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Rheological characterization of non-Brownian suspensions based on structure kinetics

Kurian J. Vachaparambil (Department of Mechanics, Kungliga Tekniska Högskolan, Stockholm, Sweden)
Gustaf Mårtensson (Electronics Material and Systems Laboratory, Department of Microtechnology and Nanoscience, Chalmers Tekniska Högskola, Gothenburg, Sweden)
Lars Essén (Mycronic AB, Täby, Sweden)

Soldering & Surface Mount Technology

ISSN: 0954-0911

Article publication date: 9 January 2018

Issue publication date: 23 January 2018



The purpose of the paper is to develop a methodology to characterize the rheological behaviour of macroscopic non-Brownian suspensions, like solder paste, based on microstructural evolution.


A structure-based kinetics model, whose parameters are derived analytically based on assumptions valid for any macroscopic suspension, is developed to describe the rheological behaviour of a given fluid. The values of the parameters are then determined based on experiments conducted at a constant shear rate. The parameter values, obtained from the model, are then adjusted using an optimization algorithm using the mean deviation from experiments as the cost function to replicate the measured rheology. A commercially available solder paste is used as the test fluid for the proposed method.


The initial parameter values obtained through the analytical model indicates a structural breakdown that is much slower than observations. But optimizing the parameter values, especially the ones associated with the structural breakdown, replicates the thixotropic behaviour of the solder paste reasonably well, but it fails to capture the structure build-up during the three interval thixotropy test.

Research limitations/implications

The structural kinetics model tends to under-predict the structure build-up rate.

Practical implications

This study details a more realistic prediction of the rheological behaviour of macroscopic suspensions like solder paste, thermal interface materials and other functional materials. The proposed model can be used to characterize different solder pastes and other functional fluids based on the structure build-up and breakdown rates. The model can also be used as the viscosity definitions in numerical simulations instead of simpler models like Carreau–Yasuda and cross-viscosity models.


The rheological description of the solder paste is critical in determining its validity for a given application. The methodology described in the paper provides a better description of thixotropy without relying on the existing rheological measurements or the behaviour predicted by a standard power-law model. The proposed model can also provide transient viscosity predictions when shear rates vary in time.



Vachaparambil, K.J., Mårtensson, G. and Essén, L. (2020), "Rheological characterization of non-Brownian suspensions based on structure kinetics", Soldering & Surface Mount Technology, Vol. 30 No. 1, pp. 57-64.



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