scholarly journals Bridge expansion after coalescence of two droplets in air: Inertial regime

2021 ◽  
Vol 33 (6) ◽  
pp. 062112
Author(s):  
Véronique Chireux ◽  
Philippe Tordjeman ◽  
Frédéric Risso
Keyword(s):  
Inertial Regime

Optimized design of obstacle sequences for microfluidic mixing in an inertial regime

Lab on a Chip ◽  
2021 ◽  
Vol 21 (20) ◽  
pp. 3910-3923
Author(s):  
Matteo Antognoli ◽  
Daniel Stoecklein ◽  
Chiara Galletti ◽  
Elisabetta Brunazzi ◽  
Dino Di Carlo
Keyword(s):  
Optimized Design ◽  
Fast Method ◽  
Microfluidic Mixing ◽  
Passive Mixing ◽  
Contact Surfaces ◽  
Inertial Regime

A fast method for designing optimal sequences of passive mixing units is provided for inertial flows. Intense mixing is achieved through highly-controlled stretching of the fluid contact surfaces.

scholarly journals Constitutive relations for compressible granular flow in the inertial regime

2019 ◽  
Vol 874 ◽  
pp. 926-951 ◽  
Author(s):  
D. G. Schaeffer ◽  
T. Barker ◽  
D. Tsuji ◽  
P. Gremaud ◽  
M. Shearer ◽  
...  
Keyword(s):  
Steady State ◽  
Granular Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Practical Interest ◽  
Time Dependent ◽  
Direct Result ◽  
Wide Range ◽  
Inertial Regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology that does not suffer from such defects is proposed. In the framework of compressible $I$-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.

scholarly journals Fluid Dynamics of Ballistic Strategies in Nematocyst Firing

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 20 ◽  
Author(s):  
Christina Hamlet ◽  
Wanda Strychalski ◽  
Laura Miller
Keyword(s):  
Immersed Boundary Method ◽  
Short Distance ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Immersed Boundary ◽  
Small Scale ◽  
Viscous Damping ◽  
Final Velocity ◽  
Inertial Regime ◽  
Surrounding Fluid

Nematocysts are stinging organelles used by members of the phylum Cnidaria (e.g., jellyfish, anemones, hydrozoans) for a variety of important functions including capturing prey and defense. Nematocysts are the fastest-known accelerating structures in the animal world. The small scale (microns) coupled with rapid acceleration (in excess of 5 million g) present significant challenges in imaging that prevent detailed descriptions of their kinematics. The immersed boundary method was used to numerically simulate the dynamics of a barb-like structure accelerating a short distance across Reynolds numbers ranging from 0.9–900 towards a passive elastic target in two dimensions. Results indicate that acceleration followed by coasting at lower Reynolds numbers is not sufficient for a nematocyst to reach its target. The nematocyst’s barb-like projectile requires high accelerations in order to transition to the inertial regime and overcome the viscous damping effects normally encountered at small cellular scales. The longer the barb is in the inertial regime, the higher the final velocity of the projectile when it touches its target. We find the size of the target prey does not dramatically affect the barb’s approach for large enough values of the Reynolds number, however longer barbs are able to accelerate a larger amount of surrounding fluid, which in turn allows the barb to remain in the inertial regime for a longer period of time. Since the final velocity is proportional to the force available for piercing the membrane of the prey, high accelerations that allow the system to persist in the inertial regime have implications for the nematocyst’s ability to puncture surfaces such as cellular membranes or even crustacean cuticle.

scholarly journals Shear Alfvén Wave Perpendicular Propagation from the Kinetic to the Inertial Regime

2004 ◽  
Vol 93 (10) ◽  
Author(s):  
Stephen Vincena ◽  
Walter Gekelman ◽  
James Maggs
Keyword(s):  
Alfven Wave ◽  
Inertial Regime

Granular shear flows at the elastic limit

2002 ◽  
Vol 465 ◽  
pp. 261-291 ◽  
Author(s):  
CHARLES S. CAMPBELL
Keyword(s):  
Stress Reduction ◽  
Particle Surface ◽  
Surface Friction ◽  
Internal Force ◽  
Force Chains ◽  
Rheological Parameter ◽  
Nonlinear Behaviour ◽  
Static Regime ◽  
Computer Simulation Studies ◽  
Inertial Regime

This paper describes computer simulation studies of granular materials under dense conditions where particles are in persistent contact with their neighbours and the elasticity of the material becomes an important rheological parameter. There are two regimes at this limit, one for which the stresses scale with both elastic and inertial properties (called the elastic–inertial regime), and a non-inertial quasi-static regime in which the stresses scale purely elastically (elastic–quasi-static). In these elastic regimes, the forces are generated by internal force chains. Reducing the concentration slightly causes a transition from an elastic to a purely inertial behaviour. This transition occurs so abruptly that a 2% concentration reduction can be accompanied by nearly three orders of magnitude of stress reduction. This indicates that granular flows near this limit are prone to instabilities such as those commonly observed in shear cells. Unexpectedly, there is no path between inertial (rapid) flow and quasi-static flow by varying the shear rate at a fixed concentration; only by reducing the concentration can one cause a transition from quasi-static to inertial flow. The solid concentrations at which this transition occurs as well as the magnitude of the stresses in the elastic regimes are strong functions of the particle surface friction, because the surface friction strongly affects the strength of the force chains. A parametric analysis of the elastic regime generated flowmaps showing the various regimes that might be realized in practice. Many common materials such as sand require such large shear rates to reach the elastic–inertial regime that it is unattainable for all practical purposes; such materials will demonstrate either an elastic–quasi-static behaviour or a pure inertial behaviour depending on the concentration – with many orders of magnitude of stress change between them. Finally, the effects of nonlinear contacts are investigated and an appropriate scaling is proposed that accounts for the nonlinear behaviour in the elastic–quasi-static regime.

A non-local rheology for dense granular flows

2009 ◽  
Vol 367 (1909) ◽  
pp. 5091-5107 ◽  
Author(s):  
Olivier Pouliquen ◽  
Yoel Forterre
Keyword(s):  
Granular Flows ◽  
Constitutive Law ◽  
Local Theory ◽  
Plane Shear ◽  
Static Regime ◽  
Entire Flow ◽  
Non Local ◽  
Inclined Planes ◽  
Inertial Regime ◽  
Dense Granular Flows

A non-local theory is proposed to model dense granular flows. The idea is to describe the rearrangements occurring when a granular material is sheared as a self-activated process. A rearrangement at one position is triggered by the stress fluctuations induced by rearrangements elsewhere in the material. Within this framework, the constitutive law, which gives the relation between the shear rate and the stress distribution, is written as an integral over the entire flow. Taking into account the finite time of local rearrangements, the model is applicable from the quasi-static regime up to the inertial regime. We have checked the prediction of the model in two different configurations, namely granular flows down inclined planes and plane shear under gravity, and we show that many of the experimental observations are predicted within the self-activated model.

scholarly journals Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study

2001 ◽  
Vol 440 ◽  
pp. 147-203 ◽  
Author(s):  
VIVIEN M. KENDON ◽  
MICHAEL E. CATES ◽  
IGNACIO PAGONABARRAGA ◽  
J.-C. DESPLAT ◽  
PETER BLADON
Keyword(s):  
Spinodal Decomposition ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Domain Size ◽  
Numerical Control ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Scaling Hypothesis ◽  
Turbulent Characteristics ◽  
Inertial Regime

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamically consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecedented range of length and time scales when expressed in reduced physical units. (These are the length and time units derived from fluid density, viscosity, and interfacial tension.) Using eight large (2563) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 [lsim ] l [lsim ] 105, 10 [lsim ] t [lsim ] 108. Our data are consistent with the dynamical scaling hypothesis that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields. Using the conventional definition of Reynolds number for this problem, Reϕ = ldl/dt, we attain values approaching 350. At Reϕ [gsim ] 100 (which requires t [gsim ] 106) we find clear evidence of Furukawa's inertial scaling (l ∼ t2/3), although the crossover from the viscous regime (l ∼ t) is both broad and late (102 [lsim ] t [lsim ] 106). Though it cannot be ruled out, we find no indication that Reϕ is self-limiting (l ∼ t1/2) at late times, as recently proposed by Grant & Elder. Detailed study of the velocity fields confirms that, for our most inertial runs, the RMS ratio of nonlinear to viscous terms in the Navier–Stokes equation, R2, is of order 10, with the fluid mixture showing incipient turbulent characteristics. However, we cannot go far enough into the inertial regime to obtain a clear length separation of domain size, Taylor microscale, and Kolmogorov scale, as would be needed to test a recent ‘extended’ scaling theory of Kendon (in which R2 is self-limiting but Reϕ not). Obtaining our results has required careful steering of several numerical control parameters so as to maintain adequate algorithmic stability, efficiency and isotropy, while eliminating unwanted residual diffusion. (We argue that the latter affects some studies in the literature which report l ∼ t2/3 for t [lsim ] 104.) We analyse the various sources of error and find them just within acceptable levels (a few percent each) in most of our datasets. To bring these under significantly better control, or to go much further into the inertial regime, would require much larger computational resources and/or a breakthrough in algorithm design.

Inertial and non-inertial focusing of a deformable capsule in a curved microchannel

2021 ◽  
Vol 929 ◽  
Author(s):  
Saman Ebrahimi ◽  
Prosenjit Bagchi
Keyword(s):  
Secondary Flow ◽  
Computational Study ◽  
Single Point ◽  
Immersed Boundary ◽  
Central Plane ◽  
Immersed Boundary Methods ◽  
Inertial Focusing ◽  
Stream Migration ◽  
Interior Face ◽  
Inertial Regime

A computational study is presented on cross-stream migration and focusing of deformable capsules in curved microchannels of square and rectangular sections under inertial and non-inertial regimes. The numerical methodology is based on immersed boundary methods for fluid–structure coupling, a finite-volume-based flow solver and finite-element method for capsule deformation. Different focusing behaviours in the two regimes are predicted that arise due to the interplay of inertia, deformation, altered shear gradient, streamline curvature effect and secondary flow. In the non-inertial regime, a single-point focusing occurs on the central plane, and at a radial location between the interior face (i.e. face with highest curvature) of the channel and the location of zero shear. The focusing position is nearly independent of capsule deformability (represented by the capillary number, $Ca$ ). A two-step migration is observed that is comprised of a faster radial migration, followed by a slower migration toward the centre plane. The focusing location progressively moves further toward the interior face with increasing curvature and width, but decreasing height. In the inertial regime, single-point focusing is observed near the interior face for channel Reynolds number $Re_{C}\sim {O}(1)$ , that is also highly sensitive to $Re_{C}$ and $Ca$ , and moves progressively toward the exterior face with increasing $Re_{C}$ but decreasing $Ca$ . As $Re_{C}$ increases by an order, secondary flow becomes stronger, and two focusing locations appear close to the centres of the Dean vortices. This location becomes practically independent of $Ca$ at even higher inertia. The inertial focusing positions move progressively toward the exterior face with increasing channel width and decreasing height. For wider channels, the equilibrium location is further toward the exterior face than the vortex centre.

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