Rheology of a dilute two-dimensional suspension of vesicles

2010 ◽  
Vol 653 ◽  
pp. 489-518 ◽  
Author(s):  
GIOVANNI GHIGLIOTTI ◽  
THIERRY BIBEN ◽  
CHAOUQI MISBAH
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Free Boundary Problems ◽  
Numerical Study ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Function Technique ◽  
Two Dimensional ◽  
Vesicle Membrane

The rheology of a dilute two-dimensional suspension of vesicles (closed bags of a lipid bilayer membrane) is studied by numerical simulations. The numerical methods used are based on the boundary integral formulation (Green's function technique) and the phase field approach, which has become a quite popular and powerful tool for the numerical study of free-boundary problems. The imposed flow is an unbounded linear shear. The goal of the present study is to elucidate the link between the rheology of vesicle suspensions and the microscopic dynamics of the constituent particles (tank-treading and tumbling motions). A comparison with emulsion rheology reveals the central role played by the membrane. In particular, at low viscosity ratio λ (defined as the viscosity of the internal fluid over that of the ambient one), the effective viscosity decreases with λ, while the opposite trend is exhibited by emulsions, according to the classical Taylor result. This fact is explained by considering the velocity field of the ambient fluid. The area-incompressibility of the vesicle membrane modifies the surrounding velocity field in a quite different manner than what a drop does. The overall numerical results in two dimensions are in reasonable agreement with the three-dimensional analytical theory derived recently in the small deformation limit (quasi-spherical shapes). The finding that the simulations in two dimensions capture the essential features of the three-dimensional rheology opens the way for extensive and large-scale simulations for semi-dilute and concentrated vesicle suspensions. We discuss some peculiar effects exhibited by the instantaneous viscosity in the tumbling regime of vesicles. Finally, the rheology is found to be relatively insensitive to shear rate.

scholarly journals Maximal heat transfer between two parallel plates

2018 ◽  
Vol 851 ◽  
Author(s):  
Shingo Motoki ◽  
Genta Kawahara ◽  
Masaki Shimizu
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Solution Branch ◽  
Search Range ◽  
Dimensional Solution

The divergence-free time-independent velocity field has been determined so as to maximise heat transfer between two parallel plates with a constant temperature difference under the constraint of fixed total enstrophy. The present variational problem is the same as that first formulated by Hassanzadeh et al. (J. Fluid Mech., vol. 751, 2014, pp. 627–662); however, the search range for optimal states has been extended to a three-dimensional velocity field. A scaling of the Nusselt number $Nu$ with the Péclet number $Pe$ (i.e., the square root of the non-dimensionalised enstrophy with thermal diffusion time scale), $Nu\sim Pe^{2/3}$, has been found in the three-dimensional optimal states, corresponding to the asymptotic scaling with the Rayleigh number $Ra$, $Nu\sim Ra^{1/2}$, expected to appear in an ultimate state, and thus to the Taylor energy dissipation law in high-Reynolds-number turbulence. At $Pe\sim 10^{0}$, a two-dimensional array of large-scale convection rolls provides maximal heat transfer. A three-dimensional optimal solution emerges from bifurcation on the two-dimensional solution branch at $Pe\sim 10^{1}$, and the three-dimensional solution branch has been tracked up to $Pe\sim 10^{4}$ (corresponding to $Ra\approx 2.7\times 10^{6}$). At $Pe\gtrsim 10^{3}$, the optimised velocity fields consist of convection cells with hierarchical self-similar vortical structures, and the temperature fields exhibit a logarithmic-like mean profile near the walls.

scholarly journals Stability of three-dimensional columnar convection in a porous medium

2017 ◽  
Vol 829 ◽  
pp. 89-111 ◽  
Author(s):  
Duncan R. Hewitt ◽  
John R. Lister
Keyword(s):  
Porous Medium ◽  
Aspect Ratio ◽  
Large Scale ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Base Flow ◽  
Apparent Difference ◽  
Exchange Flow ◽  
Two Dimensional ◽  
The Difference

The stability of steady convective exchange flow with a rectangular planform in an unbounded three-dimensional porous medium is explored. The base flow comprises a balance between vertical advection with amplitude $A$ in interleaving rectangular columns with aspect ratio $\unicode[STIX]{x1D709}\leqslant 1$ and horizontal diffusion between the columns. Columnar flow with a square planform ($\unicode[STIX]{x1D709}=1$) is found to be weakly unstable to a large-scale perturbation of the background temperature gradient, irrespective of $A$, but to have no stronger instability on the scale of the columns. This result provides a stark contrast to two-dimensional columnar flow (Hewitt et al., J. Fluid Mech., vol. 737, 2013, pp. 205–231), which, as $A$ is increased, is increasingly unstable to a perturbation on the scale of the columnar wavelength. For rectangular planforms with $\unicode[STIX]{x1D709}<1$, a critical aspect ratio is identified, below which a perturbation on the scale of the columns is the fastest growing mode, as in two dimensions. Scalings for the growth rate and the structure of this mode are identified, and are explained by means of an asymptotic expansion in the limit $\unicode[STIX]{x1D709}\rightarrow 0$. The difference between the stabilities of two-dimensional and three-dimensional exchange flow provides a potential explanation for the apparent difference in dominant horizontal scale observed in direct numerical simulations of two-dimensional and three-dimensional statistically steady ‘Rayleigh–Darcy’ convection at high Rayleigh numbers.

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

scholarly journals Numerical study of the reconnection process between magnetic cloud and heliospheric current sheet

2018 ◽  
Vol 619 ◽  
pp. A82
Author(s):  
Man Zhang ◽  
Yu Fen Zhou ◽  
Xue Shang Feng ◽  
Bo Li ◽  
Ming Xiong
Keyword(s):  
Magnetic Reconnection ◽  
Current Sheet ◽  
Dynamic Process ◽  
Large Scale ◽  
Magnetic Cloud ◽  
Numerical Study ◽  
Three Dimensional ◽  
Heliospheric Current Sheet ◽  
Reconnection Process ◽  
Magnetic Filed

In this paper, we have used a three-dimensional numerical magnetohydrodynamics model to study the reconnection process between magnetic cloud and heliospheric current sheet. Within a steady-state heliospheric model that gives a reasonable large-scale structure of the solar wind near solar minimum, we injected a spherical plasmoid to mimic a magnetic cloud. When the magnetic cloud moves to the heliospheric current sheet, the dynamic process causes the current sheet to become gradually thinner and the magnetic reconnection begin. The numerical simulation can reproduce the basic characteristics of the magnetic reconnection, such as the correlated/anticorrelated signatures in V and B passing a reconnection exhaust. Depending on the initial magnetic helicity of the cloud, magnetic reconnection occurs at points along the boundary of the two systems where antiparallel field lines are forced together. We find the magnetic filed and velocity in the MC have a effect on the reconnection rate, and the magnitude of velocity can also effect the beginning time of reconnection. These results are helpful in understanding and identifying the dynamic process occurring between the magnetic cloud and the heliospheric current sheet.

Flow Characteristics in a Three-Dimensional Rectangular Channel With a Pair of Ribs Placed Symmetrically at the Channel Walls

2000 ◽  
Author(s):  
M. Singh ◽  
P. K. Panigrahi ◽  
G. Biswas
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Complex Flow ◽  
Energy Equations

Abstract A numerical study of rib augmented cooling of turbine blades is reported in this paper. The time-dependent velocity field around a pair of symmetrically placed ribs on the walls of a three-dimensional rectangular channel was studied by use of a modified version of Marker-And-Cell algorithm to solve the unsteady incompressible Navier-Stokes and energy equations. The flow structures are presented with the help of instantaneous velocity vector and vorticity fields, FFT and time averaged and rms values of components of velocity. The spanwise averaged Nusselt number is found to increase at the locations of reattachment. The numerical results are compared with available numerical and experimental results. The presence of ribs leads to complex flow fields with regions of flow separation before and after the ribs. Each interruption in the flow field due to the surface mounted rib enables the velocity distribution to be more homogeneous and a new boundary layer starts developing downstream of the rib. The heat transfer is primarily enhanced due to the decrease in the thermal resistance owing to the thinner boundary layers on the interrupted surfaces. Another reason for heat transfer enhancement can be attributed to the mixing induced by large-scale structures present downstream of the separation point.

scholarly journals The Two Dimensional Representation of Three Dimensional Interferometer Measurements

1979 ◽  
Vol 49 ◽  
pp. 19-26
Author(s):  
R.H. Frater
Keyword(s):  
Three Dimensional ◽  
General Purpose ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
General Purpose Computer ◽  
Efficient Processing ◽  
Purpose Computer

SummaryA convolution technique for the reduction of three dimensional interferometer measurements to two dimensions is described. With the addition of relatively simple hardware to a general purpose computer the technique allows fast, efficient processing of three dimensional data.

scholarly journals A numerical study of the interaction between two ejecta in the interplanetary medium: one- and two-dimensional hydrodynamic simulations

2004 ◽  
Vol 22 (10) ◽  
pp. 3741-3749 ◽  
Author(s):  
A. Gonzalez-Esparza ◽  
A. Santillán ◽  
J. Ferrer
Keyword(s):  
Hydrodynamic Model ◽  
Physical Mechanism ◽  
Interplanetary Medium ◽  
Numerical Study ◽  
Two Dimensions ◽  
Magnetic Clouds ◽  
The Sun ◽  
Two Dimensional ◽  
Hydrodynamic Simulations

Abstract. We studied the heliospheric evolution in one and two dimensions of the interaction between two ejecta-like disturbances beyond the critical point: a faster ejecta 2 overtaking a previously launched slower ejecta 1. The study is based on a hydrodynamic model using the ZEUS-3-D code. This model can be applied to those cases where the interaction occurs far away from the Sun and there is no merging (magnetic reconnection) between the two ejecta. The simulation shows that when the faster ejecta 2 overtakes ejecta 1 there is an interchange of momentum between the two ejecta, where the leading ejecta 1 accelerates and the tracking ejecta 2 decelerates. Both ejecta tend to arrive at 1AU having similar speeds, but with the front of ejecta 1 propagating faster than the front of ejecta 2. The momentum is transferred from ejecta 2 to ejecta 1 when the shock initially driven by ejecta 2 passes through ejecta 1. Eventually the two shock waves driven by the two ejecta merge together into a single stronger shock. The 2-D simulation shows that the evolution of the interaction can be very complex and there are very different signatures of the same event at different viewing angles; however, the transferring of momentum between the two ejecta follows the same physical mechanism described above. These results are in qualitative agreement with in-situ plasma observations of "multiple magnetic clouds" detected at 1AU.

Potential Flow Field Generated by Downstream Moving Bars and Propagated on a Turbine Blade at Low Reynolds Number

2011 ◽  
Author(s):  
Ve´ronique Penin ◽  
Pascale Kulisa ◽  
Franc¸ois Bario
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Study ◽  
Three Dimensional ◽  
Potential Effect ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Wake Interaction ◽  
Rotor Stator Interaction ◽  
The Stability

During the last few decades, the size and weight of turbo-machinery have been continuously reduced. However, by decreasing the distance between rows, rotor-stator interaction is strengthened. Two interactions now have the same magnitude: wake interaction and potential effect. Studying this effect is essential to understand rotor-stator interactions. Indeed, this phenomenon influences the whole flow, including the boundary layer of the upstream and downstream blades, ergo the stability of the flow and the efficiency of the machine. A large scale turbine cascade followed by a specially designed rotating cylinder system is used. Synchronised velocity LDA measurements on the vane profile show the flow and boundary layer behavior due to the moving bars. To help the general understanding and to corroborate our experimental results, numerical investigations are carried out with an unsteady three dimensional Navier-Stokes code. Moreover, the numerical study informs about the potential disturbance to the whole flow of the cascade.

scholarly journals Three-Dimensional Response of the Supported-Deep Excavation System: Case Study of a Large Scale Underground Metro Station

Geosciences ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 76
Author(s):  
Ashraf Hefny ◽  
Mohamed Ezzat Al-Atroush ◽  
Mai Abualkhair ◽  
Mariam Juma Alnuaimi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Two Dimensional ◽  
Deep Excavation ◽  
Metro Station ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The complexities and the economic computational infeasibility associated in some cases, with three-dimensional finite element models, has imposed a motive for many investigators to accept numerical modeling simplification solutions such as assuming two-dimensional (2D) plane strain conditions in simulation of several supported-deep excavation problems, especially for cases with a relatively high aspect ratio in plan dimensions. In this research, a two-dimensional finite element model was established to simulate the behavior of the supporting system of a large-scale deep excavation utilized in the construction of an underground metro station Rod El Farrag project (Egypt). The essential geotechnical engineering properties of soil layers were calculated using results of in-situ and laboratory tests and empirical correlations with SPT-N values. On the other hand, a three-dimensional finite element model was established with the same parameters adopted in the two-dimensional model. Sufficient sensitivity numerical analyses were performed to make the three-dimensional finite element model economically feasible. Results of the two-dimensional model were compared with those obtained from the field measurements and the three-dimensional numerical model. The comparison results showed that 3D high stiffening at the primary walls’ corners and also at the locations of cross walls has a significant effect on both the lateral wall deformations and the neighboring soil vertical settlement.

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