Motion Of Capsule Research Articles

Deformation and sorting of capsules in a T-junction

We study experimentally the motion and deformation of individual capsules transported by a constant volume-flux flow of low Reynolds number, through the T-junction of a channel with rectangular cross-section. We use millimetric ovalbumin-alginate capsules which we manufacture and characterise independently of the flow experiment. Centred capsules travel at constant velocity down the straight channel leading to the T-junction where they decelerate and expand in the spanwise direction before turning into one of the two identical daughter channels. There, non-inertial lift forces act to re-centre them and relax their shape until they reach a steady state of propagation. We find that the dynamics of fixed-size capsules within our channel geometry are governed by a capillary number Ca defined as the ratio of viscous shear forces to elastic restoring forces. We quantify the elastic forces by statically compressing the capsule to 50% of its initial diameter between parallel plates rather than by the Young's modulus of the encapsulating membrane, in order to account for different membrane thickness, pre-inflation and non-linear elastic deformation. We show that the maximum extension in the T-junction of capsules of different stiffness collapses onto a master curve in Ca. Thus, it provides a sensitive measure of the relative stiffness of capsules at constant flow rate, particularly for softer capsules. We also find that the T-junction can sort fixed-size capsules according to their stiffness because the position in the T-junction from which capsules are entrained into the daughter channel depends uniquely on Ca. We demonstrate that a T-junction can be used as a sorting device by enhancing this initial capsule separation through a diffuser.

ДО ПИТАННЯ ПРО ГІДРОДИНАМІЧНИЙ ОПІР ПРИ РУСІ БРИКЕТУ У СЕРЕДОВИЩІ РІДИНИ ТА ГАЗУ

The problem of stabilizing and increasing the production of hydrocarbons is a topical issue today for most of the countries involved in oil and gas production. In order to reduce energy consumption in work on increasing productivity of oil and gas wells, the issues of intensification of hydrocarbon production due to the use of compact technologies, which involve increasing the productivity of the wells due to the supply of active chemreagents in the form of briquettes or capsules, are considered. As fillers, depending on the chosen type of well treatment technology, powder acids, surfactants, corrosion inhibitors, hydrate formation, salt deposition can be used. In the pump-compressor pipes, briquettes or capsules are fed to the outlet of the well, where the reagents they contain are activated and their or those physico-chemical technological processes of the intensification of the operation of the well-reservoir system are carried outThe effectiveness of the technological processes of compact technology depends not only on the presence and activity of chemical reagents on the well hole, but also on the sequence of introduction of briquettes or capsules into the well, and, to a large extent, from the time of their movement to the face.The motion of briquettes or capsules in the wellbore is explored, the formula for calculating the time of briquettes movement and the optimal geometric form of briquettes are determined. For technological operations using compact technology, it is recommended to use briquettes or capsules in the form of a cone with an angle at the apex of its axial section α = 30 °. As an example, the practical experience of introducing compact technology for the stabilization and increase of natural gas extraction in the deposits of Ukraine and the Republic of Poland through the removal of liquid from the faces of gas and gas condensate wells is provided by the use of conic shaped briquettes containing the surfactant. Key words: performance of wells, compact technology, surfactant, powdery acids inactive, corrosion inhibitors and saline deposition References AS USSR #1760095. 1992. Foam for removal of liquid from the bottom of the well. Svetlitsky VM, Balakirov Yu.A., Yagodovsky SI, Abramov Yu.D., Bantush V. Bull. # 33. (In Russian). AS USSR #1623293. Svetlitsky V.М., Balakirov Yu.A., Yagodovsky S.I., Ryabov Yu.G. The method of development of oil and gas wells. Not published (restricted). EgerO., Rybchych I.Y. 2003. Influence of the state of the filtration characteristics of the hinterland zone of multilayer layers on the efficiency of the development of oil and gas fields. Lviv. Liga-Press. 116 p. (In Ukrainian). Idelchik I.E. 2012. Handbook for hydraulic resistance. M. Book on Demand. 466 p. (In Russian). Kachmar Yu.D., Svetlitsky V.М. 2004. Intensity of the inflow of hydrocarbons in the well. Lviv: Center of Europe. 352 p. (In Ukrainian). Patent of Ukraine for Utility Model No 2017. Zelensky V.Yu., Krivulya S.V., Zelensky M.V., Yaschenko O., Yagodovsky S.I. Method of treatment of wells by the method of supplying chemical components on bottom. 25.04.2017 Bull. # 8. (In Ukrainian). Rabinovich E.Z. 1980. Hydraulics. M. Nedra. 278 p. (In Russian). Svetlitsky V.M., Yagodovsky S.I., Galustyan G.R. 2001. Current and overhaul of wells. K. Logos. 344 p. (In Ukrainian). Svetlitsky V.M., Yagodovsky S.I. 1998. Stimulating the operation of wellbore at the Junyuan oil and gas production fields. Kyiv. Logos. 43 p. (In Russian). Yagodovsky S.I., Balakirov Yu.A., Svetlitsky V.М. 1989. Removal of liquid from the bottoms of gas and gas condensate wells. In the book: Thermo-gas-dynamic processes and their control systems in exploration, transportation and production of oil and gas. Kharkiv. 167-171. (In Russian). Yaremiychuk R.S, Yaremiychuk Ya.S. 2007. Wells completion. Lviv: Center of Europe. 368 p. (In Ukrainian).

GLENOHUMERAL İNTERNAL ROTASYON DEFİSİTİ OLAN BİREYLERDE POSTERİOR KAPSÜL GERME EGZERSİZİNİN ANLIK ETKİSİNİN İNCELENMESİ

Purpose: To examine the immediate effect on joint position sense and range of motion of posterior capsule stretching exercise, which is recommended after glenohumeral internal rotation deficit (GIRD) that can be seen in healthy individuals. Methods: The study included 28 healthy individuals who met the inclusion criteria and were diagnosed with GIRD via goniometric measurements. In order to measure the joint position sense, the angle repetition test was performed using a laser pointer, and the range of motion (ROM) of the shoulder joints was measured via goniometer. After the measurements in both of the shoulders were completed, the posterior capsule stretching exercise was demonstrated for the extremity where the deficit was detected. After the exercise was completed, the measurements were repeated for both of the shoulders. The study included 28 healthy individuals who met the inclusion criteria and were diagnosed with GIRD via goniometric measurements. In order to measure the joint position sense, the angle repetition test was performed using a laser pointer, and the range of motion (ROM) of the shoulder joints was measured via goniometer. After the measurements in both of the shoulders were completed, the posterior capsule stretching exercise was demonstrated for the extremity where the deficit was detected. After the exercise was completed, the measurements were repeated for both of the shoulders. Results: At the end of the study, while no significant immediate change was found in joint position sense in the study group (p=0.28), significant immediate changes were determined in internal rotation (p=0.00), external rotation (p=0.021) and horizontal adduction ranges (p=0.003). Conclusion: GIRD is a condition that can be observed in healthy individuals. Posterior capsule stretching exercise immediately decreases the GIRD, but does not affect the joint position sense. The long-term effects can be examined in further studies.

Fluid-structure interaction problem of hydrodynamic motion of an independent escape capsule under variable constraint conditions

Abstract Hydrodynamic behavior of an independent escape capsule from a disabled submarine is a complex six-degrees-of-freedom motion, in which added-mass effect is strong and variable constraint conditions happen. In this paper, loosely (or weakly) coupled scheme is adopted to solve this fluid-structure interaction problem. Flow field is simulated by Fluent (version 13.0.1) and motion equations are solved by the fourth-order Runge-Kutta method separately. Unstructured dynamic mesh technology is used to trace the trajectory of capsule. Hydrodynamic force is decomposed into resistance and added mass force, and new motion equations are derived in order to handle the huge added mass. The surfaces of capsule and its chamber come into contact randomly. The variable constraint conditions are analyzed and their corresponding kinematical equations are introduced. This loosely coupled scheme is applied to study the hydrodynamic behavior of a two-dimensional capsule from a narrow space into an open domain under different ocean currents. Hydrodynamic force, motion characteristics and trajectory are obtained. The simulation indicates that the velocity and direction of flow strongly affect the motion of capsule, and the contact force leads to the jamming problem of capsule during its ejection process.

Injection of Deformable Capsules in a Reservoir: A Systematic Analysis

Motivated by red blood cell dynamics and injectable capsules for drug delivery, in this paper, a computational study of capsule ejection from a narrow channel into a reservoir is undertaken for a combination of varying deformable capsule sizes and channel dimensions. A mass-spring membrane model is coupled to an Immersed Boundary–Lattice Boltzmann model solver. The aim of the present work is the description of the capsules’ motion, deformation and the response of the fluid due to the complex particles’ dynamics. The interactions between the capsules affect the local velocity field and are responsible for the dynamics observed. Capsule membrane deformability is also seen to affect inter-capsule interaction. We observe that the train of three particles locally homogenises the velocity field and the leading capsule travels faster than the other two trailing capsules. Variations in the size of reservoir do not seem to be relevant, while the ratio of capsule diameter to channel diameter as well as the ratio of capsule diameter to inter-capsule spacing play a major role. This flow set-up has not been covered in the literature, and consequently we focus on describing capsule motion, membrane deformation and fluid dynamics, as a preliminary investigation in this field.

Understanding the motion of hard-shell capsules in dry powder inhalers.

The delivery of small drug particles from a dry powder inhaler (DPI) into the patient's peripheral airways requires the dispersion of the powder. In DPIs that contain a rotating pierced capsule, the capsule's motion is paramount to powder dispersion. Previous studies have simplified the capsule motion in an Aerolizer® inhaler as a constant rotation around a fixed center. The present work examines deviations from this simplified motion and describes the capsule collisions with the surrounding inhaler walls. High-speed photography was employed to analyze the motion of a size 3 capsule in an Aerolizer® inhaler at various flow rates ranging from 30 to 100 L/min. Frequent collisions of the capsule with the surrounding inhaler walls were observed. Computational fluid dynamics (CFD) simulations indicated that the air flow through the capsule governs the behavior of small drug particles, while inertial forces are the dominant influence on large carrier particles in the capsule. Discrete element method (DEM) simulations were employed to study the effect of the capsule-inhaler collisions on the powder discharge from a rotating capsule. The collisions vastly improved the discharge of a polydisperse model carrier powder from the capsule over a wide range of cohesiveness.

Experimental study of the wheeled capsule motion inside hydraulic pipeline

The wheeled capsule hydraulic transportation is a new technique for transporting materials. In this technique, the wheeled capsule, which is designed to contain materials, is one of the core compon...

Hydrogel micromotors with catalyst-containing liquid core and shell

Methacrylic anhydride-derived hydrogel microcapsules have unique properties, including reversibly tunable permeation, purification, and separation of dissolved molecular species. Endowing these dynamic encapsulant systems with autonomous motion will significantly enhance their efficiency and applicability. Here, hydrogel micromotors are realized using complex water-in-oil-in-water double emulsion drops and oil-in-water emulsion drops from glass capillary microfluidics and subsequent photopolymerization. Three hydrogel micromotor strategies are explored: microcapsules with thin shells and liquid cores with dispersed catalytic Pt nanoparticles, as well as water-cored microcapsules and homogeneous microparticles selectively coated with Ti/Pt catalytic layers. Autonomous motion of hydrogel particles and capsules is realized in hydrogen peroxide solutions, where generated oxygen microbubbles propel the dynamically responsive micromotors. The micromotors are balanced by weight, buoyancy, lateral capillary forces and show specific autonomous behaviours that significantly extend short range dynamic responses of hydrogels. Drop-based microfluidics represent a paradigm shift in the integration of multifunctional subsystems and high-throughput design of chemical micromachines in reasonable quantities towards their desired biomedical, environmental and flow/diffusion microreactor applications.

Numerical Investigation of Leukocyte Rolling, Adhesion and Bond Formation on Surface Coated with Varying P-Selectin Density

Leukocyte attraction towards the site of inflammation, is modulated by selectins expressed on activated endothelial cells. Scientists have studied the role of P-selectin in the progression of systemic disease in mice; the experimental results have shown that, deficiency of P-selectin results in failure to respond to an inflammation. P-selectin molecules have been shown to be a key contributor of leukocytes recruitment to sites of inflammation. To date, there are limited theoretical investigations of the effects of changes in P-selectin density on leukocytes rolling, tethering and adhesion. To address this, we have employed a 3D numerical model of an elastic capsule coated with P-selectin glycoprotein-1 (PSGL-1) molecules (representative of a leukocyte) to simulate its motion on a surface decorated with P-selectins under linear shear flow (Jadhav et. al, 2005). We utilized an immersed boundary method to solve the Stokes equation governing the motion of an elastic capsule near a plane wall. The capsule membrane is modeled using Mooney-Rivlin constitutive equation. The stochastic nature of the bond formation and breakage between P-selectin receptors and PSGL-1 ligands is simulated using Monte Carlo method, and the binding kinetics from the Bell model (Bell 1978). We have examined the effects of changes in P-selectin density (NR) on the leukocyte rolling velocity, average force per bond, leukocyte footprints on the substrate by varying NR from 30-150 μm−2 on the substrate. The results indicate that the average rolling velocity of a leukocyte decreased from 2.6 to 2.1 μm/s and the average force per bond decreased from 11.3 to 2.35 pN with increase in NR values. Correspondingly elevated stresses are shown by the leukocyte footprint at lower NR values. We are currently simulating PMN rolling on substrates with P-selectin patterns.

Path Selection of a Spherical Capsule in a Branched Channel

Capsules are liquid droplets enclosed by a thin membrane which can resist shear deformation. They are widely found in nature (e.g. red blood cells) and in numerous applications (e.g. food, cosmetic, biomedical and pharmaceutical industries [1]), where they often flow through a complicated network of tubes or channels: this is the case for RBCs in the human circulation or for artificial capsules flowing through microfluidic devices. Central to these flows is the dynamic motion of capsules at bifurcations, in particular the question of path selection. A good understanding of this problem is indeed needed to elucidate some intriguing phenomena in human circulation and to design multi-branched microfluidic devices to sort and enrich suspensions of artificial microcapsules or biological cells depending on their properties. <br/> Thanks to the extensive <i>in vivo</i> and in vitro experiments conducted on blood flows in branched capillaries and microchannels [2], it has been well established that the daughter branch with a higher flow rate receives a larger number of RBCs than the other branch: this is classically referred to as the Zweifach–Fung effect [3,4]. Similar phenomena have also been observed in experiments on suspensions, where the RBCs are modelled as flexible disks and the white blood cells as solid spheres [5], and in dilute suspensions of solid spheres [6]. This is a consequence of the plasma skimming effect due to the particle- free layer near the wall of the vessel [7] and of the particle screening effect due to the deviation of the particle trajectories from the background flow fluid streamlines as a result of the hydrodynamic interaction between the particles and vessel geometry at the bifurcation [8, 6]. <br/> In the dilute limit, the problem has, however, not been thoroughly studied experimentally, possibly due to the difficulty of manipulating individual cells. The problem has mostly been studied in recent years using two-dimensional numerical models [9, 10]. The results showed that, at equal flow rate between the two downstream channels, the capsule tends to flow into the side branch in particular when the capsule is highly deformable. But to what extent the results obtained from previous two-dimensional simulations can be applied to three-dimensional flows remains unclear. <br/> The objective of the present study is to conduct a systematic and in-depth three-dimensional numerical study of a deformable capsule in a branched tube and to determine the influence of inertia. Contrary to many biological systems, for which neglecting inertia is a good assumption, capsules are not necessarily small in size and the flow speed can be fast in some applications [11]. <br/> In the present work, we computationally study the motion of an initially spherical capsule flowing through a straight channel with an orthogonal lateral branch, using a three-dimensional immersed- boundary lattice Boltzmann method [12, 13]. Our primary focus is to study the influence of the geometry of the side branch on the capsule path selection. The capsule is enclosed by a strain-hardening membrane and contains an internal fluid of the same viscosity as the fluid in which it is suspended. It is initially centered on the axis of the feed channel. We impose the flow rate split ratio between the two downstream branches of the bifurcation. We analyze the reference cases wherein the side channel has the same cross- section as the main branch, and then compare the results to other geometries, in which the side branch has a half cross-sectional area as compared to the main branch. We consider different capsule-to-channel size ratio, flow Reynolds number (Re) and ratio of capillary to Reynolds numbers, and summarize the results in phase diagrams indicating the critical flow split ratio above which the capsule flows into the side branch. <br/> The capsule trajectory does not always obey the classical Fung's bifurcation law. For Re ≤ 5 and equal flow rate split between the two downstream branches, the capsule will enter a branch which is narrow in the spanwise direction, but will not enter a branch which is narrow in the flow direction. We show that this novel phenomenon results primarily from the background flow which is strongly influenced by the side branch cross-section geometry. For higher values of Re, the capsule relative size and deformability also play a specific role in the path selection: increasing the capillary number generally promotes cross-stream migration of the capsule towards the side branch. The present results obtained for dilute systems open new perspectives on the design of microfluidic systems with optimal channel geometries and flow conditions to enrich cell and particle suspensions.

Using multiple neutron time of flight detectors to determine the hot spot velocity.

An important diagnostic value of a shot at the National Ignition Facility is the resultant center-of-mass motion of the imploding capsule. This residual velocity reduces the efficiency of converting laser energy into plasma temperature. A new analysis method extracts the effective hot spot motion by using information from multiple neutron time-of-flight (nToF) lines-of-sight (LoSs). This technique fits a near Gaussian spectrum to the nToF scope traces and overcomes reliance on models to relate the plasma temperature to the mean energy of the emitted neutrons. This method requires having at least four nToF LoSs. The results of this analysis will be compared to an approach where each LoS is analyzed separately and a model is used to infer the mean energy of the emitted neutrons.

Ambulatory assessment of colonic motility using the electromagnetic capsule tracking system.

The Motilis 3D-Transit system tracks electromagnetic capsules as they traverse the gastrointestinal tract. The method is minimally invasive and ambulatory. Analysis has previously been limited to regional gut transit times, but new methods may allow detailed analysis of colonic motility. Parameters of colonic motility were analyzed from 34 3D-Transit recordings performed in healthy volunteers (median age 28years; 8 F). Characteristic propulsive velocities and lengths of movement were determined to quantify common movement patterns. Data from seven patients with severe chronic diarrhea were included for comparison. Lack of capsule motion accounted for 82% (75%-87%) of total colonic transit time. Propulsive velocities were distributed with peaks at 0.5cm/min (antegrade or retrograde) and 50cm/min (antegrade). Based on velocity and length of propagation, five motor patterns were identified; (a) long fast antegrade, (b) fast antegrade, (c) slow antegrade, (d) slow retrograde, and (e) fast retrograde movements. Long fast antegrade movements were median 21cm (10-96cm). Capsule progression was faster during daytime than at night (5.9cm/h vs 0.8cm/h; P<0.01). Colonic transit was faster in patients with chronic diarrhea than in healthy volunteers (5.4h vs 18.2h; P=0.04), with higher capsule velocity (20.4cm/h vs 4.4cm/h; P<0.01). The 3D-Transit system now allows detailed description of colonic motility and our results are supported by those previously suggested by manometry. It holds promise for future assessment of movement patterns to characterize different diseases and effects of treatment.

Floquet stability analysis of capsules in viscous shear flow

Observations in experiments and simulations show that the kinematic behaviour of an elastic capsule, suspended and rotating in shear flow, depends upon the flow strength, the capsule membrane material properties and its at-rest shape. We develop a linear stability description of the periodically rotating base state of this coupled system, as represented by a boundary integral flow formulation with spherical harmonic basis functions describing the elastic capsule geometry. This yields Floquet multipliers that classify the stability of the capsule motion for elastic capillary numbers $Ca$ ranging from $Ca=0.01$ to 5. Viscous dissipation rapidly damps most perturbations. However, for all cases, a single component grows or decays slowly, depending upon $Ca$, over many periods of the rotation. The transitions in this stability behaviour correspond to the different classes of rotating motion observed in previous studies.

Continuum and stochastic approach for cell adhesion process based on Eulerian fluid-capsule coupling with Lagrangian markers

This paper presents a novel development for a full Eulerian coupling method between a fluid and capsule with hyperelastic membrane to address a cell adhesion process. The capsule motion in the fluid field and their mechanical interactions are expressed in the Eulerian framework, while solving the capsule adhesion process by stochastic events of ligand-receptor bindings in a discrete level, with using Lagrangian markers distributed on the implicit surface of the capsule. In addition to this, numerical improvements of the full Eulerian method for calculating an interface normal vector and dealing with multiple capsules by introducing the temporarily constructed level set function. A numerical validity of the present development is investigated through a comparison with available numerical data in a validation problem, and a capability for the capsule adhesion is shown in a single capsule adhesion and platelet adhesion in a suspension with blood cells.

Electrophoretic Mobility of a Polyelectrolyte Capsule

The electrophoretic motion of a polyelectrolyte capsule has been considered in a uniform electric field. The capsule carries a uniformly distributed charge and is permeable to ions of different natures. An electrolyte identical to a dispersion medium is located inside the capsule. The flow in the porous layer of the capsule has been described by the Brinkman equations taking into account the effect of electrostatic forces. The distribution of ions in the vicinity of the capsule has been determined, and its electrophoretic mobility has been found in a linear approximation. The mobility of the capsule has been studied as depending on its geometric characteristics, permeability, and charge density. In particular, a complex extremal character of variations in the mobility as depending on the solid phase fraction in the capsule has been revealed at different ratios between the thicknesses of the electrical double layer and the Brinkman filtration layer.

Rotational Motion of Reentry Capsule induced in Subsonic Flow

Rotational Motion of Reentry Capsule induced in Subsonic Flow

A Locomotion Control Platform With Dynamic Electromagnetic Field for Active Capsule Endoscopy.

Conventional radiological and endoscopic techniques utilizing long tubes were ineffective in visualizing the small bowel mucosa until the development of wireless capsule endoscopy (WCE). WCE is a revolutionary endoscopic technology that can diagnose the complete gastrointestinal tract. However, the existing capsule technologies are passive, and thus they cannot be navigated to or held in a specific location. The design of an active capsule will present the opportunity to move and stop a device at any targeted locations leading to numerous medical applications such as drug delivery or collecting tissue samples for examinations in the laboratory. This paper implements a new locomotion methodology for WCE systems using an electromagnetic platform. The platform produces a dynamic electromagnetic field to control the motion of the capsule. The strength and the direction of the electromagnetic field that is generated by the platform are continuously adjusted in order to maintain the equilibrium state during the capsule movement. We present the detailed design of the proposed platform with an experimental setup with polyvinyl chloride tubes and ex vivo to demonstrate the performance of the capsule motion.

CHOBS: Color Histogram of Block Statistics for Automatic Bleeding Detection in Wireless Capsule Endoscopy Video.

Wireless capsule endoscopy (WCE) is the most advanced technology to visualize whole gastrointestinal (GI) tract in a non-invasive way. But the major disadvantage here, it takes long reviewing time, which is very laborious as continuous manual intervention is necessary. In order to reduce the burden of the clinician, in this paper, an automatic bleeding detection method for WCE video is proposed based on the color histogram of block statistics, namely CHOBS. A single pixel in WCE image may be distorted due to the capsule motion in the GI tract. Instead of considering individual pixel values, a block surrounding to that individual pixel is chosen for extracting local statistical features. By combining local block features of three different color planes of RGB color space, an index value is defined. A color histogram, which is extracted from those index values, provides distinguishable color texture feature. A feature reduction technique utilizing color histogram pattern and principal component analysis is proposed, which can drastically reduce the feature dimension. For bleeding zone detection, blocks are classified using extracted local features that do not incorporate any computational burden for feature extraction. From extensive experimentation on several WCE videos and 2300 images, which are collected from a publicly available database, a very satisfactory bleeding frame and zone detection performance is achieved in comparison to that obtained by some of the existing methods. In the case of bleeding frame detection, the accuracy, sensitivity, and specificity obtained from proposed method are 97.85%, 99.47%, and 99.15%, respectively, and in the case of bleeding zone detection, 95.75% of precision is achieved. The proposed method offers not only low feature dimension but also highly satisfactory bleeding detection performance, which even can effectively detect bleeding frame and zone in a continuous WCE video data.

Hydrodynamic mobility of a solid particle near 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 toward shearing and bending. Together with the results obtained in the first part [Daddi-Moussa-Ider and Gekle, Phys. Rev. E 95, 013108 (2017)2470-004510.1103/PhysRevE.95.013108], 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 nonvanishing resistance toward shearing. We further compute the 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.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: 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 nonvanishing resistance toward 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.