arXiv subjects

Abdallah Daddi-Moussa-Ider

Publications and source records attributed to Abdallah Daddi-Moussa-Ider.

At least 55 records · Page 3Linked to original sources

arXiv2019

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: implications for the hydrodynamics of an active microswimmer near an elastic interface

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future biomedical and technological applications. These microswimmers move autonomously through aqueous media where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than to shear resistance. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

physics.flu-dyn↗

arXiv2019

Creeping motion of a solid particle inside a spherical elastic cavity. II. Asymmetric motion

An analytical method is proposed for computing the low-Reynolds-number hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with resistance toward shear and bending. In conjunction with the results obtained in the first part [Daddi-Moussa-Ider, Löwen, and Gekle, Eur. Phys. J. E 41, 104 (2018)], in which the axisymmetric motion normal to the surface of an elastic cavity is investigated, the general motion for an arbitrary force direction can be addressed. The elastohydrodynamic problem is formulated and solved using the classic method of images through expressing the hydrodynamic flow fields as a multipole expansion involving higher-order derivatives of the free-space Green's function. In the quasi-steady limit, we demonstrate that the particle self-mobility function of a particle moving tangent to the surface of the cavity is larger than that predicted inside a rigid stationary cavity of equal size. This difference is justified by the fact that a stationary rigid cavity introduces additional hindrance to the translational motion of the encapsulated particle, resulting in a reduction of its hydrodynamic mobility. Furthermore, the motion of the cavity is investigated, revealing that the translational pair (composite) mobility, which linearly couples the velocity of the elastic cavity to the force exerted on the solid particle, is solely determined by membrane shear properties. Our analytical predictions are favorably compared with fully-resolved computer simulations based on a completed-double-layer boundary integral method.

physics.flu-dyn↗

arXiv2019

Axisymmetric flow due to a Stokeslet near a finite-sized elastic membrane

Elastic confinements play an important role in many soft matter systems and affect the transport properties of suspended particles in viscous flow. On the basis of low-Reynolds-number hydrodynamics, we present an analytical theory of the axisymmetric flow induced by a point-force singularity (Stokeslet) directed along the symmetry axis of a finite-sized circular elastic membrane endowed with resistance toward shear and bending. The solution for the viscous incompressible flow surrounding the membrane is formulated as a mixed boundary value problem, which is then reduced into a system of dual integral equations on the inner and outer sides of the domain boundary. We show that the solution of the elastohydrodynamic problem can conveniently be expressed in terms of a set of inhomogeneous Fredholm integral equations of the second kind with logarithmic kernel. Basing on the hydrodynamic flow field, we obtain semi-analytical expressions of the hydrodynamic mobility function for the translational motion perpendicular to a circular membrane. The results are valid to leading-order in the ratio of particle radius to the distance separating the particle from the membrane. In the quasi-steady limit, we find that the particle mobility near a finite-sized membrane is always larger than that predicted near a no-slip disk of the same size. We further show that the bending-related contribution to the hydrodynamic mobility increases monotonically upon decreasing the membrane size, whereas the shear-related contribution displays a minimum value when the particle-membrane distance is equal to the membrane radius. Accordingly, the system behavior may be shear or bending dominated, depending on the geometric and elastic properties of the system. Our results may find applications in the field of nanoparticle-based sensing and drug delivery systems near elastic cell membranes.

physics.flu-dyn↗

arXiv2019

Membrane penetration and trapping of an active particle

The interaction between nano- or micro-sized particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the particles can pass through cell membranes via passive endocytosis or by active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical particle (moving through an effective constant active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the active particle may either get trapped near the membrane or penetrates through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing to accurately predict most of our results analytically. This analytical theory helps identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microparticles to lipid bilayers. Our results might be useful to predict mechanical properties of synthetic minimal membranes.

cond-mat.soft↗

arXiv2018

Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal

Several recent experiments investigate the orientational and transport behavior of self-driven bacteria and colloidal particles in nematic liquid crystals. Correspondingly, we study theoretically the dynamics of a minimal model microswimmer in a uniaxially anisotropic fluid. As a first step, the hydrodynamic Green's function providing the resulting fluid flow in response to a localized force acting on the anisotropic fluid is derived analytically. On this basis, the behavior of both puller- and pusher-type microswimmers in the anisotropic fluid is analyzed. Depending on the propulsion mechanism and the relative magnitude of different involved viscosities, we find alignment of the swimmers parallel or perpendicular to the anisotropy axis. Particularly, also an oblique alignment is identified under certain circumstances. The observed swimmer reorientation results from the hydrodynamic coupling between the self-induced fluid flow and the anisotropy of the surrounding fluid, which distorts the self-generated flow field. We support parts of our results by a simplified linear stability analysis. Our theoretical predictions are in qualitative agreement with recent experimental observations on swimming bacteria in nematic liquid crystals. They support the objective of utilizing the, possibly switchable, anisotropy of a host fluid to guide individual microswimmers and active particles along a requested path, enabling controlled active transport.

cond-mat.soft↗

arXiv2018

Creeping motion of a solid particle inside a spherical elastic cavity

On the basis of the linear hydrodynamic equations, we present an analytical theory for the low-Reynolds-number motion of a solid particle moving inside a larger spherical elastic cavity which can be seen as a model system for a fluid vesicle. In the particular situation where the particle is concentric with the cavity, we use the stream function technique to find exact analytical solutions of the fluid motion equations on both sides of the elastic cavity. In this particular situation, we find that the solution of the hydrodynamic equations is solely determined by membrane shear properties and that bending does not play a role. For an arbitrary position of the solid particle within the spherical cavity, we employ the image solution technique to compute the axisymmetric flow field induced by a point force (Stokeslet). We then obtain analytical expressions of the leading order mobility function describing the fluid-mediated hydrodynamic interactions between the particle and confining elastic cavity. In the quasi-steady limit of vanishing frequency, we find that the particle self-mobility function is higher than that predicted inside a rigid no-slip cavity. Considering the cavity motion, we find that the pair-mobility function is determined only by membrane shear properties. Our analytical predictions are supplemented and validated by fully-resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied forcing frequencies.

physics.flu-dyn↗

arXiv2018

Hydrodynamic coupling and rotational mobilities near planar elastic membranes

We study theoretically and numerically the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance towards shear and bending. Using a combination of the multipole expansion and Faxen's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities, and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency, we find that the shear- and bending-related contributions to the particle mobilities may have additive or suppressive effects depending on the membrane properties in addition to the geometric configuration of the interacting particles relative to the confining membrane. To elucidate the effect and role of the change of sign observed in the particle self and pair mobilities, we consider an example involving a torque-free doublet of counterrotating particles near an elastic membrane. We find that the induced rotation rate of the doublet around its center of mass may differ in magnitude and direction depending on the membrane shear and bending properties. Near a membrane of only energetic resistance toward shear deformation, such as that of a certain type of elastic capsules, the doublet undergoes rotation of the same sense as observed near a no-slip wall. Near a membrane of only energetic resistance toward bending, such as that of a fluid vesicle, we find a reversed sense of rotation. Our analytical predictions are supplemented and compared with fully resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied frequencies.

physics.flu-dyn↗

arXiv2018

State diagram of a three-sphere microswimmer in a channel

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.

physics.flu-dyn↗

arXiv2018

A reciprocal theorem for the prediction of the normal force induced on a particle translating parallel to an elastic membrane

When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift mechanism occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry induced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach proceeds through the application of the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely-extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely-large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cut-off length beyond which the bending forces become subdominant to an external body force.

physics.flu-dyn↗

arXiv2018

Swimming trajectories of a three-sphere microswimmer near a wall

The hydrodynamic flow field generated by self-propelled active particles and swimming microorganisms is strongly altered by the presence of nearby boundaries in a viscous flow. Using a simple model three-linked sphere swimmer, we show that the swimming trajectories near a no-slip wall reveal various scenarios of motion depending on the initial orientation and the distance separating the swimmer from the wall. We find that the swimmer can either be trapped by the wall, completely escape, or perform an oscillatory gliding motion at a constant mean height above the wall. Using a far-field approximation, we find that, at leading order, the wall-induced correction has a source-dipolar or quadrupolar flow structure where the translational and angular velocities of the swimmer decay as inverse third and fourth powers with distance from the wall, respectively. The resulting equations of motion for the trajectories and the relevant order parameters fully characterize the transition between the states and allow for an accurate description of the swimming behavior near a wall. We demonstrate that the transition between the trapping and oscillatory gliding states is first order discontinuous, whereas the transition between the trapping and escaping states is continuous, characterized by non-trivial scaling exponents of the order parameters. In order to model the circular motion of flagellated bacteria near solid interfaces, we further assume that the spheres can undergo rotational motion around the swimming axis. We show that the general three-dimensional motion can be mapped onto a quasi-two-dimensional representational model by an appropriate redefinition of the order parameters governing the transition between the swimming states.

physics.flu-dyn↗

arXiv2017

Brownian motion near an elastic cell membrane: A theoretical study

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.

cond-mat.soft↗

arXiv2017

Hydrodynamic mobility of a sphere moving on the centerline of an elastic tube

Elastic channels are an important component of many soft matter systems, in which hydrodynamic interactions with confining membranes determine the behavior of particles in flow. In this work, we derive analytical expressions for the Green's functions associated to a point-force (Stokeslet) directed parallel or perpendicular to the axis of an elastic cylindrical channel exhibiting resistance against shear and bending. We then compute the leading order self- and pair mobility functions of particles on the cylinder axis, finding that the mobilities are primarily determined by membrane shear and that bending does not play a significant role. In the quasi-steady limit of vanishing frequency, the particle self- and pair mobilities near a no-slip hard cylinder are recovered only if the membrane possesses a non-vanishing shear rigidity. We further compute the membrane deformation, finding that deformation is generally more pronounced in the axial (radial) directions, for the motion along (perpendicular) to the cylinder centerline, respectively. Our analytical calculations for the Green's functions in an elastic cylinder can serve as a fundamental building block for future studies and are verified by fully resolved boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗

arXiv2017

Slow rotation of a spherical particle inside an elastic tube

In this paper, we present an analytical calculation of the rotational mobility functions of a particle rotating on the centerline of an elastic cylindrical tube whose membrane exhibits resistance towards shearing and bending. We find that the correction to the particle rotational mobility about the cylinder axis depends solely on membrane shearing properties while both shearing and bending manifest themselves for the rotational mobility about an axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing frequency, the particle rotational mobility nearby a no-slip rigid cylinder is recovered only if the membrane possesses a non-vanishing resistance towards shearing. We further show that for the asymmetric rotation along the cylinder radial axis, a coupling between shearing and bending exists. Our analytical predictions are compared and validated with corresponding boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗

arXiv2017

Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. II. Asymmetric motion

In this paper, we derive analytical expressions for the leading-order hydrodynamic mobility of a small solid particle undergoing motion tangential to a nearby large spherical capsule whose membrane possesses resistance towards shearing and bending. Together with the results obtained in the first part (Daddi-Moussa-Ider and Gekle, Phys. Rev. E {\bfseries 95}, 013108 (2017)) where the axisymmetric motion perpendicular to the capsule membrane is considered, the solution of the general mobility problem is thus determined. We find that shearing resistance induces a low-frequency peak in the particle self-mobility, resulting from the membrane normal displacement in the same way, although less pronounced, to what has been observed for the axisymmetric motion. In the zero frequency limit, the self-mobility correction near a hard sphere is recovered only if the membrane has a non-vanishing resistance towards shearing. We further compute the particle in-plane mean-square displacement of a nearby diffusing particle, finding that the membrane induces a long-lasting subdiffusive regime. Considering capsule motion, we find that the correction to the pair-mobility function is solely determined by membrane shearing properties. Our analytical calculations are compared and validated with fully resolved boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗

arXiv2016

Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. I. Axisymmetric motion

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a non-vanishing resistance towards shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗

arXiv2016

Mobility of an axisymmetric particle near an elastic interface

Using a fully analytical theory, we compute the leading order corrections to the translational, rotational and translation-rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an elastic cell membrane that exhibits resistance towards stretching and bending. The frequency-dependent mobility corrections are expressed as general relations involving separately the particle's shape-dependent bulk mobility and the shape-independent parameters such as the membrane-particle distance, the particle orientation and the characteristic frequencies associated with shearing and bending of the membrane. This makes the equations applicable to an arbitrary-shaped axisymmetric particle provided that its bulk mobilities are known, either analytically or numerically. For a spheroidal particle, these general relations reduce to simple expressions in terms of the particle's eccentricity. We find that the corrections to the translation-rotation coupling mobility are primarily determined by bending, whereas shearing manifests itself in a more pronounced way in the rotational mobility. We demonstrate the validity of the analytical approximations by a detailed comparison with boundary integral simulations of a truly extended spheroidal particle. They are found to be in a good agreement over the whole range of applied frequencies.

physics.flu-dyn↗

arXiv2016

Hydrodynamic interaction between particles near elastic interfaces

We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the finite particle size up to the 5th order in the ratio between particle diameter and wall distance as well as between diameter and interparticle distance. We find that particle motion towards a membrane with pure bending resistance always leads to mutual repulsion similar as in the well-known case of a hard-wall. In the vicinity of a membrane with shearing resistance, however, we observe an attractive interaction in a certain parameter range which is in contrast to the behavior near a hard wall. This attraction might facilitate surface chemical reactions. Furthermore, we show that there exists a frequency range in which the pair-mobility for perpendicular motion exceeds its bulk value, leading to short-lived superdiffusive behavior. Using the analytical particle mobilities we compute collective and relative diffusion coefficients. The appropriateness of the approximations in our analytical results is demonstrated by corresponding boundary integral simulations which are in excellent agreement with the theoretical predictions.

physics.flu-dyn↗

arXiv2016

Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation

We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuation-dissipation theorem we compute the Brownian motion of the particle, finding a long-lasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed point-particle approximation via boundary-integral simulations for a truly extended particle. They are found to be in excellent agreement with the analytical predictions.

physics.flu-dyn↗