
Paolo Malgaretti- Mensch
- Team Leader at Forschungszentrum Jülich
Paolo Malgaretti
- Mensch
- Team Leader at Forschungszentrum Jülich
About
122
Publications
15,820
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,546
Citations
Introduction
My research focuses on the dynamics of complex fluids. More in detail, I am interested in transport phenomena in inhomogenus systems such as porous materials and multi disperse suspensions. Recently, I have focused on the coupling between local chemical reactions and the transport phenomena that they can induce; this novel field embraces diverse systems spanning from the nanometric range of ionic fluids up to the micrometric scale of colloids and macromolecules.
Current institution
Additional affiliations
January 2014 - present
September 2007 - December 2013
Publications
Publications (122)
Janus colloidal particles show remarkable properties in terms of surface activity, self-assembly and wetting. Moreover they can perform autonomous motion if they can chemically react with the liquid in which they are immersed.
In order to understand the self-propelled motion of catalytic Janus colloids at the air-water interface, wetting and the o...
We show that when particles are suspended in an electrolyte confined between
corrugated charged surfaces, electrokinetic flows lead to a new set of
phenomena such as particle separation, mixing for low-Reynolds micro- and
nano-metric devices and negative mobility. Our analysis shows that such
phenomena arise, for incompressible fluids, due to the i...
We study the translocation of polymers across varying-section channels. Using systematic approximations, we derive a simplified model that reduces the problem of polymer translocation through varying-section channels to that of a point-like particle under the action of an effective potential. Such a model allows us to identify the relevant paramete...
Assembly and stability of mitotic spindle is governed by the interplay of various intra-cellular forces, e.g. the forces generated by motor proteins by sliding overlapping anti-parallel microtubules (MTs) polymerized from the opposite centrosomes, the interaction of kinetochores with MTs, and the interaction of MTs with the chromosomes arms. We stu...
We study the dynamics of a quantum particle in a constricted two-dimensional channel and analyze how the onset of quantum corrections impacts the (semi-)classical high-temperature behaviour, as temperature is lowered. We characterize both equilibrium and non-equilibrium (transport) properties of the system, considering the case of a narrow and diso...
We characterize the electrokinetic flow due to the transport of electrolytes embedded in nanochannels of varying cross section with inhomogeneous slip on their walls, modeled as an effective slip length on the channel wall. We show that, within linear response and Debye–Hückel regime, the transport coefficients, and so the fluxes, can be significan...
We characterize the electrokinetic flow due to the transport of electrolytes embedded in nanochannels of varying cross-section with inhomogeneous slip on their walls, modeled as an effective slip length on the channel wall. We show that, within linear response and Debye-Huckel regime, the transport coefficients, and so the fluxes, can be significan...
In this work, we compare the structural and dynamic behavior of active filaments in two dimensions using tangential and push–pull models, including a variant with passive end monomers, to bridge the two frameworks. These models serve as valuable frameworks for understanding self-organization in biological polymers and synthetic materials. At low ac...
Catalyst particles or complexes suspended in liquid films can trigger chemical reactions leading to inhomogeneous concentrations of reactants and products in the film. It is demonstrated that the sensitivity of the liquid film's gas–liquid surface tension to these inhomogeneous concentrations strongly impacts the film stability. Using linear stabil...
Liquid films of nanometric thickness are prone to spinodal dewetting driven by disjoining pressure, meaning that a non-wetting liquid film of homogeneous thickness in the range of tens of nanometers will spontaneously break into droplets. The surface energy of the underlying solid substrate heavily influences the dynamics and resulting droplet conf...
The stability of particle assemblies is strongly affected by particle shape, yet definitive laws describing key properties, such as the mean contact number and apparent friction coefficient, remain elusive. Using X-ray computed tomography and discrete element simulations, we study 70 assemblies of 3D frictional particles. Once properly rescaled, ou...
Liquid phase (scanning) transmission electron microscopy (LP-(S)TEM) enables exploring processes down to the nanoscale. This allows to unravel degradation pathways of electrocatalysts, such as silver nanostructures, which gained attention for CO 2 upconversion. However, the nanoscale resolution in LP-TEM comes at the cost of introducing new effects...
We present an analytical and computational study characterizing the structural and dynamical properties of an active filament confined in cylindrical channels. We first outline the effects of the interplay between confinement and polar self-propulsion on the conformation of the chains. We observe that the scaling of the polymer size in the channel,...
We develop a semi-analytical model for transport in structured catalytic microreactors, where both reactant and product are compressible fluids. Using lubrication and Fick–Jacobs approximations, we reduce the three-dimensional governing equations to an effective one-dimensional set of equations. Our model captures the effect of compressibility, cor...
We propose the generalization of the thin film equation (TFE) to arbitrarily many immiscible liquid layers. Then, we provide different pathways for deriving the hydrodynamic pressure within the individual layers, showing how to understand the equation as a Cahn-Hilliard-type conservation equation and providing an algorithm to derive the associated...
The release of hydrogen from liquid organic hydrogen carriers (LOHC) takes place in an endothermal dehydrogenation reaction that is accompanied by a strong volume expansion. This leads to complex hydrodynamic properties that change drastically along the reactor axis due to product gas evolution. Consequently, heat transfer into the catalytic fixed-...
We employ a lattice Boltzmann method to compute the acoustic radiation force produced by standing waves on a compressible object for the density matched case. Instead of simulating the fluid mechanics equations directly, the proposed method uses a lattice Boltzmann model that reproduces the wave equation, together with a kernel interpolation scheme...
Bacterial aggregation process is usually considered as a step prior to adhesion to a surface for the biofilm establishment. However, the formation of clusters that remain in suspension has already been described as a third microbial lifestyle. Pseudomonas extremaustralis 2E-UNGS is a microorganism native to the contaminated Reconquista River, Argen...
We develop a semi-analytical model for transport in structured catalytic microreactors, where both reactant and product are compressible fluids. Making use of the lubrication and Fick-Jacobs approximations, we reduce the three-dimensional governing equations to an effective one-dimensional set of equations. Our model captures the effect of compress...
We investigate the formation and transport of gas bubbles across a model porous electrode/catalyst using lattice Boltzmann simulations. This approach enables us to systematically examine the influence of a wide range of morphologies, flow velocities, and reaction rates on the efficiency of gas production. By exploring these parameters, we identify...
We investigate the formation and transport of gas bubbles across a model porous catalyst/electrode using lattice Boltz-mann simulations. This approach enables us to systematically examine the influence of a wide range of morphologies, flow velocities, and reaction rates on the efficiency of gas production. By exploring these parameters, we identify...
We determine the local charge dynamics of a $$z-z$$ z - z electrolyte embedded in a varying-section channel. By means of an expansion based on the length scale separation between the axial and transverse direction of the channel, we derive closed formulas for the local excess charge for both, dielectric and conducting walls, in 2 D (planar geometry...
Liquid-phase transmission electron microscopy (LP-TEM) is a powerful tool to gain unique insights into dynamics at the nanoscale. The electron probe, however, can induce significant beam effects that often alter observed phenomena such as radiolysis of the aqueous phase. The magnitude of beam-induced radiolysis can be assessed by means of radiation...
We develop a semi-analytical model of self-diffusioosmotic transport in active pores, which includes advective transport and the inverse chemical reaction that consumes solute. In previous work [Antunes et al., Phys. Rev. Lett. 129, 188003 (2022)], we have demonstrated the existence of a spontaneous symmetry breaking in fore-aft symmetric pores tha...
Polymers confined in corrugated channels, i.e., channels of varying amplitude, display multiple local maxima and minima of the diffusion coefficient upon increasing their degree of polymerization N. We propose a theoretical effective free energy for linear polymers based on a Fick-Jacobs approach. We validate the predictions against numerical data,...
Collective systems self-organize to form globally ordered spatiotemporal patterns. Finding appropriate measures to characterize the order in these patterns will contribute to our understanding of the principles of self-organization in all collective systems. Here we examine a new measure based on the entropy of the neighbor distance distributions i...
We develop a semi-analytical model of self-diffusioosmotic transport in active pores, which includes advective transport and the inverse chemical reaction which consumes solute. In previous work (Phys. Rev. Lett. 129, 188003, 2022), we have demonstrated the existence of a spontaneous symmetry breaking in fore-aft symmetric pores that enables them t...
In many practically important problems which rely on particles' transport
in realistic corrugated channels, one is interested to know
the probability that either of the extremities, (e.g., the one containing a chemically active site, or connected to a broader
channel),
is reached before the other one. In mathematical literature, the latter are ca...
Polymers confined in corrugated channels, i.e. channels of of varying amplitude, display, upon increasing their degree of polymerization $N$, a non-monotonic behavior in the diffusion coefficient. We propose a theoretical effective free energy for linear polymers based on a Fick-Jacobs approach. We validate the predictions against numerical data, o...
The response of Newtonian liquids to small perturbations is usually considered to be fully described by homogeneous transport coefficients like shear and dilatational viscosity. However, the presence of strong density gradients at the liquid/vapor boundary of fluids hints at the possible existence of an inhomogeneous viscosity. Here, we show that a...
In the last decade, the Fick–Jacobs approximation has been exploited to capture transport across constrictions. Here, we review the derivation of the Fick–Jacobs equation with particular emphasis on its linear response regime. We show that, for fore-aft symmetric channels, the flux of noninteracting systems is fully captured by its linear response...
The response of Newtonian liquids to small perturbations is usually considered to be fully described by homogeneous transport coefficients like shear and dilatational viscosity. However, the presence of strong density gradients at the liquid/vapor boundary of fluids hints at the possible existence of an inhomogeneous viscosity. Here, we show that a...
Hypothesis:
The applicability of the dynamic light scattering method for the determination of particle diffusivity under confinement without applying refractive index matching was not adequately explored so far. The confinement effect on particle diffusion in a porous material which is relevant for particle chromatography has also not yet been ful...
In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested to know the probability that either of the extremities, (e.g., the one containing a chemically active site, or connected to a broader channel), is reached before the other one. In mathematical literature, the latter are call...
In the last decade the Fick-Jacobs approximation has been exploited to capture the transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show that for fore-aft symmetric channels the flux of non-interacting systems is fully captured by its linear respons...
Electroosmosis is a fascinating effect where liquid motion is induced by an applied electric field. Counter ions accumulate in the vicinity of charged surfaces, triggering a coupling between liquid mass transport and external electric field. In nanofluidic technologies, where surfaces play an exacerbated role, electroosmosis is thus of primary impo...
Rolling is a ubiquitous transport mode utilized by living organisms and engineered systems. However, rolling at the microscale has been constrained by the requirement of a physical boundary to break the spatial homogeneity of surrounding mediums, which limits its prospects for navigation to locations with no boundaries. Here, in the absence of real...
The out of equilibrium nature of active systems can be exploited for the design of information-based engines. We design two types of an active Szilard engine that use a Maxwell demon to extract work from an active bath composed of noninteracting active Brownian particles. The two engines exploit either the quasistatic active pressure of active Brow...
The observable reaction rate of heterogeneously catalyzed reactions is known to be limited either by the intrinsic kinetics of the catalytic transformation or by the rate of pore and/or film diffusion. Here, we show that in gas generation reactions from liquid reactants, the nucleation of gas bubbles in the catalyst pore structure represents an add...
Accurate modeling of diffusive transport of nanoparticles across nanopores is a particularly challenging problem. The reason is that for such narrow pores the large surface-to-volume ratio amplifies the relevance of the nanoscopic details and of the effective interactions at the interface with pore walls. Close to the pore wall, there is no clear s...
The molecular structure of moving contact lines (MCLs) and the emergence of a corresponding macroscopic dissipation have made the MCL a paradigm of fluid dynamics. Through novel averaging techniques that remove capillary waves smearing we achieve an unprecedented resolution in molecular dynamics (MD) simulations and find that they match with the co...
Accurate modeling of diffusive transport of nanoparticles across nanopores is a particularly challenging problem. The reason is that for such narrow pores the large surface-to-volume ratio amplifies the relevance of the nanoscopic details and of the effective interactions at the interface with pore walls. Close to the pore wall, there is no clear s...
We show both numerically and analytically that a chemically patterned active pore can act as a micro- or nanopump for fluids, even if it is fore-aft symmetric. This is possible due to a spontaneous symmetry breaking which occurs when advection rather than diffusion is the dominant mechanism of solute transport. We further demonstrate that, for pump...
The molecular structure of moving contact lines (MCLs) and the emergence of a corresponding macroscopic dissipation have made the MCL a paradigm of fluid dynamics. Through novel averaging techniques that remove capillary waves smearing we achieve an unprecedented resolution in molecular dynamics simulations and find that they match with the continu...
Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field o...
Rolling is a ubiquitous mode of transport utilized by both living organisms and engineered systems. Rolling, on the microscale, has become particularly interesting for the manipulation of microswarms, since enacting such motion does not require special prefabrication techniques. However, rolling motion has to date been restricted by the need for a...
The out of equilibrium nature of active systems can be exploited for the design of information-based engines. We design two types of an active Szilard engine that use a Maxwell daemon to extract work from an active bath composed of non-interacting Active Brownian Particles (ABPs). The two engines exploit either the quasi-static active pressure of A...
We show both numerically and analytically that a chemically patterned active pore can act as a micro/nano-pump for fluids, even if it is fore-aft symmetric. This is possible due to a spontaneous symmetry breaking which occurs when advection rather than diffusion is the dominant mechanism of solute transport. We further demonstrate that, for pumping...
We present guidelines to estimate the effect of electrostatic repulsion in sedimenting dilute particle suspensions. Our results are based on combined Langevin dynamics and lattice Boltzmann simulations for a range of particle radii, Debye lengths and particle concentrations. They show a simple relationship between the slope K of the concentration-d...
The performance of a single or the collection of microswimmers strongly depends on the hydrodynamic coupling among their constituents and themselves. We present a numerical study for a single and a pair of microswimmers based on lattice Boltzmann method (LBM) simulations. Our numerical algorithm consists of two separable parts. Lagrange polynomials...
Microscopic swarms consisting of, e.g., active colloidal particles or microorganisms, display emergent behaviors not seen in equilibrium systems. They represent an emerging field of research that generates both fundamental scientific interest and practical technological value. This review seeks to unite the perspective of fundamental active matter...
The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules hampers the ability of these systems to serve as model systems for further exploring the links between inform...
The dynamics of colloidal suspension confined within porous materials strongly differs from that in the bulk. In particular, within porous materials, the presence of boundaries with complex shapes entangles the longitudinal and transverse degrees of freedom inducing a coupling between the transport of the suspension and the density inhomogeneities...
Electroosmosis is a fascinating effect where liquid motion is induced by an applied electric field. Counter ions accumulate in the vicinity of charged surfaces, triggering a coupling between liquid mass transport and external electric field. In nanofluidic technologies, where surfaces play an exacerbated role, electroosmosis is thus of primary impo...
HYPOTHESIS
The dynamics of colloidal suspension confined within porous materials strongly differs from that in the bulk. In particular, within porous materials, the presence of boundaries with complex shapes entangles the longitudinal and transverse degrees of freedom inducing a coupling between the transport of the suspension and the density inhom...
The active motion of phoretic colloids leads them to accumulate at boundaries and interfaces. Such an excess accumulation, with respect to their passive counterparts, makes the dynamics of phoretic colloids particularly sensitive to the presence of boundaries and pave new routes to externally control their single particle as well as collective beha...
The active motion of phoretic colloids leads them to accumulate at boundaries and interfaces. Such an excess accumulation, with respect to their passive counterparts, makes the dynamics of phoretic colloids particularly sensitive to the presence of boundaries and pave new routes to externally control their single particle as well as collective beha...
We derive an analytic expression for the mechanical pressure of a generic one -imensional model of confined active Brownian particles (ABPs) that is valid for all values of Péclet number Pe and all confining scenarios. Our model reproduces the known scaling of bulk pressure with Pe2 while in strong confinement pressure scales with Pe. Our analytic...
We report on the onset of anti-resonant behaviour of mass transport systems driven by time-dependent forces. Anti-resonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an anti-resonance, is typical of con...
We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confine...
We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that the their behaviour depends crucially on their size: short rings ($N \lesssim$ 100) are swelled whereas longer rings ($N \gtrsim$ 200) collapse, at sufficiently high activity. By investigating the non-equilibrium process leading to the stea...
We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that their behavior depends crucially on their size: Short rings (N≲100) swell, whereas longer rings (N≳200) collapse, at sufficiently high activity. By investigating the nonequilibrium process leading to the steady state, we find a universal ro...
Separation is an important process in various fields in science and technology, and nano-structures are now being widely used to improve the resolution and speed of separation processes. Continuous separation occurs when the components of a mixture separate at different locations in a device; this makes it possible to inject a new sample into the d...
We study the dynamics of neutral and charged rods embedded in varying-section channels. By means of systematic approximations, we derive the dependence of the local diffusion coefficient on both the geometry and charge of the rods. This microscopic insight allows us to provide predictions for the permeability of varying-section channels to rods wit...
Collective dynamics of confined colloids is crucial in diverse scenarios such as self-assembly and phase behavior in materials science, microrobot swarms for drug delivery, and microfluidic control. Yet, fine-tuning the dynamics of colloids in microscale confined spaces is still a formidable task due to the complexity of the dynamics of colloidal s...
We study the dependence of the surface tension of a fluid interface on the density profile of a third suspended phase. By means of an approximated model for the binary mixture and of a perturbative approach, we derive closed-form expressions for the free energy of the system and for the surface tension of the interface. Our results show a remarkabl...
We study the dynamics of neutral and charged rods embedded in varying-section channels. By means of systematic approximations, we derive the dependence of the local diffusion coefficient on both the geometry and charge of the rods. This microscopic insight allows us to provide predictions for the permeability of varying-section channels to rods wit...
We study the dependence of the surface tension of a fluid interface on the density profile of a third suspended phase. By means of an approximated model for the binary mixture and of a perturbative approach we derive close formulas for the free energy of the system and for the surface tension of the interface. Our results show a remarkable non-mono...
We derive an analytic expression for the mechanical pressure of a generic one-dimensional model of confined active Brownian particles (ABPs) that is valid for all values of Peclet number Pe and all confining scenarios. Our model reproduces the known scaling of bulk pressure with Pe^2 while in strong confinement pressure scales with Pe. Our analytic...
The dynamics of active colloids is very sensitive to the presence of boundaries and interfaces which therefore can be used to control their motion. Here we analyze the dynamics of active colloids adsorbed at a fluid-fluid interface. By using a mesoscopic numerical approach which relies on an approximated numerical solution of the Navier-Stokes equa...
The dynamics of active colloids is very sensitive to the presence of boundaries and interfaces which therefore can be used to control their motion. Here we analyze the dynamics of active colloids adsorbed at a fluid-fluid interface. By using a mesoscopic numerical approach which relies on an approximated numerical solution of the Navier-Stokes equa...
We characterize the dynamics of a z − z electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated with externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We s...
We characterize the dynamics of a $z-z$ electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated to externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We sho...
Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time-scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocati...
Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocati...
We study the dynamics and conformation of polymers composed by active monomers. By means of Brownian dynamics simulations we show that, when the direction of the self-propulsion of each monomer is aligned with the backbone, the polymer undergoes a coil-to-globulelike transition, highlighted by a marked change of the scaling exponent of the gyration...
We analyze the dynamics of a tracer particle embedded in a bath of hard spheres confined in a channel of varying section. By means of Brownian dynamics simulations, we apply a constant force on the tracer particle and discuss the dependence of its mobility on the relative magnitude of the external force with respect to the entropic force induced by...
We characterize the dynamics of an electrolyte embedded in a varying-section channel under the action of a constant external electrostatic field. By means of molecular dynamics simulations we determine the stationary density, charge and velocity profiles of the electrolyte. Our results show that when the Debye length is comparable to the width of t...
We characterize the dynamics of an electrolyte embedded in a varying-section channel under the action of a constant external electrostatic field. By means of molecular dynamics simulations we determine the stationary density, charge and velocity profiles of the electrolyte. Our results show that when the Debye length is comparable to the width of t...
We analyze the dynamics of a tracer particle embedded in a bath of hard spheres confined in a channel of varying section. By means of Brownian dynamics simulations we apply a constant force on the tracer particle and discuss the dependence of its mobility on the relative magnitude of the external force with respect to the entropic force induced by...
In this work, we study the constitutive behavior of interacting colloidal suspensions for moderate and high concentrations. Specifically, using a lattice Boltzmann solver, we numerically examine suspensions flowing through narrow channels, and explore the significance of the interaction potential strength on the system's macroscopic response. When...
We study the dynamics and conformation of polymers composed by active monomers. By means of Brownian dynamics simulations we show that when the direction of the self-propulsion of each monomer is aligned with the backbone, the polymer undergoes a coil-to-globule-like transition, highlighted by a marked change of the scaling exponent of the gyration...
The influence of a fluid-fluid interface on self-phoresis of chemically active, axially symmetric, spherical colloids is analyzed. Distinct from the studies of self-phoresis for colloids trapped at fluid interfaces or in the vicinity of hard walls, here we focus on the issue of self-phoresis close to a fluid-fluid interface. In order to provide phy...
The influence of a fluid-fluid interface on self-phoresis of chemically active, axially symmetric, spherical colloids is analyzed. Distinct from the studies of self-phoresis for colloids trapped at fluid interfaces or in the vicinity of hard walls, here we focus on the issue of self-phoresis close to a fluid-fluid interface. In order to provide phy...
We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motors displacement can induce the experimentally observed bidirec-tional motion of cargoes and vesicles. By means of a mean-field approach we show that sustained oscillations as well as bistable collective motor motion arise ev...
We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium the local pressure is a functional of the shape of the walls. It is shown that, due to the intrinsic non-local character of the interactions among the particles forming the flu...
We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium the local pressure is a functional of the shape of the walls. It is shown that, due to the intrinsic non-local character of the interactions among the particles forming the flu...
We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motors displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean--field approach we show that sustained oscillations as well as bistable collective motor motion arise ev...
Wetting properties of a substrate are mostly evaluated through the contact angle of droplets on these substrates, a method that works perfectly for a broad range of cases. However, in specific cases it might be difficult to macroscopically measure the contact angle and our experiments show that the behaviour of active colloids when approaching edge...
We study different types of microswimmers moving in channels with varying cross section and
thereby interacting hydrodynamically with the channel walls. Starting from the Smoluchowski equa-
tion for a dilute suspension, for which interactions among swimmers can be neglected, we derive
analytic expressions for the lateral probability distribution...