scholarly journals Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres

2012 ◽  
Vol 711 ◽  
pp. 192-211 ◽  
Author(s):  
Mingge Deng ◽  
Xuejin Li ◽  
Haojun Liang ◽  
Bruce Caswell ◽  
George Em Karniadakis
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Blood Cells ◽  
Polymer Brushes ◽  
Slip Length ◽  
Mesh Size ◽  
Homogeneous Flow ◽  
Strong Shear ◽  
Brush Height ◽  
Scaling Arguments

AbstractFabrication 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 ${\dot {\gamma } }_{0} \propto {\sigma }^{3/ 2} $, where ${\dot {\gamma } }_{0} $ is the critical transition shear rate and $\sigma $ 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.

Slip length for longitudinal shear flow over an arbitrary-protrusion-angle bubble mattress: the small-solid-fraction singularity

2017 ◽  
Vol 820 ◽  
pp. 580-603 ◽  
Author(s):  
Ory Schnitzer
Keyword(s):  
Shear Flow ◽  
Asymptotic Analysis ◽  
Solid Fraction ◽  
Asymptotic Expansions ◽  
Slip Length ◽  
Longitudinal Shear ◽  
Unidirectional Flow ◽  
Effective Slip Length ◽  
Effective Slip ◽  
Scaling Arguments

We study the effective slip length for unidirectional flow over a superhydrophobic mattress of bubbles in the small-solid-fraction limit $\unicode[STIX]{x1D716}\ll 1$. Using scaling arguments and utilising an ideal-flow analogy we elucidate the singularity of the slip length as $\unicode[STIX]{x1D716}\rightarrow 0$: relative to the periodicity it scales as $\log (1/\unicode[STIX]{x1D716})$ for protrusion angles $0\leqslant \unicode[STIX]{x1D6FC}<\unicode[STIX]{x03C0}/2$ and as $\unicode[STIX]{x1D716}^{-1/2}$ for $0<\unicode[STIX]{x03C0}/2-\unicode[STIX]{x1D6FC}=O(\unicode[STIX]{x1D716}^{1/2})$. We continue with a detailed asymptotic analysis using the method of matched asymptotic expansions, where ‘inner’ solutions valid close to the solid segments are matched with ‘outer’ solutions valid on the scale of the periodicity, where the bubbles protruding from the solid grooves appear to touch. The analysis yields asymptotic expansions for the effective slip length in each of the protrusion-angle regimes. These expansions overlap for intermediate protrusion angles, which allows us to form a uniformly valid approximation for arbitrary protrusion angles $0\leqslant \unicode[STIX]{x1D6FC}\leqslant \unicode[STIX]{x03C0}/2$. We thereby explicitly describe the transition with increasing protrusion angle from a logarithmic to an algebraic small-solid-fraction slip-length singularity.

State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping

Soft Matter ◽  
2019 ◽  
Vol 15 (27) ◽  
pp. 5511-5520 ◽  
Author(s):  
Anil K. Dasanna ◽  
Dmitry A. Fedosov ◽  
Gerhard Gompper ◽  
Ulrich S. Schwarz
Keyword(s):  
Angular Momentum ◽  
Shear Rate ◽  
Shear Flow ◽  
Red Blood Cells ◽  
Blood Cells ◽  
State Diagram ◽  
Momentum Conservation ◽  
Collision Dynamics ◽  
Multiparticle Collision Dynamics

Using multiparticle collision dynamics with angular momentum conservation, we investigated the role of shear rate, stiffness and viscosity contrast for the adhesion of biconcave deformable cells or capsules in shear flow.

scholarly journals Shear-induced microstructures and dynamics processes of phospholipid cylinders in solutions

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Yue Shan ◽  
Xiaowei Qiang ◽  
Jianzhu Ye ◽  
Xianghong Wang ◽  
Linli He ◽  
...  
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Cross Sections ◽  
Polymer Chains ◽  
Dynamic Processes ◽  
Radius Of Gyration ◽  
Particle Dynamic ◽  
Shear Direction ◽  
Shape Factors ◽  
Strong Shear

Abstract Shear-induced microstructures and their corresponding dynamic processes are investigated for phospholipid cylinders in aqueous solution by dissipative particle dynamic simulation. Various phospholipid cylinders with cross-sections, which are formed under shear-free flow, are selected to examine the effects of shear flow on their structures and dynamic processes. Shear flow induces the transition from cylinders into vesicles at weak rate and the transition into vesicle–lamella mixtures with increased shear rate and lamella structures at the strong shear rate. Then, the average radius of gyration and shape factors of the polymer chains in the dynamic processes are discussed in detail. Results show that shear flow causes the structure of the polymer chains to be elongated along the shear direction, and the configuration of the polymer chain can be rapidly transformed into an ellipsoid structure under strong shear.

Dynamics of red blood cells in oscillating shear flow

2016 ◽  
Vol 800 ◽  
pp. 484-516 ◽  
Author(s):  
Daniel Cordasco ◽  
Prosenjit Bagchi
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Red Blood Cells ◽  
Periodic Motion ◽  
Blood Cells ◽  
Large Amplitude ◽  
Chaotic Dynamics ◽  
Viscosity Ratio ◽  
Reduced Order Models ◽  
Reduced Order

We present a three-dimensional computational study of fully deformable red blood cells of the biconcave resting shape subject to sinusoidally oscillating shear flow. A comprehensive analysis of the cell dynamics and deformation response is considered over a wide range of flow frequency, shear rate amplitude and viscosity ratio. We observe that the cell exhibits either a periodic motion or a chaotic motion. In the periodic motion, the cell reverses its orientation either by passing through the flow direction (horizontal axis) or by passing through the flow gradient (vertical axis). The chaotic dynamics is characterized by a non-periodic sequence of horizontal and vertical reversals. The study provides the first conclusive evidence of the chaotic dynamics of fully deformable cells in oscillating flow using a deterministic numerical model without the introduction of any stochastic noise. In certain regimes of the periodic motion, the initial conditions are completely forgotten and the cells become entrained in the same sequence of horizontal reversals. We show that chaos is only possible in certain frequency bands when the cell membrane can rotate by a certain amount, allowing the cells to swing near the maximum shear rate. As such, the bifurcation between the horizontal and vertical attractors in phase space always occurs via a swinging inflection. While the reversal sequence evolves in an unpredictable way in the chaotic regime, we find a novel result that there exists a critical inclination angle at the instant of flow reversal which determines whether a vertical or horizontal reversal takes place, and is independent of the flow frequency. The chaotic dynamics, however, occurs at a viscosity ratio less than the physiological values. We further show that the cell shape in oscillatory shear at large amplitude exhibits a remarkable departure from the biconcave shape, and that the deformation is significantly greater than that in steady shear flow. A large compression of the cells occurs during the reversals which leads to over/undershoots in the deformation parameter. We show that due to the large deformation experienced by the cells, the regions of chaos in parameter space diminish and eventually disappear at high shear rate, in contradiction to the prediction of reduced-order models. While the findings bolster support for reduced-order models at low shear rate, they also underscore the important role that the cell deformation plays in large-amplitude oscillatory flows.

Polymer Brushes in Strong Shear Flow

1996 ◽  
Vol 464 ◽  
Author(s):  
Gary S. Grest
Keyword(s):  
Shear Flow ◽  
Polymer Brushes ◽  
Surface Force ◽  
Polymer Chains ◽  
Radius Of Gyration ◽  
Strong Shear ◽  
Theoretical Predictions ◽  
Self Consistent Field ◽  
Self Consistent Field Theory ◽  
Dynamics Simulations

ABSTRACTPolymers end-grafted to a surface in the presence of a shear flow are studied by molecular dynamics simulations. The solvent velocity field is observed to penetrate only a short distance into the brush consistent with predictions based on self-consistent field theory. The deformation of the brush is small except when the shear rate γ is very large. In this limit, while some of the polymer chains are stretched in the direction of flow, the brush height actually decreases slightly, in contrast to several theoretical predictions. When two surfaces bearing end-grafted chains are brought into contact, the normal force increases rapidly with decreasing plate separation, while the shear force is significantly smaller. For low relative velocity vw of the two walls, the surfaces slide pass each other with almost no change in the chain's radius of gyration or the amount of interpenetration, while for very large vw, there is significant stretching and some disentanglement of the chains. The results are in qualitatively good agreement with recent experiments using the surface force apparatus.

The Effect of Red Blood Cells on the ADP-induced Aggregation of Human Platelets in Flow Through Tubes

1990 ◽  
Vol 63 (01) ◽  
pp. 112-121 ◽  
Author(s):  
David N Bell ◽  
Samira Spain ◽  
Harry L Goldsmith
Keyword(s):  
Platelet Aggregation ◽  
Shear Rate ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Platelet Rich Plasma ◽  
Mean Transit Time ◽  
White Blood Cells ◽  
Aggregate Size ◽  
Human Platelets ◽  
Induced Aggregation

SummaryThe effect of red blood cells, rbc, and shear rate on the ADPinduced aggregation of platelets in whole blood, WB, flowing through polyethylene tubing was studied using a previously described technique (1). Effluent WB was collected into 0.5% glutaraldehyde and the red blood cells removed by centrifugation through Percoll. At 23°C the rate of single platelet aggregtion was upt to 9× greater in WB than previously found in platelet-rich plasma (2) at mean tube shear rates Ḡ = 41.9,335, and 1,920 s−1, and at both 0.2 and 1.0 µM ADP. At 0.2 pM ADP, the rate of aggregation was greatest at Ḡ = 41.9 s−1 over the first 1.7 s mean transit time through the flow tube, t, but decreased steadily with time. At Ḡ ≥335 s−1 the rate of aggregation increased between t = 1.7 and 8.6 s; however, aggregate size decreased with increasing shear rate. At 1.0 µM ADP, the initial rate of single platelet aggregation was still highest at Ḡ = 41.9 s1 where large aggregates up to several millimeters in diameter containing rbc formed by t = 43 s. At this ADP concentration, aggregate size was still limited at Ḡ ≥335 s−1 but the rate of single platelet aggregation was markedly greater than at 0.2 pM ADP. By t = 43 s, no single platelets remained and rbc were not incorporated into aggregates. Although aggregate size increased slowly, large aggregates eventually formed. White blood cells were not significantly incorporated into aggregates at any shear rate or ADP concentration. Since the present technique did not induce platelet thromboxane A2 formation or cause cell lysis, these experiments provide evidence for a purely mechanical effect of rbc in augmenting platelet aggregation in WB.

Heat/mass transport in shear flow over a heterogeneous surface with first-order surface-reactive domains

2015 ◽  
Vol 782 ◽  
pp. 260-299 ◽  
Author(s):  
Preyas N. Shah ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Mass Transfer ◽  
Shear Rate ◽  
Shear Flow ◽  
Reaction Rate ◽  
Patch Size ◽  
Patch Area ◽  
First Order ◽  
Effective Boundary ◽  
Order Surface ◽  
Slip Distance

Surfaces that include heterogeneous mass transfer at the microscale are ubiquitous in nature and engineering. Many such media are modelled via an effective surface reaction rate or mass transfer coefficient employing the conventional ansatz of kinetically limited transport at the microscale. However, this assumption is not always valid, particularly when there is strong flow. We are interested in modelling reactive and/or porous surfaces that occur in systems where the effective Damköhler number at the microscale can be $O(1)$ and the local Péclet number may be large. In order to expand the range of the effective mass transfer surface coefficient, we study transport from a uniform bath of species in an unbounded shear flow over a flat surface. This surface has a heterogeneous distribution of first-order surface-reactive circular patches (or pores). To understand the physics at the length scale of the patch size, we first analyse the flux to a single reactive patch. We use both analytic and boundary element simulations for this purpose. The shear flow induces a 3-D concentration wake structure downstream of the patch. When two patches are aligned in the shear direction, the wakes interact to reduce the per patch flux compared with the single-patch case. Having determined the length scale of the interaction between two patches, we study the transport to a periodic and disordered distribution of patches again using analytic and boundary integral techniques. We obtain, up to non-dilute patch area fraction, an effective boundary condition for the transport to the patches that depends on the local mass transfer coefficient (or reaction rate) and shear rate. We demonstrate that this boundary condition replaces the details of the heterogeneous surfaces at a wall-normal effective slip distance also determined for non-dilute patch area fractions. The slip distance again depends on the shear rate, and weakly on the reaction rate, and scales with the patch size. These effective boundary conditions can be used directly in large-scale physics simulations as long as the local shear rate, reaction rate and patch area fraction are known.

Dynamics of a non-spherical microcapsule with incompressible interface in shear flow

2011 ◽  
Vol 678 ◽  
pp. 221-247 ◽  
Author(s):  
P. M. VLAHOVSKA ◽  
Y.-N. YOUNG ◽  
G. DANKER ◽  
C. MISBAH
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Viscosity Ratio ◽  
Perturbation Expansion ◽  
Shear Plane ◽  
Creeping Flow ◽  
Regular Perturbation ◽  
Cell Dynamics ◽  
Initial Shape ◽  
Flow Equations

We study the motion and deformation of a liquid capsule enclosed by a surface-incompressible membrane as a model of red blood cell dynamics in shear flow. Considering a slightly ellipsoidal initial shape, an analytical solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, area-incompressibility and resistance to bending. The theory captures the observed transition from tumbling to swinging as the shear rate increases and clarifies the effect of capsule deformability. Near the transition, intermittent behaviour (swinging periodically interrupted by a tumble) is found only if the capsule deforms in the shear plane and does not undergo stretching or compression along the vorticity direction; the intermittency disappears if deformation along the vorticity direction occurs, i.e. if the capsule ‘breathes’. We report the phase diagram of capsule motions as a function of viscosity ratio, non-sphericity and dimensionless shear rate.

Effects of shear rate on rouleau formation in simple shear flow

Biorheology ◽  
1988 ◽  
Vol 25 (1-2) ◽  
pp. 113-122 ◽  
Author(s):  
T. Murata ◽  
T.W. Secomb
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Rouleau Formation

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

2002 ◽  
Author(s):  
Derek C. Tretheway ◽  
Luoding Zhu ◽  
Linda Petzold ◽  
Carl D. Meinhart
Keyword(s):  
Boundary Condition ◽  
Shear Rate ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Simulations ◽  
Bounce Back

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9–L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1−P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

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