English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we derive the closed form analytical solutions for theeffective viscosity of the suspensions of solid spheres that take into accountthe size effects. This result is obtained using the solution for the effectiveshear modulus of particulate composites developed in the framework of thestrain gradient elasticity theory. Assuming incompressibility of matrix andrigid behavior of particles and using a mathematical analogy between the theoryof elasticity and the theory of viscous fluids we derive the generalizedEinstein's formula for the effective viscosity. Generalized Brinkman's solutionfor the concentrated suspensions is derived then using differential method.Obtained solutions contain single additional length scale parameter, which canbe related to the interactions between base liquid and solid particles in thesuspensions. In the case of the large ratio the between diameter of particlesand the length scale parameter, developed solutions reduce to the classicalsolutions, however for the small relative diameter of particles an increase ofthe effective viscosity is predicted. It is shown that developed models agreewell with known experimental data. Solutions for the fibrous suspensions arealso derived and validated.

Generalized Einstein's and Brinkman's solutions for the effective viscosity of nanofluids