## GIUSEPPE PROCOPIO

Dottore di ricerca**ciclo**: XXXV

**supervisore**: prof. Massimiliano Giona

**Titolo della tesi:**Hydrodynamic characterization of finite-sized particle transport in confined microfluidic systems, Brownian motion and stochastic modeling of particle transport at microscale.

In this thesis the peculiar effects of the hydrodynamic confinement on the dynamic
of a colloid in Stokes regime has been addressed theoretically. Practical expressions,
useful to investigate transport of particles in complex geometries, have been provided
for force, torque and higher order moments on the particle and the disturbed velocity
field of the fluid.
To begin with, a new formulation of the Stokesian singularity method is developed
by introducing a bitensorial distributional formalism. This formalism overcomes the
ambiguities of the classical hydrodynamic formulation of the singularity method
that limit its application in confined problems. The formalism proposed permits
naturally to distinguish between poles and field points of tensorial singular fields
and to clearly define each singularity from its associated Stokes problem, connecting
singularities each other.
As a consequence of this approach an explicit expression for the singularity
operator is provided, giving the disturbance field due to a body once applied to
an ambient flow of the fluid. The operator is expressed in terms of the volume
moments and its expression is valid regardless the boundary conditions applied to
the surface of the body. The dualism between the singularity operator giving the
disturbance flow of a n-th order ambient flow and the n-th order Faxén operator has
been investigated. It has been found that this dualism, referred to as the Hinch-Kim
dualism, holds only if the boundary conditions satisfy a property that is referred to
as the Boundary-Condition reciprocity (BC-reciprocity, for short). If this property is
fulfilled, the Faxén operators can be expressed in terms of (m, n)-th order geometrical
moments of volume forces (defined in the Chapter 3). In addition, it is shown that in
these cases, the hydromechanics of the fluid-body system is completely determined
by the entire system of the Faxén operators. Classical boundary conditions of
hydrodynamic practice (involving slippage, fluid-fluid interfaces, porous materials,
etc.) are investigated in the light of this property. It is found the analytical expression
for the 0-th, 1-st and 2-nd Faxén operators for a sphere with Navier-slip boundary
conditions.
These results are applied in order to express the hydrodynamics of particles in
confined fluids in terms of quantities related to the geometry of the particle and the
geometry of the confinement separately using the reflection method. Specifically,
closed-form results and practical expressions for the velocity field of the fluid and
for the functional form of force and torque acting on a particle are derived in terms
of: (i) the Faxén operators of the body of the particle (given by its unbounded
geometrical moments) and (ii) the multi-poles in the domain of the confinement. The
convergence of the reflection method is examined and it is found that the expressions
obtained are also valid for distance between particle and walls of the confinement
of the same magnitude order, failing only in the limit case of the lubrication range.
The reflection
solutions obtained with the present theory, approximated to the order
O(lb /ld )^5 , are compared with the exact solution of a sphere near a planar wall,
and the expressions for forces and torques considering the more general situation of
Navier-slip boundary conditions on the body are provided.
A general formulation of the fluctuation-dissipation relations in confined geome-
tries, the paradoxes associated with no-slip boundary conditions close to a solid
boundary, and the modal representation of the inertial kernels for complex fluids
complete the present dissertation.

**Produzione scientifica**

11573/1705086 - 2024 -

**Initial management approach for localized/locally advanced disease is critical to guide metastatic castration-resistant prostate cancer care**Conteduca, Vincenza; Di Tullio, Piergiorgio; Allamprese, Rossana; Bruno, Giuseppina; Lolli, Cristian; Schepisi, Giuseppe; Rosano, Aldo; Giordano, Guido; Garofoli, Marianna; Chiuri, Vincenzo Emanuele; Fratino, Lucia; Zanardi, Elisa; Galli, Luca; Massari, Francesco; Falagario, Ugo; Rescigno, Pasquale; Fornarini, Giuseppe; Sanguedolce, Francesca; Santini, Daniele; Procopio, Giuseppe; Caffo, Orazio; Carrieri, Giuseppe; Landriscina, Matteo; De Giorgi, Ugo - 01a Articolo in rivista

**rivista:**PROSTATE CANCER AND PROSTATIC DISEASES (-LONDON:NATURE PUBLISHING GROUP. -Basingstoke: Stockton Press.) pp. - - issn: 1365-7852 - wos: WOS:001161055500002 (1) - scopus: 2-s2.0-85184928462 (1)

11573/1700983 - 2024 -

**Another normality is possible. Distributive transformations and emergent Gaussianity**Giona, Massimiliano; Pezzotti, Chiara; Procopio, Giuseppe - 01a Articolo in rivista

**rivista:**PHYSICA. A (Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598) pp. - - issn: 0378-4371 - wos: WOS:001147767500001 (1) - scopus: 2-s2.0-85180534735 (1)

11573/1724164 - 2024 -

**On the Hinch–Kim dualism between singularity and Faxén operators in the hydromechanics of arbitrary bodies in Stokes flows**Procopio, Giuseppe; Giona, Massimiliano - 01a Articolo in rivista

**rivista:**PHYSICS OF FLUIDS (American Institute of Physics:2 Huntington Quadrangle, Suite 1NO1:Melville, NY 11747:(800)344-6902, (631)576-2287, EMAIL: subs@aip.org, INTERNET: http://www.aip.org, Fax: (516)349-9704) pp. - - issn: 1070-6631 - wos: WOS:001182753500025 (0) - scopus: 2-s2.0-85187959850 (0)

11573/1724166 - 2024 -

**Thermodynamics of Irreversible Processes: Fundamental Constraints, Representations, and Formulation of Boundary Conditions**Procopio, Giuseppe; Pezzotti, Chiara; Cocco, Davide; Giona, Massimiliano - 01a Articolo in rivista

**rivista:**PHYSICS (Basel: MDPI, [2018]-) pp. 801-827 - issn: 2624-8174 - wos: (0) - scopus: (0)

11573/1674390 - 2023 -

**The fourfold way to Gaussianity. Physical Interactions, distributional models and monadic transformations**Giona, Massimiliano; Pezzotti, Chiara; Procopio, Giuseppe - 01a Articolo in rivista

**rivista:**AXIOMS (Basel : MDPI) pp. - - issn: 2075-1680 - wos: WOS:000954077800001 (2) - scopus: 2-s2.0-85151149611 (3)

11573/1663502 - 2023 -

**New formulation of the Navier–Stokes equations for liquid flows**Giona, Massimiliano; Procopio, Giuseppe; Adrover, Alessandra; Mauri, Roberto - 01a Articolo in rivista

**rivista:**JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS (Walter de Gruyter and Company:Genthinerstrasse 13, D 10785 Berlin Germany:011 49 30 260050, EMAIL: customerservice@deguyter.de, INTERNET: http://www.degruyter.de/, Fax: 011 49 30 26005338) pp. - - issn: 0340-0204 - wos: WOS:000898090600001 (4) - scopus: 2-s2.0-85144769728 (4)

11573/1673088 - 2023 -

**Modal representation of inertial effects in fluid–particle interactions and the regularity of the memory kernels**Procopio, Giuseppe; Giona, Massimiliano - 01a Articolo in rivista

**rivista:**FLUIDS (Basel: MDPI AG, 2016-) pp. - - issn: 2311-5521 - wos: WOS:000959970200001 (4) - scopus: 2-s2.0-85151147775 (4)

11573/1622165 - 2022 -

**Hydrodynamic Green functions. Paradoxes in unsteady Stokes conditions and infinite propagation velocity in incompressible viscous models**Giona, Massimiliano; Procopio, Giuseppe; Mauri, Roberto - 01a Articolo in rivista

**rivista:**MECCANICA (Berlin, New York: Springer London ; Dordrecht ; Boston : Kluwer Academic Publishers Milano : Tamburini Milano : AIMETA) pp. - - issn: 0025-6455 - wos: WOS:000769835500001 (3) - scopus: 2-s2.0-85126380322 (3)

11573/1620522 - 2022 -

**Stochastic modeling of particle transport in confined geometries. Problems and peculiarities**Procopio, Giuseppe; Giona, Massimiliano - 01a Articolo in rivista

**rivista:**FLUIDS (Basel: MDPI AG, 2016-) pp. - - issn: 2311-5521 - wos: WOS:000775507300001 (4) - scopus: 2-s2.0-85126943557 (5)

11573/1651830 - 2022 -

**Bitensorial formulation of the singularity method for Stokes flows**Procopio, Giuseppe; Giona, Massimiliano - 01a Articolo in rivista

**rivista:**MATHEMATICS IN ENGINEERING (Springfield Missouri: AIMS Press, 2018-) pp. 1-34 - issn: 2640-3501 - wos: WOS:000842875400001 (1) - scopus: 2-s2.0-85136939112 (1)

11573/1615982 - 2022 -

**Inertia-induced breakdown of acoustic sorting efficiency at high flow rates**Undvall, Eva; Garofalo, Fabio; Procopio, Giuseppe; Qiu, Wei; Lenshof, Andreas; Laurell, Thomas; Baasch, Thierry - 01a Articolo in rivista

**rivista:**PHYSICAL REVIEW APPLIED (College Park, MD : American Physical Society, [2014-]) pp. - - issn: 2331-7019 - wos: WOS:000767547400005 (4) - scopus: 2-s2.0-85126648999 (5)

11573/1628885 - 2022 -

**Comparison between one- and two-way coupling approaches for estimating effective transport properties of suspended particles undergoing Brownian sieving hydrodynamic chromatography**Venditti, Claudia; Cerbelli, Stefano; Procopio, Giuseppe; Adrover, Alessandra - 01a Articolo in rivista

**rivista:**PHYSICS OF FLUIDS (American Institute of Physics:2 Huntington Quadrangle, Suite 1NO1:Melville, NY 11747:(800)344-6902, (631)576-2287, EMAIL: subs@aip.org, INTERNET: http://www.aip.org, Fax: (516)349-9704) pp. - - issn: 1070-6631 - wos: WOS:000790490000002 (8) - scopus: 2-s2.0-85128822571 (8)

11573/1571242 - 2021 -

**Generalized reflection method for the stokes equation in confined geometries. Applications to microfluidics and particle transport**Procopio, G.; Adrover, A.; Giona, M. - 01a Articolo in rivista

**rivista:**CHEMICAL ENGINEERING TRANSACTIONS (Milano : Sauro Pierucci Milano : AIDIC) pp. 1153-1158 - issn: 2283-9216 - wos: (0) - scopus: 2-s2.0-85109493809 (0)