Understanding transport of an elastic, spherical particle through a confining channel

Abstract

The transport of soft particles through narrow channels or pores is ubiquitous in biological systems and industrial processes. On many occasions, the particles deform and temporarily block the channel, inducing a built-up pressure. This pressure buildup often has a profound effect on the behavior of the respective system; yet, it is difficult to be characterized. In this work, we establish a quantitative correlation between the built-up pressure and the material and geometry properties through experiments and mechanics analysis. We fabricate microgels with a controlled diameter and elastic modulus by microfluidics. We then force them to individually pass through a constrictive or straight confining channel and monitor the pressure variation across the channel. To interpret the pressure measurement, we develop an analytical model based on the Neo-Hookean material law to quantify the dependence of the maximum built-up pressure on the radius ratio of the elastic sphere to the channel, the elastic modulus of the sphere, and two constant parameters in the friction constitutive law between the sphere and the channel wall. This model not only agrees very well with the experimental measurement conducted at large microgel deformation but also recovers the classical theory of contact at small deformation. Featuring a balance between accuracy and simplicity, our result could shed light on understanding various biological and engineering processes involving the passage of elastic particles through narrow channels or pores.

On the Determination of Mechanical Properties of Aqueous Microgels—Towards High-Throughput Characterization

“…Techniques exploiting squeezing of microgels in tapered microchannels, forcing them through constrictions or exposing the soft entities to fluid shear stress or elongational stress, one at a time, have been reported. In the case of microgels passing through constrictive microfluidic channels, several analytical mechanical models have been proposed [ 86 , 87 , 88 ] to define relations between the measured pressure, the radius ratio of the elastic sphere to the channel and the global elastic property of the microgels, thus underpinning the analysis of experimental observations. These models are limited to microfluidic channels with a diameter smaller than an unperturbed microgel size.…”

Highly tough and elastic microspheric gel for transarterial catheter embolization in treatment of liver metastasis tumor

“…Besides, spherical microgels are more likely to be trapped in the vasculature, which can help to block the flow of blood, so as to cause embolization. However, non-spherical particles may not be as effective at embolization, as they may not be able to effectively block the flow of blood [ 23 ].…”

Fabrications and Applications of Micro/Nanofluidics in Oil and Gas Recovery: A Comprehensive Review

“…A simple geometry, such as a capillary tube, can be used to analyze the transport of a particle. − Li et al synthesized a microgel with a controlled diameter and elastic modulus by microfluidics. They correlated the injection pressure and particle size, channel size and particle elasticity when a single microgel was transported in a straight confining channel . They also proposed a generalized capillary bundle model to quantitively study the injection pressure of the microgel .…”