Dynamics of a vesicle in general flow

Abstract

An approach to quantitatively study vesicle dynamics as well as biologically-related micro-objects in a fluid flow, which is based on the combination of a dynamical trap and a control parameter, the ratio of the vorticity to the strain rate, is suggested. The flow is continuously varied between rotational, shearing, and elongational in a microfluidic 4-roll mill device, the dynamical trap, that allows scanning of the entire phase diagram of motions, i.e., tank-treading (TT), tumbling (TU), and trembling (TR), using a single vesicle even at ‫؍‬ in/out ‫؍‬ 1, where in and out are the viscosities of the inner and outer fluids. This cannot be achieved in pure shear flow, where the transition between TT and either TU or TR is attained only at >1. As a result, it is found that the vesicle dynamical states in a general are presented by the phase diagram in a space of only 2 dimensionless control parameters. The findings are in semiquantitative accord with the recent theory made for a quasi-spherical vesicle, although vesicles with large deviations from spherical shape were studied experimentally. The physics of TR is also uncovered. U nderstanding the rheology of biofluids remains a great challenge, whose progress relies, in a large part, on detailed studies of the dynamics of a single cell. Vesicles are a model system used to study the dynamic behavior of biological cells, similar in some respects to red blood cells, and their dynamics in shear flow have been the subject of intensive theoretical (1-8), numerical (9-13), and experimental (14-18) investigations.A vesicle is a droplet of viscous fluid encapsulated by a phospholipid bilayer membrane suspended in a fluid of either the same or different viscosity as the inner one. Both the volume and the surface area of the vesicle are conserved. The former means that the vesicle membrane is considered to be impermeable, at least on the time scale of the experiment, and the latter means that the membrane dilatation is neglected since it is 2D fluid (1,2). Experimental, theoretical, and computational efforts during the last decade led to the observation and characterization of 3 states in vesicle dynamics in shear flow. The existence of the first 2, tank-treading (TT) and tumbling (TU), and the transition between them were already predicted by a phenomenological model of Keller and Skalak (19) and its further extensions (2,11,12). Two control parameters, the excess area ⌬ ϭ A/R 2 -4 and the viscosity contrast ϭ in / out , determine the transition line c (⌬) between TT and TU, which is independent of the shear rate ␥ in the approximation of a fixed vesicle shape, with the vesicle inclination angle with respect to the flow direction as the only dynamical variable (2,9,10,16-19). Here, R is the effective vesicle radius, related to the volume via V ϭ 4/3R 3 , A is the vesicle surface area, and in and out are the viscosities of the inner and outer fluids. Another analytical approach based on a quasi-spherical vesicle approximated by a spherical harmonics expansion used a perturb...

Dynamic modes of microcapsules in steady shear flow: Effects of bending and shear elasticities

“…(4) becomes Jeffery's equation [62] for solid ellipsoidal objects, where φ is kept in the original position. These results show good agreement with recent experiments of lipid vesicles [7][8][9].…”

“…Recently, the dynamics of lipid vesicles in steady shear flow was intensively investigated [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. A lipid vesicle can be considered as a microcapsule in the small limit of the shear modulus µ → 0.…”

Locomotion, wrinkling, and budding of a multicomponent vesicle in viscous fluids

“…see [11,28,53,16]. It has also been reported recently that a time-dependent flow with a switch in the direction of the velocity gradient can also lead to bud formation [6]. Here our flow field is far more complicated than the elongation flow.…”

“…Finken and Seifert [18] performed a mathematical analysis and derived analytical results both for the threshold value of the shear rate and for the critical wavelength of the wrinkling. Kantsler et al also found that vesicle wrinkling may occur in time-dependent elongation flow [19,6]. It has been suggested that the winkling phenomena are related to the dynamical instability induced by negative surface tension of the membrane [20].…”

“…As the principal components of living organisms, membranes contain a mixture of materials including lipids, proteins, and cholesterols that may decompose into coexisting domains of different phases [1,2,3]. To facilitate their biological functions such as solute and chemical transport [4], membranes interact with their fluid surroundings in surprising ways and exhibit rich shape transition behaviors [5,6]. At the continuum level, the mathematical description of morphological changes due to these coupled physical phenomena poses a highly challenging nonlinear moving boundary problem.…”