We show that vortex rings forming in suspensions and polymer solutions exhibit similar behaviour in terms of vortex-core growth, vorticity redistribution and circulation when compared at loadings (i.e. volume fraction in suspensions and concentration in polymer solutions) normalised by their respective critical loading. This suggests that the collective, loading-driven dynamics of dispersed particles or polymer chains can outweigh the unique characteristics of the dispersion and govern certain aspects of the flow response. Using a confined vortex ring as a canonical structure, we synthesise experimental data spanning dilute to concentrated regimes for both media, with our analysis indicating that similar collective dynamics exist in both systems. Specifically, the vortex-core growth rate relative to the unloaded case increases approximately linearly with normalised loading while circulation remains nearly unchanged over the measured parameter range. Shared collective dynamics are further suggested by radial vorticity profiles scaled according to loading, which reveal structural markers that align along consistent non-dimensional radii, demonstrating a topological self-similarity between flow fields despite fundamentally different disperse phases. Turbulent kinetic energy trends expose the limits of this correspondence: with increasing Reynolds number, turbulence rises in suspensions but remains largely unchanged in polymer solutions, reflecting differences in how semi-rigid particles and flexible chains interact with small-scale fluctuations. Altogether, these results uncover shared collective dynamics and support the cautious use of polymer analogues to study suspension flows within an equivalent loading regime. However, the limited test matrix motivates further experiments involving different flow media to assess the generality of these findings.

This study presents a combined analytical and experimental investigation into the rising dynamics of Newtonian droplets in viscoelastic fluids, focusing on discontinuous transitions in droplet velocity. Although velocity jumps have been observed in gas bubbles, this work is the first systematic investigation of the phenomenon in Newtonian droplets. Analytically, a triple-perturbation approach is developed using Reynolds (Re), Deborah (De) and capillary (Ca) numbers as expansion parameters. The surrounding viscoelastic medium is modelled using the nonlinear-Giesekus constitutive equation. The analysis reveals that increasing Deborah number intensifies and reorients normal stresses – particularly the polar ($\theta$-direction) and hoop components – along the droplet interface. These stresses migrate rearward with increasing elasticity, resulting in localised elongational flows and concentrated radial stresses near the rear stagnation point, which indicates the onset of elastic instabilities. Experimentally, Newtonian droplets are introduced into a variety of exterior fluids: (i) quasilinear Boger fluids, which are constant-viscosity viscoelastic solutions that isolate elastic effects; and (ii) a strongly nonlinear viscoelastic solution, which exhibits both high elasticity and significant shear-thinning behaviour. Equivalent Newtonian fluids of matched viscosity are also used as controls. Viscoelastic fluids are solutions of polyacrylamide in the water–glycerine mixture. Across all experiments, the dimensionless ranges were $\textit{Re}\approx 6\times 10^{-4}{-}4.59$, $\textit{De}\approx 0.057{-}0.802$ and $\textit{Ca}\approx 0.0026{-}0.638$, framing the scope of applicability. The experimental observations challenge the classical expectation of smooth droplet motion and demonstrate that Newtonian droplets in viscoelastic environments can exhibit sharp, weak or no velocity jumps, depending on the balance between elasticity, viscosity and deformability.

The addition of polymers to turbulent pipe flows induces significant drag reduction and fundamentally modifies turbulent flow structures. This study presents a fractal dimension analysis of polymeric turbulent pipe flows using velocity fields captured via two-dimensional particle image velocimetry in the streamwise-radial plane. Two experimental datasets were generated: one by varying the polymer concentration at a constant Reynolds number ($\textit{Re}$) and another by varying $\textit{Re}$ at a fixed polymer concentration. Friction factors were measured concurrently to quantify the extent of drag reduction. The two-dimensional fractal dimension was evaluated for isosurfaces of turbulent kinetic energy. While Newtonian turbulence exhibits a nearly constant fractal dimension at length scales exceeding a critical threshold, the introduction of polymers causes the fractal dimension to decrease monotonically with increasing concentration. Conversely, the fractal dimension remains insensitive to changes in the Reynolds number. The ratio of the critical length scale to the Kolmogorov scale varies according to both $\textit{Re}$ and polymer concentration; however, this scale ratio becomes independent of both parameters once the maximum drag reduction asymptote is reached. Spatial analysis of the one-dimensional fractal dimension across radial positions helps to further reveal the evolution of turbulence fractality. The results demonstrate that while flow inertia promotes the formation of space-filling structures, viscoelastic effects smooth these structures and transition them towards sheet-like or linear geometries. Finally, the correlation between the fractal dimension and turbulence intermittency is discussed.

Small interfering RNA (siRNA) is an emerging therapeutic modality for a varietyof diseases, including cancer, as siRNA can silence target genes in asequence-specific manner. The effective delivery of siRNA remains a majorchallenge due to rapid clearance by macrophages in the systemic environment.Nonspecific interactions with the serum proteins in the bloodstream contributeto macrophage uptake, limiting circulation time, thereby reducing the effectivedelivery of siRNA to the target site. Here, we report the efficient delivery ofsiRNA to cancer cells using hyaluronic acid (HA)-coated cationic polymericnanovector (PONI-Guan)/siRNA polyplexes. The guanidinium-functionalized polymersself-assemble with siRNA and enable cytosolic delivery. HA serves as anoninteracting protective shield on the polyplexes that prevent macrophageuptake in vitro. These nanovectors facilitate efficient siRNAdelivery to 4T1 triple-negative breast cancer cells in vitro,with a 4:1 selectivity relative to macrophages. Further, HA-coated polyplexesdemonstrated efficient STAT3 gene knockdown (~50%) in 4T1 cells. Intravenousadministration of HA-coated polyplexes in 4T1 tumor-bearing mice showedsignificantly (~50%) decreased accumulation in clearance organs, in comparisonto the PONI-Guan polyplexes. Collectively, HA-coated polyplexes provide aneffective strategy for selective siRNA delivery to tumor cells while avoidingmacrophage uptake.

To investigate how polymers influence energy transfer in three-dimensional turbulence, we conduct experiments in homogeneous bulk turbulence generated by a von Kármán swirling flow, using tomographic particle image velocimetry. A filtering approach is applied to the measured three-dimensional velocity fields to extract subgrid-scale (SGS) statistics, focusing on the filtered strain-rate tensor and SGS stress tensor. We find that polymer additives induce significant changes in the tensorial geometry: the strain-rate tensor shows a tendency towards an eigenvalue ratio of $1 : 0 : -1$, while the SGS stress tensor favours a $2 : -1 : -1$ configuration. The local energy flux – quantified by the inner product of the strain-rate and SGS stress tensors – is systematically suppressed by polymers and becomes increasingly intermittent. This suppression is linked to a reduced energy transfer efficiency, associated with the misalignment between the principal eigendirections of the two tensors. Anisotropic effects are also observed in the energy flux components, indicating that polymers affect vertical and horizontal energy transfer differently. Finally, the obtained SGS statistics allow for an a priori assessment of SGS models. Our results reveal that the nonlinear gradient model significantly outperforms the Smagorinsky model, particularly in polymer-laden turbulence. The diminished alignment between the strain-rate and SGS stress tensors may underlie the limitations of the Smagorinsky model, which assumes a scalar eddy-viscosity closure. These results provide new experimental insights into the SGS dynamics of polymeric turbulence and highlight the potential of nonlinear models for large-eddy simulations of viscoelastic flows.

We report an experimental study on the effects of polymer additives in the dissipative-scale flow field properties in turbulent Rayleigh–Bénard convection. The experiments were conducted in a cylindrical convection cell with a minute amount of polyacrylamide long-chain polymer. The local velocity gradient tensor was measured using an integrated home-made measurement system (J. Fluid Mech., 2024, vol. 984, p. A8). Although the single-roll large-scale circulation persists (owing to the slight tilt of the convection cell), polymers induce an anisotropic suppression of the dissipative-scale flow properties. The normal velocity gradient components are suppressed more than the shear components. The mean energy dissipation rate in both centre and side regions decreases, then levels off with increasing polymer concentration and the final reduction ratio exceeds 50 % in each region. In the side region, adding polymers has a stronger stabilising effect on the strain rate than the rotation. The anisotropic suppression of the velocity gradient tensor affects dissipation-rotation co-occurrence probability, velocity gradient triple decomposition and local streamline topology. Adding polymers also induces a deceleration effect and increases the contribution of local buoyancy in driving the flow. These results reveal that the addition of polymers can non-trivially manipulate dissipative-scale turbulence fields and energy cascades.

Amorphous materials transition from solid-like to liquid-like behaviour (yield) under large stresses. Their constituent elements are caged in metastable configurations due to their neighbours. Microscale interactions between these elements lead to a large energy barrier to break the cages and trigger a plastic rearrangement. Thermal fluctuations can alter the yielding point as the elements hop to new configurations in anticipation. This work bridges the gap between molecular-scale physics and bulk rheology in thermal amorphous materials by connecting a classical density functional theory to a thermally activated elastoplastic model (EPM). We use a model system of solvent-free polymer-grafted nanoparticles which show rheological characteristics similar to those of soft glassy materials. We formulate the evolution of the free energy in a deforming array of polymer-grafted nanoparticles to obtain the energy landscape as an input to our EPM. We examine how the apparent yield stress depends on the shape of the energy landscape, thermal fluctuations and the rate of deformation. Our general scaling analyses reveal different regimes of structural relaxation governed by the applied shear rate and the inherent time scale for thermal hops. The complex interplay between mechanical loading and thermal fluctuations is further characterized by performing a variety of shear tests with different deformation history. The proposed framework provides an understanding of the yielding transition by integrating across a vast range of length and time scales.

The deposition of droplets onto a swollen polymer network induces the formation of a wetting ridge at the contact line. Current models typically consider either viscoelastic effects or poroelastic effects, while polymeric gels often exhibit both properties. In this study, we investigate the growth of the wetting ridge using a comprehensive large-deformation theory that integrates both dissipative mechanisms – viscoelasticity and poroelasticity. In the purely poroelastic case, following an initial instantaneous incompressible deformation, the growth dynamics exhibits scale-free behaviour, independent of the elastocapillary length or system size. A boundary layer of solvent imbibition between the solid surface (in contact with the reservoir) and the region of minimal chemical potential is created. At later times, the ridge equilibrates on the diffusion time scale given by the elastocapillary length. When viscoelastic properties are incorporated, our findings show that, during the early stages (prior to the viscoelastic relaxation time scale), viscoelastic effects dominate the growth dynamics of the ridge and solvent transport is significantly suppressed. Beyond the relaxation time, the late-time dynamics closely resembles that of the purely poroelastic case. These findings are discussed in light of recent experiments, showing how our approach offers a new interpretation framework for wetting of polymer networks of increasing complexity.

The effectiveness of polymer drag reduction by targeted injection is studied in comparison with that of a uniform concentration (or polymer ocean) in a turbulent channel flow. Direct numerical simulations are performed using a pseudo-spectral code to solve the coupled equations of a viscoelastic fluid using the finitely extensible nonlinear elastic dumbbell model with the Peterlin approximation. Light and heavy particles are used to carry the polymer in some cases, and polymer is selectively injected into specific flow regions in the other cases. Drag reduction is computed for a polymer ocean at a viscosity ratio of $\beta = 0.9$ for simulation validation, and then various methods of polymer addition at $\beta = 0.95$ are compared for their drag-reduction performance and general effect on the flow. It was found that injecting polymer directly into regions of high axial strain inside and around coherent vortical structures was the most effective at reducing drag, while injecting polymer very close to the walls was the least effective. The targeting methods achieved up to 2.5 % higher drag reduction than an equivalent polymer ocean, offering a moderate performance boost in the low drag-reduction regime.

We investigate the scale-by-scale transfers of energy, enstrophy and helicity in homogeneous and isotropic polymeric turbulence using direct numerical simulations. The study relies on the exact scale-by-scale budget equations, derived from the governing model equations, that fully capture the back-reaction of polymers on the fluid dynamics. Polymers act as dynamic sinks and sources and open alternative routes for interscale transfer whose significance is modulated by their elasticity, quantified through the Deborah number (${\textit{De}}$). Polymers primarily deplete the nonlinear energy cascade at small scales, by attenuating intense forward and inverse transfer events. At sufficiently high ${\textit{De}}$, a polymer-driven flux emerges and dominates at small scales, transferring on average energy from larger to smaller scales, while allowing for localised backscatter. For enstrophy, polymers inhibit the stretching of vorticity, with fluid–polymer interactions becoming the primary enstrophy source at high ${\textit{De}}$. Accordingly, an analysis of the small-scale flow topology reveals that polymers promote two-dimensional straining states and enhance the occurrence of shear and planar extensional flows, while suppressing extreme rotation events. Helicity, injected at large scales, exhibits a transfer mechanism analogous to energy, being dominated by nonlinear dynamics at large scales and by polymer-induced fluxes at small scales. Polymers enhance the breakdown of small-scale mirror symmetry, as indicated by a monotonic increase in relative helicity with ${\textit{De}}$ across all scales.

In 2019, in this journal, I discussed approaches for controlling the movement of molecules, in particular macromolecules, with an emphasis on how this enabled advances in the field of drug delivery – a field that has impacted billions of people worldwide. Since 2019, there have been advances in our work and this field including a striking demonstration in which drug delivery nanoparticles were crucial to the success of mRNA therapies and the Covid-19 vaccine. In this paper, I provide updates in such areas as i) developing new methods for oral drug delivery systems, ii) delivery of molecules to specific sites of the body, iii) new types of delivery systems, and iv) examples of machine learning/artificial intelligence in these areas. I also discuss advances in mRNA technology as it relates to drug delivery and the development of nanoparticles to protect and deliver vaccines, which saved and improved the lives of hundreds of millions of people throughout the world.

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (1973, Arch. Rat. Mech. Anal. vol. 49, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Giesekus model. We begin by neglecting inertia to focus on the interaction between gravity, viscoelasticity and surface tension. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface shape on this short time scale, and recover the steady-state shape on a longer time scale. In contrast to the work of Joseph and Fosdick, which used the method of successive approximations to determine the steady shape of the interface, we explicitly derive the interface shape for both steady and transient cases. Subsequently, we reintroduce small but finite inertial effects to investigate their interaction with viscoelasticity, and propose a criterion for determining the conditions under which rod climbing occurs. Through numerical computations, we obtain the transient interface shapes, highlighting the interplay between time-dependent viscoelastic and inertial effects.

Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau–Yasuda model, we discovered that linear instability can arise when the power-law index falls below 0.35. This inelastic non-axisymmetric instability can universally arise in generalised Newtonian fluids that extend the power-law model. The viscosity ratio from infinite to zero shear rate can significantly impact instability, even if it is small. Two branches of finite-amplitude travelling-wave solutions bifurcate subcritically from the linear critical point. The solutions exhibit sublaminar drag reduction, a phenomenon not possible in the Newtonian case.

An addition of polymers can significantly reduce drag in wall-bounded turbulent flows, such as pipes or channels. This phenomenon is accompanied by a noticeable modification of the mean-velocity profile. Starting from the premise that polymers reduce vortex stretching, we derive a theoretical prediction for the mean-velocity profile. After assessing this prediction by numerical experiments of turbulence with reduced vortex stretching, we show that the theory successfully describes experimental measurements of drag reduction in pipe flow.

The extensional rheology of dilute suspensions of spheres in viscoelastic/polymeric liquids is studied computationally. At low polymer concentration $c$ and Deborah number $\textit{De}$ (imposed extension rate times polymer relaxation time), a wake of highly stretched polymers forms downstream of the particles due to larger local velocity gradients than the imposed flow, indicated by $\Delta \textit{De}_{\textit{local}}\gt 0$. This increases the suspension’s extensional viscosity with time and $\textit{De}$ for $De \lt 0.5$. When $\textit{De}$ exceeds 0.5, the coil-stretch transition value, the fully stretched polymers from the far-field collapse in regions with $\Delta \textit{De}_{\textit{local}} \lt 0$ (lower velocity gradient) around the particle’s stagnation points, reducing suspension viscosity relative to the particle-free liquid. The interaction between local flow and polymers intensifies with increasing $c$. Highly stretched polymers impede local flow, reducing $\Delta \textit{De}_{\textit{local}}$, while $\Delta \textit{De}_{\textit{local}}$ increases in regions with collapsed polymers. Initially, increasing $c$ aligns $\Delta \textit{De}_{\textit{local}}$ and local polymer stretch with far-field values, diminishing particle–polymer interaction effects. However, beyond a certain $c$, a new mechanism emerges. At low $c$, fluid three particle radii upstream exhibits $\Delta \textit{De}_{\textit{local}} \gt 0$, stretching polymers beyond their undisturbed state. As $c$ increases, however, $\Delta \textit{De}_{\textit{local}}$ in this region becomes negative, collapsing polymers and resulting in increasingly negative stress from particle–polymer interactions at large $\textit{De}$ and time. At high $c$, this negative interaction stress scales as $c^2$, surpassing the linear increase of particle-free polymer stress, making dilute sphere concentrations more effective at reducing the viscosity of viscoelastic liquids at larger $\textit{De}$ and $c$.

Lubricant viscoelasticity arises due to a finite polymer relaxation time ($\lambda$) which can be exploited to enhance lubricant performance. In applications such as bearings, gears, biological joints, etc., where the height-to-length ratio ($H_0 / \ell _x$) is small and the shear due to the wall velocity ($U_0$) is high, a simplified two-dimensional computational analysis across the channel length and height reveals a finite increase in the load-carrying capacity of the film purely due to polymer elasticity. In channels with a finite length-to-width ratio, $a$, the spanwise effects can be significant, but the resulting mathematical model is computationally intensive. In this work, we propose simpler reduced-order models, namely via (i) a first-order perturbation in the Deborah number ($\lambda U_0 / \ell _x$) and (ii) the viscoelastic Reynolds approach extended from Ahmed & Biancofiore (J. Non-Newtonian Fluid Mech., vol. 292, 2021, 104524). We predict the variation in the net vertical force exerted on the channel walls (for a fixed film height) versus increasing viscoelasticity, modelled using the Oldroyd-B constitutive relation, and the channel aspect ratio. The models predict an increase in the net force, which is zero for the Newtonian case, versus both the Deborah number and the channel aspect ratio. Interestingly, for a fixed $\textit{De}$, this force varies strongly between the two limiting cases (i) $a \ll 1$, an infinitely wide channel, and (ii) $a \gg 1$, an infinitely short channel, implying a change in the polymer response. Furthermore, we observe a different trend (i) for a spanwise-varying channel, in which a peak is observed between the two limits, and (ii) for a spanwise-uniform channel, where the largest load value is for $a \ll 1$. When $a$ is O($1$), the viscoelastic response varies strongly and spanwise effects cannot be ignored.

Additive manufacturing is enabling on-demand fabrication of desirable polymer designs. Due to the technology’s widespread use, there is a need to ensure sustainable design approaches are practiced. Here, thermoplastics for fused deposition modeling is reviewed for life-cycle stages, mechanical properties, and design strategies. Life-cycle stages assessed include formulation, processing, applications, and end-of-life as well as recycling processes. Mechanical properties are considered for recyclable thermoplastics, with fillers to enhance functionality. Finally, design methods are considered to create mechanically efficient designs, such as metamaterials, that reduce material usage and processing time. The review highlights the great potential for creating sustainable designs with additively manufactured polymers, and their mechanical capabilities for broad applications.

Direct numerical simulation (DNS) studies of power-law (PL) fluids are performed for purely viscous-shear-thinning ($n\in [0.5,0.75]$), Newtonian ($n=1$) and purely viscous-shear-thickening ($n=2.0$) fluids, considering two Reynolds numbers ($Re_{\tau }\in [395,590]$), and both smooth and rough surfaces. We carefully designed a numerical experiment to isolate key effects and simplify the complex problem of turbulent flow of non-Newtonian fluids over rough surfaces, enabling the development of a theoretical model to explain the observed phenomena and provide predictions. The DNS results of the present work were validated against literature data for smooth and rough Newtonian turbulent flows, as well as smooth shear-thinning cases. A new analytical expression for the mean velocity profile – extending the classical Blasius $1/7$ profile to power-law fluids – was proposed and validated. In contrast to common belief, the decrease in $n$ leads to smaller Kolmogorov length scales and the formation of larger structures, requiring finer grids and longer computational domains for accurate simulations. Our results confirm that purely viscous shear-thinning fluids exhibit drag reduction, while shear-thickening fluids display an opposite trend. Interestingly, we found that viscous-thinning turbulence shares similarities with Newtonian transitional flows, resembling the behaviour of shear-thinning, extensional-thickening viscoelastic fluids. This observation suggests that the extensional and elastic effects in turbulent flows within constant cross-section geometries may not be significant. However, the shear-thickening case exhibits characteristics similar to high-Reynolds-number Newtonian turbulence, suggesting that phenomena observed in such flows could be studied at significantly lower Reynolds numbers, reducing computational costs. In the analysis of rough channels, we found that the recirculation bubble between two roughness elements is mildly influenced by the thinning nature of the fluid. Moreover, we observed that shear-thinning alters the flow in the fully rough regime, where the friction factor typically reaches a plateau. Our results indicate the possibility that, at sufficiently high Reynolds numbers, this plateau may not exist for shear-thinning fluids. Finally, we provide detailed turbulence statistics for different rheologies, allowing, for the first time, an in-depth study of the effects of rheology on turbulent flow over rough surfaces.

This paper presents a theoretical model for the electro-osmotic flow (EOF) of semi-dilute polyelectrolyte (PE) solutions in nanochannels. We use mean-field theories to describe the properties of electric double layer and viscosity of PE solutions that are prerequisites for constructing the EOF model. The EOF model is validated via a good match to the existing experimental results. Based on the validated EOF model, we conduct a comprehensive analysis of EOF of semi-dilute PE solutions in nanochannels. First, we observe considerable EOF of PE solutions in the uncharged nanochannels, which is in stark contrast to EOF of simple electrolyte solutions. The analyses show that the EOF of PE solutions in uncharged nanochannels is triggered by the external electric field acting on the near-wall non-electroneutral regions resulting from the confinement-induced inhomogeneous distribution of PE monomers. Although the solutions are electroneutral as a whole, the presence of local non-electroneutral regions and the mismatch between non-electroneutral regions and high-viscosity regions lead to the net EOF in uncharged nanochannels. Furthermore, we reveal that the EOF mobility $\mu _{{eof}}$ in uncharged nanochannels exhibits a scaling law $\mu _{{eof}} \propto a^{-0.44}$ (wherein $a$ denotes monomer Kuhn length) and is inversely proportional to the PE chain length, while it decreases nonlinearly with the charge fraction of the PE chains. Moreover, the EOF mobility reaches its maximum at specific bulk monomer concentration, and increases with the nanochannel height before converging to that under no confinement. Second, we analyse the EOF of PE solutions in nanochannels with various wall effects, such as surface charge density, slip length and adsorption length. When the surface charge is absent, the adsorption length significantly influences the direction and magnitude of the EOF, whereas the slip length has no effect. When the wall becomes increasingly charged, the influence of adsorption length on EOF gradually diminishes, while the importance of the slip length progressively intensifies and the EOF is highly influenced by the co-action of various wall effects in a complicated manner. When the surface wall is oppositely charged to polymer monomers, the EOF mobility varies nonlinearly with the surface charge density, while a zero net flow of EOF followed by a direction reversal is discovered when the wall is likely charged to polymer monomers.