Two-Particle Microrheology of Quasi-2D Viscous Systems

Abstract

We study the spatially correlated motions of colloidal particles in a quasi-2D system (Human Serum Albumin (HSA) protein molecules at an air-water interface) for different surface viscosities ηs. We observe a transition in the behavior of the correlated motion, from 2-D interface dominated at high ηs to bulk fluid-dependent at low ηs. The correlated motions can be scaled onto a master curve which captures the features of this transition. This master curve also characterizes the spatial dependence of the flow field of a viscous interface in response to a force. The scale factors used for the master curve allow for the calculation of the surface viscosity ηs that can be compared to one-particle measurements.PACS numbers: 83.10. Mj, 87.68.+z, 87.16.Dg Diffusion in three dimensions has been well understood since 1905, when two authors showed that the motion of particles suspended in a fluid is related to the fluid's viscosity [1,2]. This observation has been generalized in a technique called microrheology, which measures the thermal motion of tracer particles introduced in a viscoelastic material. From the motions of the particles, the material dependent properties can be determined, such as the elastic modulus, G ′ (ω), and the viscous modulus, G ′′ (ω) [3]. This has been applied to measure the viscoelasticity of bulk materials such as polymer solutions [4], biomaterials [5] and hydrogels [6]. A closely related question is the motion of tracer particles in a two-dimensional system such as lipid molecules at an air-water interface [7] or lipid rafts in cell membranes [8]. For example, in a purely viscous 2-D system, one might imagine that the diffusive properties are related to the two-dimensional viscosity, and that by following the motion of tracer particles one could determine this viscosity. However, in most cases of practical interest, a strictly two-dimensional surface is an idealization and in reality the surface is adjacent to three-dimensional fluid reservoirs. For example, recent experiments study diffusion in biological systems such as cell membranes [8,9] which are surrounding a 3-D cell and immersed in a 3-D fluid. This coupling modifies the behavior of tracer particles and makes interpretation of the results trickier [10,11,12].Furthermore, in many cases in 3D, tracers are known to modify the structure of the medium in their vicinity, leading to erroneous measurements of rheological quantities [13]. Another possibility is that pre-existing inhomogeneities such as pores in an otherwise rigid material can entrain the tracers, resulting in measurements that underestimate the bulk viscoelasticity of the material in question [5]. To overcome these difficulties, a new method known as two-particle microrheology has been established [13], which looks at the cross-correlated thermal motions of pairs of particles. The correlated motion of two beads is driven by long-wavelength modes in the system, and is therefore independent of the local environment of the tracers. While two-particle microrheology has been a...

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