| Popis: |
The first part is concerned with fluid-dynamical aspects of biological cell adhesion to a substrate. A mathematical model of a two-dimensional cell immersed in a viscous fluid interacting with a plane adhesive surface is developed. This model is used to explore how viscous stresses and elastic cell membrane forces mediate the adhesion of fluid-borne cells under the action of specific receptor-ligand bonds. The cell is modelled as an extensible membrane under tension that contains inviscid fluid of constant volume; molecular binding forces are described through a contact potential that is long-range attractive but short-range repulsive. Using lubrication theory to describe the thin-film flow between the cell and the plane wall, models are presented for the sedimentation of a cell onto a wall under adhesive forces, and also its removal under the action of an external force. Numerical simulations show how these events are dominated respectively by quasi-steady spreading and peeling motions, such are captured using an asymptotic analysis. The analysis is extended to model a cell "tank-treading" over an adhesive wall in an external shear flow. The relation between cell rolling speed and shear rate is determined : at low speeds it is linear and independent of the viscosity of the suspending fluid; at higher speeds it is nonlinear and viscosity-dependent. The rolling cell model is then extended to include the effects of non-equilibrium binding kinetics. Secondly, to understand how the internal viscosity of a droplet of fluid affects the speed at which it moves down an inclined wall under gravity, we consider a two-dimensional problem in which a droplet of fluid with viscosity lm is suspended in a second fluid of viscosity m, and moves down the wall by rolling, sliding, or a combination of both. For wall tilt angles q << 1 and negligible inertia, the problem admits a solution in which the drop moves at constant speed supported by a lubricating layer below the drop. We give scaling arguments showing how the drop shape, drop motion, sliding speed and the thickness of the lubricating film depend on l, q and the drop Bond number. Asymptotic and numerical methods are used to calculate the sliding speed and film thickness in various sliding and rolling regimes. The results are compared with experiments, and the scaling estimates are tentatively extended to the three-dimensional case. |
