compared with the experimental results.

scholarly journals Elastohydrodynamical instabilities of active filaments, arrays and carpets analyzed using slender body theory

2020 ◽  
Author(s):  
Ashok S. Sangani ◽  
Arvind Gopinath
Keyword(s):  
Critical Force ◽  
Slender Body ◽  
Critical Parameters ◽  
Neutral Stability ◽  
Slender Body Theory ◽  
Follower Forces ◽  
Freely Suspended ◽  
Filament Spacing ◽  
The Stability ◽  
Body Theory

ABSTRACTThe rhythmic motions and wave-like planar oscillations in filamentous soft structures are ubiquitous in biology. Inspired by these, recent work has focused on the creation of synthetic colloid-based active mimics that can be used to move, transport cargo, and generate fluid flows. Underlying the functionality of these mimics is the coupling between elasticity, geometry, dissipation due to the fluid, and active force or moment generated by the system. Here, we use slender body theory to analyze the linear stability of a subset of these - active elastic filaments, filament arrays and filament carpets - animated by follower forces. Follower forces can be external or internal forces that always act along the filament contour. The application of slender body theory enables the accurate inclusion of hydrodynamic effects, screening due to boundaries, and interactions between filaments. We first study the stability of fixed and freely suspended sphere-filament assemblies, calculate neutral stability curves separating stable oscillatory states from stable straight states, and quantify the frequency of emergent oscillations. When shadowing effects due to the physical presence of the spherical boundary are taken into account, the results from the slender body theory differ from that obtained using local resistivity theory. Next, we examine the onset of instabilities in a small cluster of filaments attached to a wall and examine how the critical force for onset of instability and the frequency of sustained oscillations depend on the number of filaments and the spacing between the filaments. Our results emphasize the role of hydrodynamic interactions in driving the system towards perfectly in-phase or perfectly out of phase responses depending on the nature of the instability. Specifically, the first bifurcation corresponds to filaments oscillating in-phase with each other. We then extend our analysis to filamentous (line) array and (square) carpets of filaments and investigate the variation of the critical parameters for the onset of oscillations and the frequency of oscillations on the inter-filament spacing. The square carpet also produces a uniform flow at infinity and we determine the ratio of the mean-squared flow at infinity to the energy input by active forces. We conclude by analyzing the bending and buckling instabilities of a straight passive filament attached to a wall and placed in a viscous stagnant flow - a problem related to the growth of biofilms, and also to mechanosensing in passive cilia and microvilli. Taken together, our results provide the foundation for more detailed non-linear analyses of spatiotemporal patterns in active filament systems.

Experimental studies of the deformation of a synthetic capsule in extensional flow

1993 ◽  
Vol 250 ◽  
pp. 587-608 ◽  
Author(s):  
K. S. Chang ◽  
W. L. Olbricht
Keyword(s):  
Elastic Modulus ◽  
Large Strain ◽  
Extensional Flow ◽  
Experimental Studies ◽  
Small Deformation ◽  
Polymeric Membrane ◽  
Roll Mill ◽  
Independent Technique ◽  
Freely Suspended ◽  
Flow Experiments

Experiments are described to study the motion and deformation of a synthetic, liquid-filled capsule that is freely suspended in hyperbolic extensional flow. The capsule is a composite particle consisting of a viscous liquid drop surrounded by a thin polymeric membrane. The method used to fabricate capsules suitable for macroscopic flow experiments is described. The deformation of the capsule is measured as a function of strain rate for an extensional flow generated in a four-roll mill. The data agree well with results from small-deformation theory developed by Barthes-Biesel and co-workers, provided the deformation of the capsule is not too large. Using the theory to correlate the experimental data produces an estimate for the elastic modulus of the membrane that agrees reasonably well with the elastic modulus obtained by an independent technique. However, for sufficiently large strain rates, the membrane exhibits strain hardening and a permanent change in its structure, both of which are reflected in the shape of the capsule.

scholarly journals Nutritional and Rheological Features of Lentil Protein Isolate for Yoghurt-Like Application

Foods ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 1692
Author(s):  
Theresa Boeck ◽  
Emanuele Zannini ◽  
Aylin W. Sahin ◽  
Juergen Bez ◽  
Elke K. Arendt
Keyword(s):  
Laser Scanning ◽  
Base Material ◽  
Small Deformation ◽  
Protein Isolate ◽  
Protein Supplementation ◽  
Water Holding Capacity ◽  
Laser Scanning Microscopy ◽  
Confocal Laser ◽  
Deformation Analysis ◽  
Water Holding

The substitution of animal protein with proteins of plant origin is a viable way to decrease the negative impact caused by animal husbandry on the environment. Pulse consumption has been widely promoted as a nutritious contribution to protein supplementation. In this study, an emulsion of lentil (Lens culinaris) protein isolate is fermented with lactic acid bacteria (LAB) to manufacture a yoghurt alternative and the techno-functional properties compared to a dairy- and a soy-based product with similar protein contents. The yoghurt-like products are subjected to large and small deformation analysis, quantification of fermentable oligosaccharides, disaccharides, monosaccharides and polyols (FODMAP), water holding capacity tests, protein profile analysis and the gel structure is visualised by confocal laser scanning microscopy (CLSM). The lentil yoghurt alternative shows good water holding capacity, high firmness and consistency values in large deformation analysis, with cohesiveness and viscosity not significantly different from that of dairy yoghurt. The high gel strength and rigidity of the lentil yoghurt gels measured by small deformation analysis is well-reflected in the dense protein matrix in the CLSM graphs. FODMAP content of the lentil yoghurt is very low, making it suitable for consumption by irritable bowel syndrome (IBS) patients. Our results show that lentil protein isolate is an excellent base material for producing a plant-based yoghurt alternative.

Sign in / Sign up

Export Citation Format

Share Document