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  • 1. Balestra, G.
    et al.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Gallaire, F.
    Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton’s theory to empirical models2018In: Microfluidics and Nanofluidics, ISSN 1613-4982, E-ISSN 1613-4990, Vol. 22, no 6, article id 67Article in journal (Refereed)
    Abstract [en]

    The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, Ca, from 10 - 4 to 1 and inner-to-outer viscosity ratios, λ, from 0, i.e. a bubble, to high-viscosity droplets. Theoretical asymptotic results obtained in the limit of small capillary number are combined with accurate numerical simulations at larger Ca. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers (Ca< 10 - 3) agrees well with Bretherton’s scaling for bubbles as long as λ< 1. For larger viscosity ratios, the film thickness increases monotonically, before saturating for λ> 10 3 to a value 2 2 / 3 times larger than the film thickness of a bubble. At larger capillary numbers, the film thickness follows the rational function proposed by Aussillous and Quéré (Phys Fluids 12(10):2367–2371, 2000) for bubbles, with a fitting coefficient which is viscosity-ratio dependent. This coefficient modifies the value to which the film thickness saturates at large capillary numbers. The velocity of the droplet is found to be strongly dependent on the capillary number and viscosity ratio. We also show that the normal viscous stresses at the front and rear caps of the droplets cannot be neglected when calculating the pressure drop for Ca> 10 - 3.

  • 2.
    Gallino, Giacomo
    et al.
    Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
    Zhu, Lailai
    KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Gallaire, Francois
    Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
    The Hydrodynamics of a Micro-Rocket Propelled by a Deformable Bubble2019In: FLUIDS, ISSN 2311-5521, Vol. 4, no 1, article id 48Article in journal (Refereed)
    Abstract [en]

    We perform simulations to study the hydrodynamics of a conical-shaped swimming micro-robot that ejects catalytically produced bubbles from its inside. We underline the nontrivial dependency of the swimming velocity on the bubble deformability and on the geometry of the swimmer. We identify three distinct phases during the bubble evolution: immediately after nucleation the bubble is spherical and its inflation barely affects the swimming speed; then the bubble starts to deform due to the confinement gradient generating a force that propels the swimmer; while in the last phase, the bubble exits the cone, resulting in an increase in the swimmer velocity. Our results shed light on the fundamental hydrodynamics of the propulsion of catalytic conical swimmers and may help to improve the efficiency of these micro-machines.

  • 3. Hadikhani, P.
    et al.
    Hashemi, S. M. H.
    Balestra, G.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Princeton University, United States.
    Modestino, M. A.
    Gallaire, F.
    Psaltis, D.
    Inertial manipulation of bubbles in rectangular microfluidic channels2018In: Lab on a Chip, ISSN 1473-0197, E-ISSN 1473-0189, Vol. 18, no 7, p. 1035-1046Article in journal (Refereed)
    Abstract [en]

    Inertial microfluidics is an active field of research that deals with crossflow positioning of the suspended entities in microflows. Until now, the majority of the studies have focused on the behavior of rigid particles in order to provide guidelines for microfluidic applications such as sorting and filtering. Deformable entities such as bubbles and droplets are considered in fewer studies despite their importance in multiphase microflows. In this paper, we show that the trajectory of bubbles flowing in rectangular and square microchannels can be controlled by tuning the balance of forces acting on them. A T-junction geometry is employed to introduce bubbles into a microchannel and analyze their lateral equilibrium position in a range of Reynolds (1 < Re < 40) and capillary numbers (0.1 < Ca < 1). We find that the Reynolds number (Re), the capillary number (Ca), the diameter of the bubble (D), and the aspect ratio of the channel are the influential parameters in this phenomenon. For instance, at high Re, the flow pushes the bubble towards the wall while large Ca or D moves the bubble towards the center. Moreover, in the shallow channels, having aspect ratios higher than one, the bubble moves towards the narrower sidewalls. One important outcome of this study is that the equilibrium position of bubbles in rectangular channels is different from that of solid particles. The experimental observations are in good agreement with the performed numerical simulations and provide insights into the dynamics of bubbles in laminar flows which can be utilized in the design of flow based multiphase flow reactors.

  • 4.
    Liu, Ying
    et al.
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Rallabandi, Bhargav
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA.;Univ Calif Riverside, Dept Mech Engn, Riverside, CA 92521 USA..
    Zhu, Lailai
    KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Gupta, Ankur
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Stone, Howard A.
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Pattern formation in oil-in-water emulsions exposed to a salt gradient2019In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 4, no 8, article id 084307Article in journal (Refereed)
    Abstract [en]

    Flow instabilities can occur in a fluid system with two components that have significantly different diffusivities and that have opposite effects on the fluid density, as is the scenario in traditional double-diffusive convection. Here, we experimentally show that an oil-in-water emulsion exposed to salt concentration gradients generates a flowerlike pattern driven by vertical and azimuthal instabilities. We also report numerical and analytical studies to elaborate on the mechanism, the instability criteria, and the most unstable modes that determine the details of the observed patterns. We find that the instability is driven by buoyancy and stems from the differential transport between the dissolved salt and the suspended oil droplets, which have opposing effects on the density of the medium. Consequently, we identify a criterion for the development of the instability that involves the relative densities and concentrations of the salt and oil droplets. We also argue that the typical wave number of the pattern formed scales with the Peclet number of the salt, which here is equivalent to the Rayleigh number since the flow is driven by buoyancy. We find good agreement of these predictions with both experiments and numerical simulations.

  • 5. Nadal, Francois
    et al.
    Pak, On Shun
    Zhu, LaiLai
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Ecole Polytech Fed Lausanne, Switzerland.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lauga, Eric
    Rotational propulsion enabled by inertia2014In: The European Physical Journal E Soft matter, ISSN 1292-8941, E-ISSN 1292-895X, Vol. 37, no 7, p. 1-14Article in journal (Refereed)
    Abstract [en]

    The fluid mechanics of small-scale locomotion has recently attracted considerable attention, due to its importance in cell motility and the design of artificial micro-swimmers for biomedical applications. Most studies on the topic consider the ideal limit of zero Reynolds number. In this paper, we investigate a simple propulsion mechanism --an up-down asymmetric dumbbell rotating about its axis of symmetry-- unable to propel in the absence of inertia in a Newtonian fluid. Inertial forces lead to continuous propulsion for all finite values of the Reynolds number. We study computationally its propulsive characteristics as well as analytically in the small-Reynolds-number limit. We also derive the optimal dumbbell geometry. The direction of propulsion enabled by inertia is opposite to that induced by viscoelasticity.

  • 6. Nason, F.
    et al.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Dubini, G.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Numerical simulation of a deformable cell in microchannels2013In: Computational Methods for Coupled Problems in Science and Engineering V: A Conference Celebrating the 60th Birthday of Eugenio Onate, COUPLED PROBLEMS 2013, 2013, p. 685-695Conference paper (Refereed)
    Abstract [en]

    The main goal of this work is to numerically investigate the behavior of a cell flowing in a microfluidic system. In particular, we want to model flow-induced deformations of an isolated cell to quantitatively evaluate the cell response when subjected to a representative range of flow rates in a realistic geometry, with specific interest in the case of cell trapping. This research will help optimize operating conditions as well as the design of cell manipulation/culture micro-devices, so as to guarantee cell viability and ultimately improve high-throughput performance.

  • 7.
    Pak, Shun
    et al.
    Dept. of Mechanical and Aerospace Engineering University of California, San Diego, USA.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lauga, Eric
    Dept. of Mechanical and Aerospace Engineering, University of California, San Diego, USA.
    Micropropulsion and microrheology in complex fluids via symmetry breaking2012In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 10, p. 103102-Article in journal (Refereed)
    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.

  • 8.
    Pietrzyk, Kyle
    et al.
    Santa Clara Univ, Dept Mech Engn, Santa Clara, CA 95053 USA..
    Nganguia, Herve
    Indiana Univ Penn, Dept Math & Comp Sci, Indiana, PA 15705 USA..
    Datt, Charu
    Univ British Columbia, Dept Mech Engn, Vancouver, BC V6T 1Z4, Canada..
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Elfring, Gwynn J.
    Univ British Columbia, Dept Mech Engn, Vancouver, BC V6T 1Z4, Canada..
    Pak, On Shun
    Santa Clara Univ, Dept Mech Engn, Santa Clara, CA 95053 USA..
    Flow around a squirmer in a shear-thinning fluid2019In: Journal of Non-Newtonian Fluid Mechanics, ISSN 0377-0257, E-ISSN 1873-2631, Vol. 268, p. 101-110Article in journal (Refereed)
    Abstract [en]

    Many biological fluids display shear-thinning rheology, where the viscosity decreases with an increasing shear rate. To better understand how this non-Newtonian rheology affects the motion of biological and artificial micro swimmers, recent efforts have begun to seek answers to fundamental questions about active bodies in shear-thinning fluids. Previous analyses based on a squirmer model have revealed non-trivial variations of propulsion characteristics in a shear-thinning fluid via the reciprocal theorem. However, the reciprocal theorem approach does not provide knowledge about the flow surrounding the squirmer. In this work, we fill in this missing information by calculating the non-Newtonian correction to the flow analytically in the asymptotic limit of small Carreau number. In particular, we investigate the local effect due to viscosity reduction and the non-local effect due to induced changes in the flow; we then quantify their relative importance to locomotion in a shear-thinning fluid. Our results demonstrate cases where the non-local effect can be more significant than the local effect. These findings suggest that caution should be exercised when developing physical intuition from the local viscosity distribution alone around a swimmer in a shear-thinning fluid.

  • 9. Reigh, Shang Yik
    et al.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Gallaire, Francois
    Lauga, Eric
    Swimming with a cage: low-Reynolds-number locomotion inside a droplet2017In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 13, no 17, p. 3161-3173Article in journal (Refereed)
    Abstract [en]

    Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of a comparable size in another viscous fluid. Meditated solely by hydrodynamic interactions, the encaged swimmer is seen to be able to propel the droplet, and in some situations both remain in a stable co-swimming state. The problem is tackled using both an exact analytical theory and a numerical implementation based on a boundary element method, with a particular focus on the kinematics of the co-moving swimmer and the droplet in a concentric configuration, and we obtain excellent quantitative agreement between the two. The droplet always moves slower than a swimmer which uses purely tangential surface actuation but when it uses a particular combination of tangential and normal actuations, the squirmer and droplet are able to attain the same velocity and stay concentric for all times. We next employ numerical simulations to examine the stability of their concentric co-movement, and highlight several stability scenarios depending on the particular gait adopted by the swimmer. Furthermore, we show that the droplet reverses the nature of the far-field flow induced by the swimmer: a droplet cage turns a pusher swimmer into a puller, and vice versa. Our work sheds light on the potential development of droplets as self-contained carriers of both chemical content and self-propelled devices for controllable and precise drug deliveries.

  • 10.
    Rorai, Cecilia
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Nason, F.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Casagrande, G.
    Dubini, G.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI).
    Hydrodynamic focusing of an elastic capsule in stokes flow: An exploratory numerical study2015In: Procedia IUTAM, Elsevier, 2015, p. 41-49Conference paper (Refereed)
    Abstract [en]

    We study numerically the motion of an elastic capsule in a simple microfluidic device, a sheath flow focuser, designed to align (or focus) particles at the center of a microchannel. The geometry of the device is given, while the flow conditions are varied, and the outflux is constant. The efficiency is expressed in terms of the distance required to achieve focusing and the functioning is characterized by the deformations and stresses undergone by the capsule membrane. Calculations are performed for a 'stiff' and 'soft' capsule, corresponding to a capillary number equal to Ca = 0.05 and Ca = 0.3 based on the outflow rate. We report that as the sheath flow is increased the focusing efficiency grows and plateaus beyond a certain threshold, displaying a drop in the efficiency gain. Differently, the deformations and stresses undergone by the capsule membrane grow for the entire range of the flow parameters considered. This should be kept in mind if the stresses exerted on the membrane have to be minimized or need to be below certain characteristic thresholds typical of the specific application considered. Especially large initial offsets and stiff capsules benefit from focusing.

  • 11.
    Rorai, Cecilia
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Touchard, Antoine
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Brandt, L.uca
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Motion of an elastic capsule in a constricted microchannel2015In: The European Physical Journal E Soft matter, ISSN 1292-8941, E-ISSN 1292-895X, Vol. 38, no 5Article in journal (Refereed)
    Abstract [en]

    We study the motion of an elastic capsule through a microchannel characterized by a localized constriction. We consider a capsule with a stress-free spherical shape and impose its steady-state configuration in an infinitely long straight channel as the initial condition for our calculations. We report how the capsule deformation, velocity, retention time, and maximum stress of the membrane are affected by the capillary number, Ca , and the constriction shape. We estimate the deformation by measuring the variation of the three-dimensional surface area and a series of alternative quantities easier to extract from experiments. These are the Taylor parameter, the perimeter and the area of the capsule in the spanwise plane. We find that the perimeter is the quantity that best reproduces the behavior of the three-dimensional surface area. This is maximum at the centre of the constriction and shows a second peak after it, whose location depends on the Ca number. We observe that, in general, area-deformation-correlated quantities grow linearly with Ca , while velocity-correlated quantities saturate for large Ca but display a steeper increase for small Ca . The velocity of the capsule divided by the velocity of the flow displays, surprisingly, two different qualitative behaviors for small and large capillary numbers. Finally, we report that longer constrictions and spanwise wall bounded (versus spanwise periodic) domains cause larger deformations and velocities. If the deformation and velocity in the spanwise wall bounded domains are rescaled by the initial equilibrium deformation and velocity, their behavior is undistinguishable from that in a periodic domain. In contrast, a remarkably different behavior is reported in sinusoidally shaped and smoothed rectangular constrictions indicating that the capsule dynamics is particularly sensitive to abrupt changes in the cross section. In a smoothed rectangular constriction larger deformations and velocities occur over a larger distance.

  • 12.
    Shukla, Isha
    et al.
    Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
    Kofman, Nicolas
    Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
    Balestra, Gioele
    Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland.;Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA.
    Gallaire, Francois
    Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
    Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 874, p. 1021-1040, article id PII S0022112019004531Article in journal (Refereed)
    Abstract [en]

    We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number $Ca$ lying between $0.03$ and $0.35$ , where $Ca=\unicode[STIX]{x1D707}_{o}U_{d}/\unicode[STIX]{x1D6FE}$ is built with the surrounding oil viscosity $\unicode[STIX]{x1D707}_{o}$ , the droplet velocity $U_{d}$ and surface tension $\unicode[STIX]{x1D6FE}$ . The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quere (Phys. Fluids, vol. 12 (10), 2000, pp. 2367-2371) model with fitting parameters. The droplet also exhibits the 'catamaran' shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet's motion.

  • 13.
    Ungarish, Marius
    et al.
    Technion Israel Inst Technol, Dept Comp Sci, IL-32000 Haifa, Israel..
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Stone, Howard A.
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Inertial gravity current produced by the drainage of a cylindrical reservoir from an outer or inner edge2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 874, p. 185-209Article in journal (Refereed)
    Abstract [en]

    We consider the time-dependent flow of a fluid of density rho(1) in a vertical cylindrical container embedded in a fluid of density rho(2) (<rho(1)) whose side boundary is suddenly removed and the fluid drains freely from the edge. We show that in the inertial-buoyancy regime (large initial Reynolds number) the flow is modelled by the shallow-water equations and bears similarities to a gravity current released from a lock (the dam-break problem) driven by the reduced gravity g' = (1 - rho(2)/rho(1))g. This formulation is amenable to an efficient finite-difference solution. Moreover, we demonstrate that similarity solutions exist, and show that the flow created by the dam break approaches the predicted self-similar behaviour when the volume ratio nu(t)/nu(0) approximate to 1/2 where t is time elapsed from the dam break. We considered two cases of drainage: (i) outward from the outer boundary in a full-radius reservoir; and (ii) inward from the inner radius in an annular-shaped reservoir. For the first case the similarity solution is expressed analytically, while the second case is more complicated and requires a numerical solution. In both cases nu(t)/nu(0) decays like t(-2), but the details are different. The similarity solutions admit an adjustable virtual-origin constant, which we determine by matching with the finite-difference solution. The analysis is valid for both Boussinesq and non-Boussinesq systems, and a wide range of geometric parameters (inner and outer radii, and height). The importance of the neglected viscous terms increases with time, and eventually the inertial-buoyancy model becomes invalid. An estimate for this occurrence is also provided. The predictions of the model are compared to results of direct numerical simulations; there is good agreement for the position of the interface and for the averaged radial velocity, and excellent agreement for nu(t)/nu(0). A box model is used for estimating the effect of a partial (over a sector) dam break. This study is an extension of the work for a rectangular reservoir of Momen et al. (J. Fluid Mech., vol. 827, 2017, pp. 640-663). We demonstrate that there are some similarities, but also significant differences, between the rectangular and the cylindrical reservoirs concerning the velocity, shape of the interface and rate of drainage, which are of interest in applications. The overall conclusion is that this simple model captures very well the flow field under consideration.

  • 14. Xue, Nan
    et al.
    Khodaparast, Sepideh
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Nunes, Janine K.
    Kim, Hyoungsoo
    Stone, Howard A.
    Laboratory layered latte2017In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 8, article id 1960Article in journal (Refereed)
    Abstract [en]

    Inducing thermal gradients in fluid systems with initial, well-defined density gradients results in the formation of distinct layered patterns, such as those observed in the ocean due to double-diffusive convection. In contrast, layered composite fluids are sometimes observed in confined systems of rather chaotic initial states, for example, lattes formed by pouring espresso into a glass of warm milk. Here, we report controlled experiments injecting a fluid into a miscible phase and show that, above a critical injection velocity, layering emerges over a time scale of minutes. We identify critical conditions to produce the layering, and relate the results quantitatively to double-diffusive convection. Based on this understanding, we show how to employ this single-step process to produce layered structures in soft materials, where the local elastic properties vary step-wise along the length of the material.

  • 15.
    Yu, Yingxian Estella
    et al.
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics. Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA.;KTH Mech, Linne Flow Ctr, SE-10044 Stockholm, Sweden.;KTH Mech, Swedish E Sci Res Ctr SeRC, SE-10044 Stockholm, Sweden..
    Shim, Suin
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Eggers, Jens
    Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England..
    Stone, Howard A.
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Time-dependent motion of a confined bubble in a tube: transition between two steady states2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 857, article id R4Article in journal (Refereed)
    Abstract [en]

    When a confined bubble translates steadily in a cylindrical capillary tube, without the consideration of gravity effects, a uniform thin film of liquid separates the bubble surface and the tube wall. In this work, we investigate how this steady state is established by considering the transitional motion of the bubble as it adjusts its film thickness profile between two steady states, characterized by two different bubble speeds. During the transition, two uniform film regions coexist, separated by a step-like transitional region. The transitional motion also requires modification of the film solution near the rear of the bubble, which depends on the ratio of the two capillary numbers. These theoretical results are verified by experiments and numerical simulations.

  • 16.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Numerical investigation of swimming micro-organisms in complex environments2012Licentiate thesis, comprehensive summary (Other academic)
  • 17.
    Zhu, Lailai
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Simulation of individual cells in flow2014Doctoral 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.

  • 18.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    The motion of a deforming capsule through a corner2015In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 770, p. 374-397Article in journal (Refereed)
    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.

  • 19.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Do-Quang, Minh
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lauga, Eric
    Dept. of Mechanical and Aerospace Engineering, University of California, San Diego, USA.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Locomotion by tangential deformation in a polymeric fluid2011In: Physical Reivew E, ISSN 1539-3755, Vol. 83, no 1, p. 011901-Article in journal (Refereed)
    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.

  • 20.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland.;Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08540 USA.
    Gallaire, Francois
    Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland..
    Bifurcation Dynamics of a Particle-Encapsulating Droplet in Shear Flow2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 119, no 6, article id 064502Article in journal (Refereed)
    Abstract [en]

    To understand the behavior of composite fluid particles such as nucleated cells and double emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its concentric particle-droplet configuration, we numerically explore other eccentric and time-periodic equilibrium solutions, which emerge spontaneously via supercritical pitchfork and Hopf bifurcations. We present the loci of these solutions around the codimension-two point. We adopt a dynamic system approach to model and characterize the coupled behavior of the two bifurcations. By exploring the flow fields and hydrodynamic forces in detail, we identify the role of hydrodynamic particle-droplet interaction which gives rise to these bifurcations.

  • 21.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lauga, Eric
    Dept. of Mechanical and Aerospace Engineering, University of California, San Diego, USA.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Low-Reynolds number swimming in a capillary tube2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 726, p. 285-311Article in journal (Refereed)
    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.

  • 22.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lauga, Eric
    Dept. of Mechanical and Aerospace Engineering, University of California, San Diego, USA.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Self-propulsion in viscoelastic fluids: pushers vs. pullers2012In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 5, p. 051902-Article in journal (Refereed)
    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.

  • 23.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Rabault, Jean
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    The dynamics of a capsule in a wall-bounded oscillating shear flow2014Report (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.

     

  • 24.
    Zhu, LaiLai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Rabault, Jean
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Ecole Polytech, F-91128 Palaiseau, France.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    The dynamics of a capsule in a wall-bounded oscillating shear flow2015In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 27, no 7, article id 071902Article in journal (Refereed)
    Abstract [en]

    The motion of an initially spherical capsule in a wall-bounded oscillating shear flow is investigated via an accelerated boundary integral implementation. The neo-Hookean model is used as the constitutive law of the capsule membrane. The maximum wall-normal migration is observed when the oscillation period of the imposed shear is of the order of the relaxation time of the elastic membrane; hence, the optimal capillary number scales with the inverse of the oscillation frequency and the ratio agrees well with the theoretical prediction in the limit of high-frequency oscillation. The migration velocity decreases monotonically with the frequency of the applied shear and the capsule-wall distance. We report a significant correlation between the capsule lateral migration and the normal stress difference induced in the flow. The periodic variation of the capsule deformation is roughly in phase with that of the migration velocity and normal stress difference, with twice the frequency of the imposed shear. The maximum deformation increases linearly with the membrane elasticity before reaching a plateau at higher capillary numbers when the deformation is limited by the time over which shear is applied in the same direction and not by the membrane deformability. The maximum membrane deformation scales as the distance to the wall to the power 1/3 as observed for capsules and droplets in near-wall steady shear flows.

  • 25.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Rorai, Cecilia
    Mitra, Dhrubaditya
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    A microfluidic device to sort capsules by deformabilityManuscript (preprint) (Other academic)
  • 26.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. Laboratory of Fluid Mechanics and Instabilities, Switzerland .
    Rorai, Cecilia
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Mitra, Dhrubaditya
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    A microfluidic device to sort capsules by deformability: a numerical study2014In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 10, no 39, p. 7705-7711Article in journal (Refereed)
    Abstract [en]

    Guided by extensive numerical simulations, we propose a microfluidic device that can sort elastic capsules by their deformability. The device consists of a duct embedded with a semi-cylindrical obstacle, and a diffuser which further enhances the sorting capability. We demonstrate that the device can operate reasonably well under changes in the initial position of the capsule. The efficiency of the device remains essentially unaltered under small changes of the obstacle shape (from semi-circular to semi-elliptic cross-section). Confinement along the direction perpendicular to the plane of the device increases its efficiency. This work is the first numerical study of cell sorting by a realistic microfluidic device.

  • 27.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA.
    Stone, Howard A.
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Propulsion driven by self-oscillation via an electrohydrodynamic instability2019In: Physical Review Fluids, ISSN 2469-990X, Vol. 4, no 6, article id 061701Article in journal (Refereed)
    Abstract [en]

    Oscillations of flagella and cilia play an important role in biology, which motivates the idea of functional mimicry as part of bioinspired applications. Nevertheless, it still remains challenging to drive their artificial counterparts to oscillate via a steady, homogeneous stimulus. Combining theory and simulations, we demonstrate a strategy to achieve this goal by using an elastoelectrohydrodynamic instability (based on the Quincke rotation instability). In particular, we show that applying a uniform dc electric field can produce self-oscillatory motion of a microrobot composed of a dielectric particle and an elastic filament. Upon tuning the electric field and filament elasticity, the microrobot exhibits three distinct behaviors: a stationary state, undulatory swimming, and steady spinning, where the swimming behavior stems from an instability emerging through a Hopf bifurcation. Our results imply the feasibility of engineering self-oscillations by leveraging the elastoviscous response to control the type of bifurcation and the form of instability. We anticipate that our strategy will be useful in a broad range of applications imitating self-oscillatory natural phenomena and biological processes.

  • 28.
    Zhu, Lailai
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Stone, Howard A.
    Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
    Rotation of a low-Reynolds-number watermill: theory and simulations2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 849, p. 57-75Article in journal (Refereed)
    Abstract [en]

    Recent experiments have demonstrated that small-scale rotary devices installed in a microfluidic channel can be driven passively by the underlying flow alone without resorting to conventionally applied magnetic or electric fields. In this work, we conduct a theoretical and numerical study on such a flow-driven 'watermill' at low Reynolds number, focusing on its hydrodynamic features. We model the watermill by a collection of equally spaced rigid rods. Based on the classical resistive force (RF) theory and direct numerical simulations, we compute the watermill's instantaneous rotational velocity as a function of its rod number N, position and orientation. When N >= 4, the RF theory predicts that the watermill's rotational velocity is independent of N and its orientation, implying the full rotational symmetry (of infinite order), even though the geometrical configuration exhibits a lower-fold rotational symmetry; the numerical solutions including hydrodynamic interactions show a weak dependence on N and the orientation. In addition, we adopt a dynamical system approach to identify the equilibrium positions of the watermill and analyse their stability. We further compare the theoretically and numerically derived rotational velocities, which agree with each other in general, while considerable discrepancy arises in certain configurations owing to the hydrodynamic interactions neglected by the RP theory. We confirm this conclusion by employing the RP-based asymptotic framework incorporating hydrodynamic interactions for a simpler watermill consisting of two or three rods and we show that accounting for hydrodynamic interactions can significantly enhance the accuracy of the theoretical predictions.

1 - 28 of 28
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