An existing approach for deriving analytical expressions for slip-flow properties of Stokes flow is generalised and applied to a range of micro and nanoscale applications. The technique, which exploits the reciprocal theorem, can generate first-order predictions of the impact of Navier or Maxwell slip boundary conditions on surface moments of the traction force (e.g. on drag and torque). This article brings dedicated focus to the technique, generalises it to predict first-order slip effects on arbitrary moments of the surface traction, numerically verifies the technique on a number of cases and applies the method to a range of micro and nano-scale applications. Applications include predicting: the drag on translating spheres with varying slip length; the efficiency of a micro journal bearing; the speed of a self-propelled particle (a ‘squirmer’); and the pressure drop required to drive flow through long, straight micro/nano channels. Certain general results are also obtained. For example, for low-slip Stokes flow: any surface distribution of positive slip length will reduce the drag on any translating particle; and any perimetric distribution of positive slip length will reduce the pressure loss through a straight channel flow of arbitrary cross-section.

Particle diffusometry (PD) is a technique of measuring the diffusion coefficient of a fluid sample by seeding it with tracer particles and observing their motion under a microscope. In microfluidic set-ups, the observed particles are often defocused and their motion is affected by factors such as fluid flow, which leads to high errors for conventional and deep learning-based PD (DPD) algorithms. This work improves the performance of DPD models by updating their architecture, avoiding temporal averaging in the input, and exploring the impact of various choices during training. These models provide state-of-the-art performance for generalised datasets regardless of particle shapes, concentration, flow or image noise and are called DPD-v2. These models provide a mean absolute error of 0.09$\unicode{x03BC}$m2s−1 for Gaussian particles and 0.07$\unicode{x03BC}$m2s−1 for defocused particles, which is 2x–4x lower errors as compared with the two following best methods. The performance of DPD-v2 models increases with crop size and the use of multiple stacks of images. The outputs of the DPD-v2 models were compared against the outputs from conventional algorithms on Gaussianised experimental no flow datasets, which provided < 0.5$\unicode{x03BC}$m2s−1 mean absolute difference. Hence, the DPD-v2 models can be used in real-world scenarios.

In this study, we introduce a method, applied for the first time to manipulate human cells, by leveraging the controlled activation and deactivation of microbubble streaming – previously used for rigid polymer particles. This innovative technique enables automatic detection and non-destructive sorting of target cells within a microchannel, directing them into a collection chamber for further analysis or removal. A major focus was the quantification of shear stress distribution induced by the microbubble streaming, which confirmed the method’s biocompatibility. Even with prolonged exposure, no damage to live cells was observed, reinforcing the safety and viability of using microstreaming. These findings demonstrate the potential of microbubble streaming as a powerful tool for lab-on-a-chip systems and biomedical diagnostics.

Microstructured surfaces with pillar arrays are widely used to control the wetting morphology and spreading dynamics of droplets. In both simulations and experiments, it is shown that fabricating the surface with various microstructures is a very effective method for achieving the desired symmetry of the moving contact line. However, the method for characterizing miscellaneous pillar-arrayed microstructured surfaces is still insufficient. This paper presents the configurational entropy to characterize the microstructured surfaces with pillar arrays. By calculating the configurational entropy of pillar-arrayed microstructured surfaces, the relationship between the configurational entropy and the wetting morphology of droplets is obtained. For pillar-arrayed microstructured surfaces with the configurational entropy S > 0, the droplet wetting morphology may be much more complex than those with S = 0. The relationship is found to be consistent with the previous results. Furthermore, the wetting dynamics has been analysed. This study may be useful to understand the mechanism of droplet wetting on pillar-arrayed microstructured surfaces and provide insights for the design and manufacture of microstructured surfaces.

Properties and functions of materials assembled from nanofibrils critically depend on alignment. A material with aligned nanofibrils is typically stiffer compared with a material with a less anisotropic orientation distribution. In this work, we investigate nanofibril alignment during flow focusing, a flow case used for spinning of filaments from nanofibril dispersions. In particular, we combine experimental measurements and simulations of the flow and fibril alignment to demonstrate how a numerical model can be used to investigate how the flow geometry affects and can be used to tailor the nanofibril alignment and filament shape. The confluence angle between sheath flow and core flow, the aspect ratio of the channel and the contractions in the sheath and/or core flow channels are varied. Successful spinning of stiff filaments requires: (i) detachment of the core flow from the top and bottom channel walls and (ii) a high and homogeneous fibril alignment. Somewhat expected, the results show that the confluence angle has a relatively small effect on alignment compared with contractions. Contractions in the sheath flow channels are seen to be beneficial for detachment, and contractions in the core flow channel are found to be an efficient way to increase and homogenise the degree of alignment.

As a novel type of catalytic Janus micromotor (JM), a double-bubble-powered Janus micromotor has a distinct propulsion mechanism that is closely associated with the bubble coalescence in viscous liquids and corresponding flow physics. Based on high-speed camera and microscopic observation, we provide the first experimental results of the coalescence of two microbubbles near a JM. By performing experiments with a wide range of Ohnesorge numbers, we identify a universal scaling law of bubble coalescence, which shows a cross-over at dimensionless time $\tilde{t}$ = 1 from an inertially limited viscous regime with linear scaling to an inertial regime with 1/2 scaling. Due to the confinement from the nearby solid JM, we observe asymmetric neck growth and find the combined effect of the surface tension and viscosity. The bubble coalescence and detachment can result in a high propulsion speed of ∼0.25 m s−1 for the JM. We further characterise two contributions to the JM’s displacement propelled by the coalescing bubble: the counteraction from the liquid due to bubble deformation and the momentum transfer during bubble detachment. Our findings provide a better understanding of the flow dynamics and transport mechanism in micro- and nano-scale devices like the swimming microrobot and bubble-powered microrocket.

The steady-state current–voltage response of ion-selective systems varies as the number of ion-selective components is varied. For the highly investigated unipolar system, including only one ion-selective component, it has been shown that above a supercritical voltage, an electroosmotic instability is triggered, leading to overlimiting currents. In contrast, the effects of this instability on the current–voltage response of the second most common system of a bipolar system, including two oppositely charged permselective regions, have yet to be reported. Using numerical simulations, we investigate the steady-state electrical response of bipolar systems as we vary the ratio of the charge within the two oppositely charged regions. The responses are divided into those with an internal symmetry related to the surface charge and those without. In contrast to the unipolar systems, bipolar systems with the internal symmetry do not exhibit overlimiting currents and their steady-state response is identical to the convectionless steady-state response. In contrast, the systems without the internal symmetry exhibit much more complicated behaviour. For positive voltages, they have overlimiting currents, while for negative voltages, they do not have overlimiting currents. Our findings contribute to a more profound understanding of the behaviour of the current–voltage response in bipolar systems.

The most common method to characterize the electrical response of a nanofluidic system is through its steady-state current–voltage response. In Part 1, we demonstrated that this current–voltage response depends on the geometry, the layout of the surface charge and the effects of advection. We demonstrated that each configuration has a unique steady-state signature. Here, we will elucidate the behaviour of the time-transient response. Similar to the steady-state response, we will show that each configuration has its own unique time-transient signature when subjected to electroosmotic instability. We show that bipolar systems behave differently than unipolar systems. In unipolar systems, the instability appears only at one end of the system. In contrast, in bipolar systems the instability will either appear on both sides of the nanochannel or not at all. If it does appear on both sides, the instability will eventually vanish on one or both sides of the system. In Part 1, these phenomena were explained using steady-state considerations of the behaviour of the fluxes. Here, we will examine the time-transient behaviour to reveal the governing principles that are, on the one hand, not so different from unipolar systems and, on the other hand, remarkably different.

We model the slip length tribometer (SLT), originally presented by Pelz et al. (J. Fluid Mech., vol. 948, 2022, p. A8) in OpenFOAM. The plate tribometer is especially designed to simultaneously measure viscosity and slip length for lubrication gaps in the range of approximately 10 $\mathrm {\mu }$m at temperatures and surface roughnesses relevant to technical applications, with a temperature range of $-30$ to $100\,^\circ \mathrm {C}$ and surface roughness ranging from $10\ \mathrm {nm}$ to $1\ \mathrm {\mu }\mathrm {m}$. A simplified analytical model presented by Pelz et al. (J. Fluid Mech., vol. 948, 2022, p. A8) infers the slip length of the plate from the experimentally measured torque and the plate gap height. The present work verifies the analytical model using axisymmetric flow simulations and presents the effect of inlet on the numerical velocity profiles. The simulation results are in very good agreement with the results of the analytical model. The main conclusion drawn from this study is the validation of the Navier-slip boundary condition as an effective model for partial slip in computational fluid dynamics simulations and the negligible influence of the inlet on the fluid flow between the SLT's plates.