arXiv subjects

Fridolin Okkels

Publications and source records attributed to Fridolin Okkels.

10 recordsLinked to original sources

arXiv2018

A Viscoelastic Catastrophe

We use a differential constitutive equation to model the flow of a viscoelastic flow in a cross-slot geometry, which is known to exhibit bistability above a critical flow rate. The novelty lies in two asymmetric modifications to the geometry, which causes a change in the bifurcation diagram such that one of the stable solutions becomes disconnected from the solution at low flow speeds. First we show that it is possible to mirror one of the modifications such that the system can be forced to the disconnected solution. Then we show that a slow decrease of the flow rate, can cause the system to go through a drastic change on a short time scale, also known as a catastrophe. The short time scale could lead to a precise and simple experimental measurement of the flow conditions at which the viscoelastic catastrophe occurs. Since the phenomena is intrinsically related to the extensional rheology of the fluid, we propose to exploit the phenomena for in-line extensional rheometry.

physics.flu-dyn↗

arXiv2009

Optimal homogenization of perfusion flows in microfluidic bio-reactors; a numerical study

To ensure homogeneous conditions within the complete area of perfused microfluidic bio-reactors, we develop a general design of a continuously feed bio-reactor with uniform perfusion flow. This is achieved by introducing a specific type of perfusion inlet to the reaction area. The geometry of these inlets are found using the methods of topology optimization and shape optimization. The results are compared with two different analytic models, from which a general parametric description of the design is obtained and tested numerically. Such a parametric description will generally be beneficial for the design of a broad range of microfluidic bioreactors used for e.g. cell culturing and analysis, and in feeding bio-arrays.

physics.flu-dyn↗

arXiv2009

Topology and shape optimization of induced-charge electro-osmotic micropumps

For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the topology and shape of the dielectric solid. In particular, we extend existing conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial design field. Our results show the importance of the topology and shape of the dielectric solid in ICEO systems and point to new designs of ICEO micropumps with significantly improved performance.

physics.flu-dyn↗

arXiv2006

Scaling behavior of optimally structured catalytic microfluidic reactors

In this study of catalytic microfluidic reactors we show that, when optimally structured, these reactors share underlying scaling properties. The scaling is predicted theoretically and verified numerically. Furthermore, we show how to increase the reaction rate significantly by distributing the active porous material within the reactor using a high-level implementation of topology optimization.

physics.flu-dyn↗

arXiv2006

A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow

We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier-Stokes flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes flow [Int. J. Num. Meth. Fluids 2003; 41:77--107]. We analyze the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as Femlab code in an appendix.

physics.flu-dyn↗

arXiv2005

Reexamination of Hagen-Poiseuille flow: shape-dependence of the hydraulic resistance in microchannels

We consider pressure-driven, steady state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C = P^2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.

physics.flu-dyn↗

arXiv2003

Reaction-diffusion dynamics: confrontation between theory and experiment in a microfluidic reactor

We confront, quantitatively, the theoretical description of the reaction-diffusion of a second order reaction to experiment. The reaction at work is \ca/CaGreen, and the reactor is a T-shaped microchannel, 10 $μ$m deep, 200 $μ$m wide, and 2 cm long. The experimental measurements are compared with the two-dimensional numerical simulation of the reaction-diffusion equations. We find good agreement between theory and experiment. From this study, one may propose a method of measurement of various quantities, such as the kinetic rate of the reaction, in conditions yet inaccessible to conventional methods.

physics.flu-dyn↗

arXiv2000

Temporal Structures in Shell Models

The intermittent dynamics of the turbulent GOY shell-model is characterised by a single type of burst-like structure, which moves through the shells like a front. This temporal structure is described by the dynamics of the instantaneous configuration of the shell-amplitudes revealing a approximative chaotic attractor of the dynamics.

nlin.CD↗

arXiv1998

Chaotic Behavior in Shell Models and Shell Maps

We study the chaotic behavior of the ``GOY'' shell model by measuring the variation of the maximal Lyapunov exponent with the parameter $ε$ which determines the nature of the second invariant (the generalized ``helicity'' invariant). After a Hopf bifurcation, we observe a critical point at $ε_c \sim 0.38704$ above which the maximal Lyapunov exponent grows nearly linearly. For high values of $ε$ the evolution becomes regular again which can be explained by a simple analytic argument. A model with few shells shows two transitions. To simplify the model substantially we introduce a shell map which exhibits similar properties as the``GOY'' model.

chao-dyn↗

arXiv1997

Dynamical Organization around Turbulent Bursts

The detailed dynamics around intermittency bursts is investigated in turbulent shell models. We observe that the amplitude of the high wave number velocity modes vanishes before each burst, meaning that the fixed point in zero and not the Kolmogorov fixed point determines the intermittency. The phases of the field organize during the burst, and after a burst the field oscillates back to the laminar level. We explain this behavior from the variations in the values of the dissipation and the advection around the zero fixed point.

chao-dyn↗