2 results
Blood flow in small tubes: quantifying the transition to the non-continuum regime
- Huan Lei, Dmitry A. Fedosov, Bruce Caswell, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 722 / 10 May 2013
- Published online by Cambridge University Press:
- 28 March 2013, pp. 214-239
-
- Article
- Export citation
-
In small vessels blood is usually treated as a Newtonian fluid down to diameters of ${\sim }200~\mathrm{\mu} \mathrm{m} $. We investigate the flow of red blood cell (RBC) suspensions driven through small tubes (diameters $10\text{{\ndash}} 150~\mathrm{\mu} \mathrm{m} $) in the range marking the transition from arterioles and venules to the largest capillary vessels. The results of the simulations combined with previous simulations of uniform shear flow and experimental data show that for diameters less than ${\sim }100~\mathrm{\mu} \mathrm{m} $ the suspension’s stress cannot be described as a continuum, even a heterogeneous one. We employ the dissipative particle dynamics (DPD) model, which has been successfully used to predict human blood bulk viscosity in homogeneous shear flow (Fedosov et al. Proc. Natl Acad. Sci. USA, vol. 108, 2011, pp. 11772–11777). In tube flow the cross-stream stress gradient induces an inhomogeneous distribution of RBCs featuring a centreline cell density peak, and a cell-free layer (CFL) next to the wall. For a neutrally buoyant suspension the imposed linear shear-stress distribution together with the differentiable velocity distribution allow the calculation of the local viscosity across the tube section. The viscosity across the section as a function of the strain rate is found to be essentially independent of tube size for the larger diameters and is determined by the local haematocrit ($H$) and shear rate. Other RBC properties such as asphericity, deformation, and cell-flow orientation exhibit similar dependence for the larger tube diameters. As the tube size decreases below ${\sim }100~\mathrm{\mu} \mathrm{m} $ in diameter, the viscosity in the central region departs from the large-tube similarity function of the shear rate, since $H$ increases significantly towards the centreline. The dependence of shear stress on tube size, in addition to the expected local shear rate and local haematocrit, implies that blood flow in small tubes cannot be described as a heterogeneous continuum. Based on the analysis of the DPD simulations and on available experimental results, we propose a simple velocity-slip model that can be used in conjunction with continuum-based simulations.
Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres
- Mingge Deng, Xuejin Li, Haojun Liang, Bruce Caswell, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 711 / 25 November 2012
- Published online by Cambridge University Press:
- 03 September 2012, pp. 192-211
-
- Article
- Export citation
-
Fabrication of functionalized surfaces using polymer brushes is a relatively simple process and parallels the presence of glycocalyx filaments coating the luminal surface of our vasculature. In this paper, we perform atomistic-like simulations based on dissipative particle dynamics (DPD) to study both polymer brushes and glycocalyx filaments subject to shear flow, and we apply mean-field theory to extract useful scaling arguments on their response. For polymer brushes, a weak shear flow has no effect on the brush density profile or its height, while the slip length is independent of the shear rate and is of the order of the brush mesh size as a result of screening by hydrodynamic interactions. However, for strong shear flow, the polymer brush is penetrated deeper and is deformed, with a corresponding decrease of the brush height and an increase of the slip length. The transition from the weak to the strong shear regime can be described by a simple ‘blob’ argument, leading to the scaling , where is the critical transition shear rate and is the grafting density. Furthermore, in the strong shear regime, we observe a cyclic dynamic motion of individual polymers, causing a reversal in the direction of surface flow. To study the glycocalyx layer, we first assume a homogeneous flow that ignores the discrete effects of blood cells, and we simulate microchannel flows at different flow rates. Surprisingly, we find that, at low Reynolds number, the slip length decreases with the mean flow velocity, unlike the behaviour of polymer brushes, for which the slip length remains constant under similar conditions. (The slip length and brush height are measured with respect to polymer mesh size and polymer contour length, respectively.) We also performed additional DPD simulations of blood flow in a tube with walls having a glycocalyx layer and with the deformable red blood cells modelled accurately at the spectrin level. In this case, a plasma cell-free layer is formed, with thickness more than three times the glycocalyx layer. We then find our scaling arguments based on the homogeneous flow assumption to be valid for this physiologically correct case as well. Taken together, our findings point to the opposing roles of conformational entropy and bending rigidity – dominant effects for the brush and glycocalyx, respectively – which, in turn, lead to different flow characteristics, despite the apparent similarity of the two systems.