India, December 20, 2025

Mathematical modeling of complex fluids and flows involves
applying mathematical and computational techniques to
understand the behavior of fluids exhibiting non-Newtonian
and/or multi-phase characteristics. Examples of such fluids
include suspensions, emulsions, polymers, and biological
fluids.

Description:

 

Mathematical modeling of complex fluids and flows involves  

applying mathematical and computational techniques to  

understand the behavior of fluids exhibiting non-Newtonian  

and/or multi-phase characteristics. Examples of such fluids  

include suspensions, emulsions, polymers, and biological  

fluids. The complexity of these systems arises from the  

interaction of multiple components—such as particles,  

droplets, or macromolecules—as well as their non-linear and  

often time-dependent rheological properties. 

 

To model complex fluids and flows a variety of mathematical  

approaches are employed. Continuum-based methods such as the  

Navier–Stokes equations describe the macroscopic behavior of  

fluids while discrete methods such as molecular dynamics and  

Monte Carlo simulations explore the interactions at a  

microscopic level. These techniques allow researchers to  

investigate how individual interactions collectively  

influence macroscopic properties like viscosity, elasticity,  

and yield stress. Moreover, numerical simulations are  

increasingly used to predict and optimize complex fluid  

behavior in applications spanning microfluidics,  

pharmaceuticals, food processing, and the oil and gas  

industry. Insights gained from these simulations help in  

designing efficient and effective processing strategies for  

handling complex fluids in practical systems.