1,721,124 research outputs found
Hydrodynamic characterization of finite-sized particle transport in confined microfluidic systems, Brownian motion and stochastic modeling of particle transport at microscale
Full text linkIn this thesis, the peculiar effects of the hydrodynamic confinement on the dynamic of a colloid in the Stokes regime have been addressed theoretically. Practical expressions, useful to investigate the transport of particles in complex geometries, have been provided for force, torque and higher order moments on the particle and for 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 limits its application in confined problems.
The formalism proposed permits naturally to distinguish between pole and field points of tensorial singular fields and to clearly define each singularity from its associated Stokes problem.
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 of 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 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 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 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 distances 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 ("lb" being the characteristic size of the body and "ld" the characteristic distance from the confinement boundaries) 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 geometries, 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.
Specifically, the general setting of the overdamped approximation in confined geometries is provided, by explicitly expressing the thermal contributions associated with the rigid rototranslational motion of a body. In passing, the extension of fluctuation-dissipation results to non-equilibrium conditions, such as those arising in thermophoretic flows in the presence of a steady temperature profile is developed.
The influence of boundary conditions on the fluctuational form of the force acting on a rigid particle near a solid wall is addressed, showing that the classical Stokesian paradox of infinite touching time in the presence of no-slip boundary conditions can be resolved by considering the arbitrarily small slippage effects on both surfaces, leading to an integrable logarithmic singularity.
Finally, a preliminary extension of fluid-particle interactions either in a time-dependent Stokes regime or in the presence of complex (viscoelastic) flows is addressed, focusing on the modal representation of the dissipative and fluid inertial memory kernels, and on the fluctional form of the latter.
Specifically, it is shown that for a viscoelastic fluid, characterized by a finite and non-vanishing relaxation rate, the generalized Basset kernel is a regular function of time, also close to t=0, which is not the case of a Newtonian fluid for which the Basset kernel scales inversely with the square root of t
Bitensorial formulation of the singularity method for Stokes flows
Full text linkThis paper develops the bitensorial formulation of the system of singularities associated with unbounded and bounded Stokes flows. The motivation for this extension is that Stokesian singularities and hydrodynamic fundamental solutions are multi-point functions, and bitensor calculus provides either the proper geometrical setting, in order to avoid inconsistencies and misunderstandings on the role of the different tensorial indices, or a way for compactly deriving hydrodynamic properties. A first relevant result is to provide a clear definition of the singularities (both bounded and unbounded) in Stokes flow, specifying the associated differential equations and boundary conditions. Using this formalism for bounded flows, we show the existence of an integro-differential operator providing the whole system of hydrodynamic singularities by acting on the unbounded Green function (Stokeslet) at its pole and we derive its explicit representation in terms of moments. In the case of an immersed body in a unbounded fluid, we show that, the operator furnishing the disturbance field of a purely -th order ambient flow, is a generalized -th order Faxén operator, i.e., it yields the -th moment on the body if applied to a generic ambient flow, and that a generic disturbance field can be expressed by a summation of the generalized -th order Faxén operators. Furthermore, we find that the operator providing the disturbance of an ambient flow coincides with the reflection operator for the Stokes solutions in the same flow geometry. We apply this result to the paradigmatic case of fundamental singularities for the Stokes flow bounded by a plane. In this way, we obtain in an alternative and easy way the image system for the Sourcelet and the Rotlet (already derived in the literature) and for the Source Doublet and the Strainlet (presented here for the first time)
On the Hinch–Kim dualism between singularity and Faxén operators in the hydromechanics of arbitrary bodies in Stokes flows
No full textWe generalize the multipole expansion and the structure of the Faxen operator in Stokes flows obtained for bodies with no-slip to generic boundary conditions, addressing the assumptions under which this generalization is conceivable. We show that a disturbance field generated by a body immersed in an ambient flow can be expressed, independently on the boundary conditions, as a multipole expansion, the coefficients of which are the moments of the volume forces. We find that the dualism between the operator giving the disturbance field of an nth order ambient flow and the nth order Faxen operator, referred to as the Hinch-Kim dualism, holds only if the boundary conditions satisfy a property that we call Boundary-Condition reciprocity (BC-reciprocity). If this property is fulfilled, the Faxen operators can be expressed in terms of the (m, n)th order geometrical moments of the volume forces (defined in the article). In addition, it is shown that in these cases, the hydromechanics of the fluid-body system is completely determined by the entire set of the Faxen operators. Finally, classical boundary conditions of hydrodynamic applications are investigated in light of this property: boundary conditions for rigid bodies, Newtonian drops at the mechanical equilibrium, porous bodies modeled by the Brinkman equations are BC-reciprocal, while deforming linear elastic bodies, deforming Newtonian drops, non-Newtonian drops, and porous bodies modeled by the Darcy equations do not have this property. For Navier-slip boundary conditions on a rigid body, we find the analytical expression for low order Faxen operators. By using these operators, the closed form expressions for the flow past a sphere with arbitrary slip length immersed in shear and quadratic flows are obtained
Another normality is possible. Distributive transformations and emergent Gaussianity
No full textA distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations (CMT) in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism characterizing the application of Central Limit Theorem, as it is based on the iteration of a random transformation preserving the ensemble variance. Gaussianity emerges as a “supergeneric” property of ensemble statistics, in the case the energy constraint is quadratic in the norm of the variables. This result puts in a different light the occurrence of equilibrium Gaussian distributions in kinetic variables (velocity, momentum), as it shows mathematically that, in the absence of any other dynamic mechanisms, almost Gaussian distributions stem from the low-velocity approximations of the physical conservation principles. Whenever, the energy constraint is not expressed in terms of quadratic functions non-Gaussian distributions arise. This is case of relativistic collisional interactions where the Jüttner distribution is recovered from CMT
Hydrodynamic Green functions. Paradoxes in unsteady Stokes conditions and infinite propagation velocity in incompressible viscous models
Full text linkWe present a simple representation of the hydrodynamic Green functions grounded on the free propagation of a vector field without any constraints (such as incompressibility) coupled with a gradient gauge in order to enforce these constraints. This approach involves the solution of two scalar problems: a couple of Poisson equations in the case of the Stokes regime, and a system of diffusion/Poisson equations for unsteady Stokes flows. The explicit and closed-form expression of the Green function for unsteady Stokes flow is developed. The relevance of this approach resides in its conceptual simplicity and it enables us to focus on the intrinsic singularities (Stokesian paradoxes) associated with the propagation of the stresses in incompressible flows under unsteady Stokes conditions, determining the occurrence of power-law tails in the velocity profile arbitrarily far away from the location of the impulsive force
Stochastic modeling of particle transport in confined geometries. Problems and peculiarities
Full text linkThe equivalence between parabolic transport equations for solute concentrations and stochastic dynamics for solute particle motion represents one of the most fertile correspondences in statistical physics originating from the work by Einstein on Brownian motion. In this article, we analyze the problems and the peculiarities of the stochastic equations of motion in microfluidic confined systems. The presence of solid boundaries leads to tensorial hydrodynamic coefficients (hydrodynamic resistance matrix) that depend also on the particle position. Singularity issues, originating from the non-integrable divergence of the entries of the resistance matrix near a solid no-slip boundary, determine some mass-transport paradoxes whenever surface phenomena, such as surface chemical reactions at the walls, are considered. These problems can be overcome by considering the occurrence of non vanishing slippage. Added-mass effects and the influence of fluid inertia in confined geometries are also briefly addressed
Comparison between one- and two-way coupling approaches for estimating effective transport properties of suspended particles undergoing Brownian sieving hydrodynamic chromatography
No full textSimplified one-way coupling approaches are often used to model transport properties of diluted particle suspensions for predicting the performance of microcapillary hydrodynamic chromatography (MHDC). Recently, a one-way coupling approach was exploited to optimize the geometry and operating conditions of an unconventional double-channel geometry with a square cross-section, where a Brownian sieving mechanism acting alongside the MHDC separation drive (BS-MHDC) is enforced to boost separation resolution. In this article, a cylindrical geometry enforcing the same BS-MHDC separation drive is thoroughly investigated by following a two-way coupling, fully three-dimensional approach, and results are compared with those obtained enforcing the one-way coupling analysis. Device geometry and operating conditions are optimized by maximizing the separation resolution. The effective velocity and dispersion coefficient of spherical, finite-sized particles of different diameters are computed, and two-phase effects are discussed in detail. Similar to the square channel device, the cylindrical double-channel geometry allows for a sizable reduction in the column length and in the analysis time (a factor above 12 for the length and a factor larger than 3 for the processing time) when compared to the standard MHDC configuration ensuring the same separation resolution. As expected, the one-way coupling approach overestimates the separation performance of both the BS-MHDC and the standard MHDC devices with respect to the two-way coupling analysis. But, surprisingly, the enhancement factor of the BS-MHDC over the standard MHDC is underestimated by the single-phase approximation as it doubles when wall/particle interactions are properly accounted for with a two-phase description
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Thermodynamics of Irreversible Processes: Fundamental Constraints, Representations, and Formulation of Boundary Conditions
No full textStarting from the analysis of the lack of positivity of the Cattaneo heat equation, this work addresses the thermodynamic relevance of the positivity constraint in irreversible thermodynamics, that is at least as significant as the entropic constraints. The fulfillment of this condition in hyperbolic models leads to the parametrization of the concentration fields with respect to internal variables associated with the microscopic dynamics. Using Brownian motion theory as a landmark example for deriving macroscopic transport equations from the equations of motion at the particle/molecular level, we discuss two typical problems involving hydrodynamic interactions at the microscale: surface chemical reactions at a solid interface of a diffusing reactant, and mass-balance equations in a complex viscoelastic fluid, in which the physics of the interaction leads either to overcoming the parabolic diffusion model or to considering the parametrization of the concentration with respect to the degrees of freedom associated with the relaxation dynamics of the solvent fluid
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