arXiv subjects

Ali Gürbüz

Publications and source records attributed to Ali Gürbüz.

5 recordsLinked to original sources

arXiv2026

Effects of surface viscosities on the motion of a droplet enclosing a translating particle

We investigate the influence of interfacial rheology on the motion of a compound particle consisting of a viscous droplet enclosing a translating rigid particle in the Stokes flow regime. The droplet interface is modeled using the Boussinesq-Scriven constitutive law, incorporating both surface shear and dilatational viscosities. An exact analytical solution is derived for the concentric configuration, and the analysis is extended to eccentric geometries using a spectral boundary integral method, enabling a systematic examination of confinement, viscosity contrast, and interfacial properties. For concentric configurations, we show that the induced droplet velocity is independent of surface shear viscosity, while surface dilatational viscosity can either enhance or suppress the droplet motion depending on the interplay between confinement and viscosity ratio. This behavior is rationalized in terms of competing effects between reduced interfacial mobility and increased driving force required to maintain the prescribed particle speed. In contrast, when the particle is eccentrically positioned within the droplet, a dependence on surface shear viscosity emerges, leading to a consistent enhancement of droplet motion that becomes more pronounced with increasing eccentricity. The analytical and numerical results are in excellent agreement and reveal how interfacial rheology, confinement, and symmetry breaking jointly govern the dynamics of compound particle systems. These findings provide mechanistic insight and establish a quantitative benchmark for future studies of active compound particles with complex interfaces.

physics.flu-dyn↗

arXiv2026

Collinear Swimming of a Squirmer Pair in Newtonian and Shear-Thinning Fluids

Pairwise hydrodynamic interactions of microswimmers form the fundamental building blocks for understanding their more complex collective behaviors. In this work, we revisit the canonical problem of two interacting squirmers swimming along their common line of centers in both Newtonian and shear-thinning fluids. For the Newtonian case, we first derive an exact, closed-form solution for the axisymmetric Stokes flow generated by the interacting pair, thereby complementing prior analyses based on the reciprocal theorem approach by providing direct access to the detailed knowledge of the flow around the swimmers. The analytical solution is then used to cross-validate numerical simulations based on the finite element method. The combined theoretical and numerical investigation reveals co-swimming configurations in which the two squirmers develop identical velocities over a range of separations. We rationalize these behaviors through symmetry arguments and quantify their propulsion performance in terms of the speed and energetic cost of swimming. Furthermore, motivated by the prevalence of shear-thinning biological fluids encountered by microswimmers, we examine how this ubiquitous non-Newtonian rheological behavior modifies the propulsion characteristics of these co-swimming pairs. Taken together, our results establish quantitative benchmarks for interacting squirmers in both Newtonian and shear-thinning fluids, laying the groundwork for future studies of many-body dynamics of microswimmers in complex fluid environments.

physics.flu-dyn↗

arXiv2024

Propulsion of a three-sphere micro-robot in a porous medium

Microorganisms and synthetic microswimmers often encounter complex environments consisting of networks of obstacles embedded into viscous fluids. Such settings include biological media, such as mucus with filamentous networks, as well as environmental scenarios, including wet soil and aquifers. A fundamental question in studying their locomotion is how the impermeability of these porous media impact their propulsion performance compared with the case that in a purely viscous fluid. Previous studies showed that the additional resistance due to the embedded obstacles leads to an enhanced propulsion of different types of swimmers, including undulatory swimmers, helical swimmers, and squirmers. In this work we employ a canonical three-sphere swimmer model to probe the impact of propulsion in porous media. The Brinkman equation is utilized to model a sparse network of stationary obstacles embedded into an incompressible Newtonian liquid. We present both a far-field theory and numerical simulations to characterize the propulsion performance of the swimmer in such porous media. In contrast to enhanced propulsion observed in other swimmer models, our results reveal that both the propulsion speed and efficiency of the three-sphere swimmer are largely reduced by the impermeability of the porous medium. We attribute the substantial reduction in propulsion performance to the screened hydrodynamic interactions among the spheres due to the more rapid spatial decays of flows in Brinkman media. These results highlight how enhanced or hindered propulsion in porous media is largely dependent on individual propulsion mechanisms. The specific example and physical insights provided here may guide the design of synthetic microswimmers for effective locomotion in porous media in their potential biological and environmental applications.

physics.flu-dyn↗

arXiv2023

The effect of axisymmetric confinement on propulsion of a three-sphere microswimmer

Swimming at the microscale has recently garnered substantial attention due to the fundamental biological significance of swimming microorganisms and the wide range of biomedical applications for artificial microswimmers. These microswimmers invariably find themselves surrounded by different confining boundaries, which can impact their locomotion in significant and diverse ways. In this work, we employ a widely used three-sphere swimmer model to investigate the effect of confinement on swimming at low Reynolds numbers. We conduct theoretical analysis via the point-particle approximation and numerical simulations based on the finite element method to examine the motion of the swimmer along the centerline in a capillary tube. The axisymmetric configuration reduces the motion to one-dimensional movement, which allows us to quantify how the degree of confinement affects the propulsion speed in a simple manner. Our results show that the confinement does not significantly affect the propulsion speed until the ratio of the radius of the tube to the radius of the sphere is in the range of $\mathcal{O}(1)-\mathcal{O}(10)$, where the swimmer undergoes substantial reduction in its propulsion speed as the radius of the tube decreases. We provide some physical insights into how reduced hydrodynamic interactions between moving spheres under confinement may hinder the propulsion of the three-sphere swimmer. We also remark that the reduced propulsion performance stands in stark contrast to the enhanced helical propulsion observed in a capillary tube, highlighting how the manifestation of confinement effects can vary qualitatively depending on the propulsion mechanisms employed by the swimmers.

physics.flu-dyn↗

arXiv2021

Fully Implicit Spectral Boundary Integral Computation of Red Blood Cell Flow

An approach is presented for implicit time integration in computations of red blood cell flow by a spectral boundary integral method. The flow of a red cell in ambient fluid is represented as a boundary integral equation (BIE), whose structure is that of an implicit ordinary differential equation (IODE). The cell configuration and velocity field are discretized with spherical harmonics. The IODE is integrated in time using a multi-step implicit method based on backward difference formulas, with variable order and adaptive time-stepping controlled by local truncation error and convergence of Newton iterations. Jacobians of the IODE, required for Newton's method, are implemented as Jacobian matrix-vector products that are nothing but directional derivatives. Their computation is facilitated by the weakly singular format of the BIE, and these matrix-vector products themselves amount to computing a second BIE. Numerical examples show that larger time steps are possible and that the number of matrix-vector products is comparable to explicit methods.

math.NA↗