title: Front microrheology of the non-Newtonian behaviour of blood: scaling theory of erythrocyte aggregation by aging.
abstract: We introduce a new framework to study the non-Newtonian behaviour of fluids at the microscale based on the analysis of front advancement. We apply this methodology to study the non-linear rheology of blood in microchannels. We carry out experiments in which the non-linear viscosity of blood samples is quantified at different haematocrits and ages. Under these conditions, blood exhibits a power-law dependence on the shear rate. In order to analyse our experimental data, we put forward a scaling theory which allows us to define an adhesion scaling number. This theory yields a scaling behaviour of the viscosity expressed as a function of the adhesion capillary number. By applying this scaling theory to samples of different ages, we are able to quantify how the characteristic adhesion energy varies as time progresses. This connection between microscopic and mesoscopic properties allows us to estimate quantitatively the change in the cell-cell adhesion energies as the sample ages.
authors.affiliation: Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Diagonal 645, E-08028 Barcelona, Spain. a.hernandezmachado@gmail.com and Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain.
authors.forename: C
authors.initials: C
authors.lastname: Trejo-Soto
authors.affiliation: Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain and Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain and Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain.
authors.forename: E
authors.identifier: http://orcid.org/0000-0001-8238-1422
authors.initials: E
authors.lastname: Costa-Miracle
authors.affiliation: Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain.
authors.forename: I
authors.initials: I
authors.lastname: Rodriguez-Villarreal
authors.affiliation: Servicio de Hemoterapia y Hemostasia, Hospital Clinic de Barcelona, Barcelona, Spain.
authors.forename: J
authors.initials: J
authors.lastname: Cid
authors.affiliation: GISC and Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, E-28015 Madrid, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Castro
authors.affiliation: Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain and Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain and Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain and ICREA, Pg. Llus Companys 23, 08010 Barcelona, Spain.
authors.forename: T
authors.initials: T
authors.lastname: Alarcon
authors.affiliation: Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Diagonal 645, E-08028 Barcelona, Spain. a.hernandezmachado@gmail.com and Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain and Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain and Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain.
authors.forename: A
authors.identifier: http://orcid.org/0000-0002-0397-5255
authors.initials: A
authors.lastname: Hernandez-Machado