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Simulation of individual cells in flow
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, simulations are performed to study the motion ofindividual cells in flow, focusing on the hydrodynamics of actively swimming cells likethe self-propelling microorganisms, and of passively advected objects like the red bloodcells. In particular, we develop numerical tools to address the locomotion ofmicroswimmers in viscoelastic fluids and complex geometries, as well as the motion ofdeformable capsules in micro-fluidic flows.

For the active movement, the squirmer is used as our model microswimmer. The finiteelement method is employed to study the influence of the viscoelasticity of fluid on theperformance of locomotion. A boundary element method is implemented to study swimmingcells inside a tube. For the passive counterpart, the deformable capsule is chosen as the modelcell. An accelerated boundary integral method code is developed to solve thefluid-structure interaction, and a global spectral method is incorporated to handle theevolving cell surface and its corresponding membrane dynamics.

We study the locomotion of a neutral squirmer with anemphasis on the change of swimming kinematics, energetics, and flowdisturbance from Newtonian to viscoelastic fluid. We also examine the dynamics of differentswimming gaits resulting in different patterns of polymer deformation, as well as theirinfluence on the swimming performance. We correlate the change of swimming speed withthe extensional viscosity and that of power consumption with the phase delay of viscoelasticfluids. Moreover, we utilise the boundary element method to simulate the swimming cells in astraight and torus-like bent tube, where the tube radius is a few times the cell radius. Weinvestigate the effect of tube confinement to the swimming speed and power consumption. Weanalyse the motions of squirmers with different gaits, which significantly affect thestability of the motion. Helical trajectories are produced for a neutralsquirmer swimming, in qualitative agreement with experimental observations, which can beexplained by hydrodynamic interactions alone.

We perform simulations of a deformable capsule in micro-fluidic flows. We look atthe trajectory and deformation of a capsule through a channel/duct with a corner. Thevelocity of capsule displays an overshoot as passing around the corner, indicating apparentviscoelasticity induced by the interaction between the deformable membrane and viscousflow. A curved corner is found to deform the capsule less than the straight one. In addition, we propose a new cell sorting device based on the deformability of cells. Weintroduce carefully-designed geometric features into the flow to excite thehydrodynamic interactions between the cell and device. This interaction varies andclosely depends on the cell deformability, the resultant difference scatters the cellsonto different trajectories. Our high-fidelity computations show that the new strategy achievesa clear and robust separation of cells. We finally investigate the motion of capsule in awall-bounded oscillating shear flow, to understand the effect of physiological pulsation to thedeformation and lateral migration of cells. We observe the lateral migration velocity of a cellvaries non-monotonically with its deformability.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , xvi, 55 p.
Series
TRITA-MEK, ISSN 0348-467X
Keyword [en]
Hydrodynamic interaction, swimming microorganisms, capsule, Stokes flow, finite element method, boundary integral method, general geometry Ewald method, spectral element method, viscoelastic fluid, cellular deformation, flow cytometry, cell sorting, microrheology
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-142557ISBN: 978-91-7595-036-5 (print)OAI: oai:DiVA.org:kth-142557DiVA: diva2:703338
Public defence
2014-03-28, Sal E1, Lindstedtsvägen 3, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20140313

Available from: 2014-03-13 Created: 2014-03-06 Last updated: 2014-03-14Bibliographically approved
List of papers
1. Locomotion by tangential deformation in a polymeric fluid
Open this publication in new window or tab >>Locomotion by tangential deformation in a polymeric fluid
2011 (English)In: Physical Reivew E, ISSN 1539-3755, Vol. 83, no 1, 011901- p.Article in journal (Refereed) Published
Abstract [en]

In several biologically relevant situations, cell locomotion occurs in polymeric fluids with Weissenberg number larger than 1. Here we present results of three-dimensional numerical simulations for the steady locomotion of a self-propelled body in a model polymeric (Giesekus) fluid at low Reynolds number. Locomotion is driven by steady tangential deformation at the surface of the body (the so-called squirming motion). In the case of a spherical squirmer, we show that the swimming velocity is systematically less than that in a Newtonian fluid, with a minimum occurring for Weissenberg numbers of order 1. The rate of work done by the swimmer always goes up compared to that occurring in the Newtonian solvent alone but is always lower than the power necessary to swim in a Newtonian fluid with the same viscosity. The swimming efficiency, defined as the ratio between the rate of work necessary to pull the body at the swimming speed in the same fluid and the rate of work done by swimming, is found to always be increased in a polymeric fluid. Further analysis reveals that polymeric stresses break the Newtonian front-back symmetry in the flow profile around the body. In particular, a strong negative elastic wake is present behind the swimmer, which correlates with strong polymer stretching, and its intensity increases with Weissenberg number and viscosity contrasts. The velocity induced by the squirmer is found to decay in space faster than in a Newtonian flow, with a strong dependence on the polymer relaxation time and viscosity. Our computational results are also extended to prolate spheroidal swimmers and smaller polymer stretching are obtained for slender shapes compared to bluff swimmers. The swimmer with an aspect ratio of two is found to be the most hydrodynamically efficient.

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-30511 (URN)10.1103/PhysRevE.83.011901 (DOI)000286754100001 ()2-s2.0-78751500433 (Scopus ID)
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20110315

Available from: 2011-03-15 Created: 2011-02-28 Last updated: 2014-03-13Bibliographically approved
2. Self-propulsion in viscoelastic fluids: pushers vs. pullers
Open this publication in new window or tab >>Self-propulsion in viscoelastic fluids: pushers vs. pullers
2012 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 5, 051902- p.Article in journal (Refereed) Published
Abstract [en]

We use numerical simulations to address locomotion at zero Reynolds number in viscoelastic (Giesekus) fluids. The swimmers are assumed to be spherical, to self-propel using tangential surface deformation, and the computations are implemented using a finite element method. The emphasis of the study is on the change of the swimming kinematics, energetics, and flow disturbance from Newtonian to viscoelastic, and on the distinction between pusher and puller swimmers. In all cases, the viscoelastic swimming speed is below the Newtonian one, with a minimum obtained for intermediate values of the Weissenberg number, We. An analysis of the flow field places the origin of this swimming degradation in non-Newtonian elongational stresses. The power required for swimming is also systematically below the Newtonian power, and always a decreasing function of We. A detail energetic balance of the swimming problem points at the polymeric part of the stress as the primary We-decreasing energetic contribution, while the contributions of the work done by the swimmer from the solvent remain essentially We-independent. In addition, we observe negative values of the polymeric power density in some flow regions, indicating positive elastic work by the polymers on the fluid. The hydrodynamic efficiency, defined as the ratio of the useful to total rate of work, is always above the Newtonian case, with a maximum relative value obtained at intermediate Weissenberg numbers. Finally, the presence of polymeric stresses leads to an increase of the rate of decay of the flow velocity in the fluid, and a decrease of the magnitude of the stresslet governing the magnitude of the effective bulk stress in the fluid.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012
Keyword
Mixed Finite-Element, Hydrodynamic Interaction, Model Microorganisms, Nutrient-Uptake, Flow, Suspension, Particles, Stress, Viscosity, Rheology
National Category
Mechanical Engineering Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-96939 (URN)10.1063/1.4718446 (DOI)000304826100002 ()2-s2.0-84861980665 (Scopus ID)
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note

Updated from "Submitted" to "Published". QC 20140127

Available from: 2012-06-13 Created: 2012-06-13 Last updated: 2017-12-07Bibliographically approved
3. Low-Reynolds number swimming in a capillary tube
Open this publication in new window or tab >>Low-Reynolds number swimming in a capillary tube
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 726, 285-311 p.Article in journal (Refereed) Published
Abstract [en]

We use the boundary element method to study the low-Reynolds-number locomotion of a spherical model microorganism in a circular tube. The swimmer propels itself by tangential or normal surface motion in a tube whose radius is of the order of the swimmer size. Hydrodynamic interactions with the tube walls significantly affect the average swimming speed and power consumption of the model microorganism. In the case of swimming parallel to the tube axis, the locomotion speed is always reduced (respectively, increased) for swimmers with tangential (respectively, normal) deformation. In all cases, the rate of work necessary for swimming is increased by confinement. Swimmers with no force dipoles in the far field generally follow helical trajectories, solely induced by hydrodynamic interactions with the tube walls, and in qualitative agreement with recent experimental observations for Paramecium. Swimmers of the puller type always display stable locomotion at a location which depends on the strength of their force dipoles: swimmers with weak dipoles (small alpha) swim in the centre of the tube while those with strong dipoles (large alpha) swim near the walls. In contrast, pusher swimmers and those employing normal deformation are unstable and end up crashing into the walls of the tube. Similar dynamics is observed for swimming into a curved tube. These results could be relevant for the future design of artificial microswimmers in confined geometries.

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-96940 (URN)10.1017/jfm.2013.225 (DOI)000319736300012 ()2-s2.0-84880231544 (Scopus ID)
Note

QC 20140311. Updated from "Submitted" to "Published"

Available from: 2012-06-13 Created: 2012-06-13 Last updated: 2017-12-07Bibliographically approved
4. The motion of a deforming capsule through a corner
Open this publication in new window or tab >>The motion of a deforming capsule through a corner
2015 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 770, 374-397 p.Article in journal (Refereed) Published
Abstract [en]

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner, as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner.

Keyword
biological fluid dynamics, boundary integral methods, capsule/cell dynamics
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-142671 (URN)10.1017/jfm.2015.157 (DOI)000354190500011 ()2-s2.0-84927128753 (Scopus ID)
Funder
Swedish Research CouncilEU, European Research Council, simcomics-280117; 2013-CoG-616186Swedish e‐Science Research Center
Note

QC 20150609. Updated from manuscript to article in journal.

Available from: 2014-03-11 Created: 2014-03-11 Last updated: 2017-12-05Bibliographically approved
5. A microfluidic device to sort capsules by deformability
Open this publication in new window or tab >>A microfluidic device to sort capsules by deformability
(English)Manuscript (preprint) (Other academic)
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-142672 (URN)
Note

QS 2014

Available from: 2014-03-11 Created: 2014-03-11 Last updated: 2014-03-13Bibliographically approved
6. Micropropulsion and microrheology in complex fluids via symmetry breaking
Open this publication in new window or tab >>Micropropulsion and microrheology in complex fluids via symmetry breaking
2012 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 10, 103102- p.Article in journal (Refereed) Published
Abstract [en]

Many biological fluids have polymeric microstructures and display non-Newtonian rheology. We take advantage of such nonlinear fluid behavior and combine it with geometrical symmetry-breaking to design a novel small-scale propeller able to move only in complex fluids. Its propulsion characteristics are explored numerically in an Oldroyd-B fluid for finite Deborah numbers while the small Deborah number limit is investigated analytically using a second-order fluid model. We then derive expressions relating the propulsion speed to the rheological properties of the complex fluid, allowing thus to infer the normal stress coefficients in the fluid from the locomotion of the propeller. Our simple mechanism can therefore be used either as a non-Newtonian micro-propeller or as a micro-rheometer.

Keyword
Biological fluids, Complex fluids, Deborah numbers, Micro propulsion, Micro-rheometers, Microrheology, Non-newtonian, Non-Newtonian rheology, Nonlinear fluids, Normal stress, Oldroyd-B fluid, Polymeric microstructures, Propulsion characteristics, Rheological property, Second-order fluids, Symmetry-breaking
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-96941 (URN)10.1063/1.4758811 (DOI)000310595100021 ()2-s2.0-84868629219 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20121205. Updated from submitted to published.

Available from: 2012-06-13 Created: 2012-06-13 Last updated: 2017-12-07Bibliographically approved
7. The dynamics of a capsule in a wall-bounded oscillating shear flow
Open this publication in new window or tab >>The dynamics of a capsule in a wall-bounded oscillating shear flow
2014 (English)Report (Other academic)
Abstract [en]

The motion of an initially spherical capsule in a wall-bounded oscillating shear flow is studied via an accelerated boundary integral implementation. Neo-Hookean model is used as the constitutive law of the membrane of capsule. The lateral migration velocity of the capsule varies non-monotonically with its capillary number. It is negatively related with the initial height of the capsule above the wall. A positive correlation between the lateral migration velocity and normal stress difference is identified. The correlation becomes strongest for the capsule with the highest lateral migration velocity. For a fixed capillary number, the lateral migration velocity decreases linearly with the frequency of oscillating shear, and approaches an asymptotic value of zero for high frequency. The deformation of capsule displays a wave-like variation in time and its frequency is twice that of the underlying shear. A phase delay is observed between the variation of capsule deformation with that of the oscillatory flow, more pronounced for a more deformable capsule.

 

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-142673 (URN)
Funder
Swedish Research Council
Note

QC 20140311

Available from: 2014-03-11 Created: 2014-03-11 Last updated: 2014-03-13Bibliographically approved

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