Prediction of Anomalous Blood Viscosity in Confined Shear Flow

Abstract

Red blood cells play a major role in body metabolism by supplying oxygen from the microvasculature to different organs and tissues. Understanding blood flow properties in microcirculation is an essential step towards elucidating fundamental and practical issues. Numerical simulations of a blood model under a confined linear shear flow reveal that confinement markedly modifies the properties of blood flow. A nontrivial spatiotemporal organization of blood elements is shown to trigger hitherto unrevealed flow properties regarding the viscosity η, namely ample oscillations of its normalized value ½η ¼ ðη − η 0 Þ=ðη 0 ϕÞ as a function of hematocrit ϕ (η 0 ¼ solvent viscosity). A scaling law for the viscosity as a function of hematocrit and confinement is proposed. This finding can contribute to the conception of new strategies to efficiently detect blood disorders, via in vitro diagnosis based on confined blood rheology. It also constitutes a contribution for a fundamental understanding of rheology of confined complex fluids. Introduction.-Blood flow in microcirculation is essential for delivery of nutrients and removal of metabolic waste products to or from tissues. These functions are ensured by proper regulation of blood flow down to the capillary level. One of the main factors controlling capillary circulation is microvascular resistance to blood flow. This effect, in spite of extensive investigation, is still to be fully elucidated, and some fundamental issues remain open. Blood is to good approximation a suspension of red blood cells (RBCs). Blood rheology is dictated by dynamics of RBCs and their interaction with blood vessel walls. A significant research effort has been devoted so far to macroscopic rheology [1,2]. Most of the research on rheology in confined geometries has focused on the famous Fahraeus-Lindqvist (FL) effect [3][4][5] (see recent review [6]), where confinement has been shown to strongly affect the rheology, with a decrease in apparent viscosity as the diameter of a vessel decreases. These advances have not exhausted yet the intricate behavior inherent to rheology of confined blood, as reported in this Letter.A property that is commonly of interest for nonconfined suspensions is the viscosity as a function of the volume fraction ϕ, ηðϕÞ. In the dilute regime, i.e., when hydrodynamic interactions between suspended entities can be neglected, η takes the generic form η ¼ η 0 ð1 þ a 1 ϕÞ, where η 0 is the viscosity of the suspending fluid and a 1 is a quantity (the so-called intrinsic viscosity), that depends, in general, on the properties of the suspension. For example, for rigid particles, a 1 is just a universal number and is equal to 5=2; this is the famous Einstein result [7,8]. a 1 was calculated by Taylor [9] for emulsions, and extended to vesicle suspensions (a blood model) quite recently [10]. When the volume fraction increases, hydrodynamic interactions among suspended

Numerical–experimental observation of shape bistability of red blood cells flowing in a microchannel

“…[mm/s] u Other Table S1: Experimental data: The table lists for each applied pressure drop ∆P the total number of analyzed cells N all 0 at position x = 0 mm in the channel and the total number of analyzed cells N all 10 at position x = 10 mm. For the latter we also show the number of croissants, slippers and "others", together with the measured velocities u 10 . The uncertainties are the standard deviation.…”

“…Understanding and being able to predict these shapes is of high importance for a variety of reasons. From a fundamental point of view, it serves as the foundation in a bottom-up approach to understand the properties of red blood cell suspensions which are chiefly determined by single particle behavior [7][8][9][10][11][12]. From an applied perspective, a series of recent investigations have devised promising approaches for sorting cells based on their mechanical properties either in lateral displacement devices [13] or using high-speed video microscopy [14].…”

Disorder Suppresses Chaos in Viscoelastic Flows

“…This condition is often characterized by a Weissenberg number, Wi = τγ > Wi cr ∼ 1, wherė γ is the typical shear rate and τ is the fluid relaxation time [2]. Purely elastic instabilities manifest as spatiotemporal chaotic flow and elastic turbulence [3,4] in a wide range of natural and industrial applications: Elasticity generates secondary flows of DNA and blood suspensions in biological systems [5,6], hydrodynamic resistance increases [7] along with power consumption and cost in polymer processing, and elastic instabilities enhance mixing and dispersion in microfluidic and porous media flows [8][9][10]. Experimental [11][12][13][14][15] and numerical [16][17][18] efforts have characterized the onset and impact of elastic instabilities in well-defined geometries including cross slot [13,17], Couette [19,20], Poiseuille [8,21], and ordered pillar array flows [12,22,23].…”

Characterizing elastic turbulence in channel flows at low Reynolds number

“…Purely elastic instabilities are found in many practical flows and understanding these instabilities is fundamental to our knowledge of how biological fluids (e.g. blood, vesicles, mucus) flow [13][14][15][16], chemical and polymer industries where flow instabilities have been plaguing processing for years [17,18], and micro-and nano-fluidics where purely elastic instabilities were proposed as a way of effective mixing at small length scales [11,[19][20][21].…”