Aim and scope
Heterogeneous systems (HS) are ubiquitous in nature and are made
of dissimilar parts which make nonuniform the physical properties
of the system. The aim of the project is the development of multi-scale
mathematical models to characterize their mechanical, thermal,
and chemical behavior into a unified framework allowing to understand
the main features of systems and predict the effects of microscopic
interactions on transport processes and macroscopic behaviors.
Multi-scale models will be tackled based on an interdisciplinary
analytical and numerical approach with a supporting experimental
activity. The proposed research topics require sophisticated
mathematical techniques that will take strong advantage of the
diverse scientific background and expertise of the research units
involved in this proposal.
The project
MMHS
focuses on topics mainly related to biological and bio-inspired applications.
It is structured into four research lines (suspensions and granular systems,
models for fluid and solid components in HS, smart materials, and microscopic
dynamical models for HS) with
different intimately interconnected objectives.
As for the first two lines we will consider multiphase systems, i.e., HS
in which single-phase regions are separated by an interface. Examples are
dispersed multiphase systems which are characterized by finite particles,
drops or bubbles, distributed in a region of continuous phase. In particular
we will study suspensions, i.e., dispersed multiphase systems where solid
particles mixed to a fluid component stay suspended throughout the fluid,
and one of our goals will be the study of the rheology of blood, which is
an example of dense suspension of deformable cells of different kind, also
artificial as in the case of applications of medical interest.
The third line concerns materials, including biological soft materials,
with nonuniform microscopic physical properties. Heterogeneity is, indeed,
a tool commonly adopted in Nature and based on evolutionary optimization,
that delivers incredible macroscopic behaviors starting from material
properties at the lowest scales. For example, in typical protein materials,
we observe at the macromolecular scale the existence of complex architectures
of hard (folded and linked) regions immersed in soft domains with a typical
entropic regulated elasticity, often joined to a multi-scale hierarchical
material design. We will study the complex
energetic exchanges between the different components and scales to deduce
how these materials can show their incredible stability, adaptation and
healing properties unreached by artificial materials. In this framework,
relying also on microscopic dynamical models (fourth line), we will
investigate how the presence of irregularities affects currents of
particles pushed through
the HS and, conversely, how moving particles affect the structure
of the material, e.g., in the context of polymer gels which morph
and shape-shift by liquid transport.
