Explore the vast range of titles available.

The impact of fluid drops on solid substrates is a cardinal fluid dynamics phenomenon intrinsically related to many fields. Although these impacting objects are very often non-spherical and non-Newtonian, previous studies have mainly focused on spherical Newtonian drops. As a result, both shape and rheological effects on the drop-spreading dynamics remain largely unexplored. In the present work we use a mixed approach combining experiments with multiphase three-dimensional numerical simulations to extend the work reported by Luu & Forterre (J. Fluid Mech., vol. 632, 2009, pp. 301–327) by highlighting the fundamental role of shape in the normal impact of viscoplastic drops. Such complex fluids are highly common in various industrial domains and ideally behave either like a rigid body or a shear-rate-dependent liquid, according to the stress solicitation. Spherical, prolate, cylindrical and prismatic drops are considered. The results show that, under negligible capillary effects, the impacting kinetic energy of the drop is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: (i) inertio-viscous, (ii) inertio-plastic, and (iii) mixed inertio-visco-plastic. These regimes are deeply affected by the drop initial aspect ratio, which in turn reveals the possibility of using drop shape to control spreading. The physical mechanisms driving the considered phenomenon are underlined by energy budget analyses and scaling laws. The results are summarised in a two-dimensional diagram linking the drop maximum spreading, minimum height and final shape with different spreading regimes through a single dimensionless parameter, here called the impact number.

Normal and oblique drop impact on a solid surface is numerically analysed for yield stress fluids. A rich diversity of results are generated as a consequence of the exploration of the inertial, elastic, plastic and thixotropic features of the process, as well as the inclination of the solid surface. We show that drops of more thixotropic fluids have a higher tendency to bounce in the normal impact, and to roll or to bounce in the case of an oblique drop impact. Concerning elasticity, we found a critical value for the elastic Ohnesorge number above which no bouncing takes place. Experimental findings such as the fact that the stored energy due to the elasticity of the fluid drop plays a role similar to the stored energy of an interfacial nature in inelastic fluid drops are corroborated in the present study.

When two fluid drops touch, they coalesce due to surface tension. At early times, there is only a relatively small fluid bridge joining the drops. An asymptotic solution is presented for an inertial regime of early-time coalescence, in which inertial forces balance surface tension at leading order. It is demonstrated that viscosity nevertheless has a leading-order effect. Radial momentum is created at the tightly curved edge of the fluid bridge by the net force $2\\gamma$ (per unit length) due to surface tension. This momentum is left behind the radially expanding bridge edge in a thin viscous wake. The divergent volume flux in the wake entrains fluid from above and below the bridge, and drives an inviscid irrotational flow in the drops on the scale of the bridge radius. This flow widens the gap between the drops ahead of the bridge, and the larger gap width results in a lower rate of coalescence. Including viscosity in this way improves the agreement between theory and the available experimental and numerical data.

Experiments on microfluidic core–annular flows demonstrated a transition from a continuous core jet to core-fluid drops and slugs separated by the annular fluid films/slugs due to absolute instability. The flows in the higher-generation airways could be modelled as core–annular flow with the laminar core airflow and annular airway surface liquid (ASL). Thus, if an absolute instability exists in the higher-generation airways, then it could lead to ASL film/slug-induced airway closure, necessitating the present study. Taking cues from previous studies, we derive an evolution equation using the lubrication approximation. The analysis, using the dispersion relation obtained from the evolution equation, predicts the existence of the critical capillary number $Ca_c$ such that, for $Ca < Ca_c$, the flow will be absolutely unstable for vanishing Reynolds number $Re$. The parameter $Ca_c$ exhibits the scaling as $Ca_c \\sim (1-H)^2/\\mu _r$, where $1-H$ is the dimensionless thickness of the ASL, and $\\mu _r$ is the ratio of the air viscosity to the ASL viscosity. In agreement with the experimental observations, for a healthy lung, the analysis predicts absolute instability triggered airway closure only at the end of expiration during a breathing cycle. For a diseased lung, the ASL thickness and viscosity drastically increase the possibility of absolutely unstable flow and, thus, airway closure. Increasing inertial effect (i.e. $Re$) exacerbates airway closure by curtailing the convectively unstable region. Similarly, the ASL shear thinning widens the absolute instability parametric region. Thus, the present analysis demonstrates a pathway for airway closure in the higher-generation airways due to absolute instability.

By adding minute concentrations of a high-molecular-weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times and high polymer extensibilities, for which the evolution can be divided into two distinct regimes. For times smaller than the polymer relaxation time over which the beads-on-string structure develops, we give a simplified local description, which still retains the essential physics of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops.

While the dynamics of Newtonian fluid drops on an inclined non-wettable surface has been widely reported, that of viscoplastic drops is less well known. Combining experimental and theoretical analysis, we reveal unique behaviours of viscoplastic drops on an inclined superhydrophobic surface: (i) decoupled rolling, sliding and sticking motions and (ii) two distinct rolling modes, i.e. viscous rolling and rigid-body rolling. First, determined by the relative magnitudes of gravitational, yield and adhesive stresses, a viscoplastic drop rolls, slides or sticks on a superhydrophobic surface. To the best of our knowledge, this is the first distinct differentiation of viscoplastic drop motions on a superhydrophobic surface, which is a clear departure from the previous observations of Newtonian drops on superhydrophobic surfaces and viscoplastic drops on hydrophilic/hydrophobic surfaces. We subcategorized two types of rolling as liquid-like viscous rolling and solid-like rigid-body rolling. With a low Deborah number (i.e. dimensionless viscoplastic relaxation time), the viscoplastic drop shows a viscous rolling as a Newtonian drop does on an inclined surface. With a high Deborah number, however, the viscoplastic drop does not have enough time to be ‘fluid’. Consequently, the ellipsoidal drop deforms to be more spherical as it goes down the inclined surface, and tumbles, as if a solid body initiates its rolling by ‘tipping’.

When two small fluid drops are sufficiently close, the van der Waals force overcomes surface tension and deforms the surfaces into contact, initiating coalescence. The dynamics of surface deformation across an inviscid gap falls into two distinct regimes (Stokes and inertial–viscous) characterized by the forces that balance the van der Waals attraction at leading order (viscosity, and both inertia and viscosity). The previously studied Stokes regime holds for very viscous drops but fails for less viscous drops as inertia becomes significant before contact is reached. We show that the subsequent inertial–viscous dynamics is self-similar as contact is approached, with the gap width decreasing as $t{'^{3/8}}$ and the radial scale of the deformed region decreasing as $t{'^{1/2}}$ as $t{'}\\to 0$, for time until contact $t'$. The self-similar behaviour is universal and is the generic asymptotic behaviour observed in time-dependent simulations. The unique self-similar gap profile of the inertial–viscous regime suggests new initial conditions for the coalescence of the drops after contact.

Recent technological advances have led to a novel class of microfluidic devices which can be rapidly fabricated by printing a fluid onto a solid substrate with flows generated passively via surface tension. The nonlinear dependence between flow and the heights of the conduits, however, prevent straightforward calculation of the resulting dynamics. In this paper we use matched asymptotic expansions to predict how flow through these devices can be tuned by changing their geometry. We begin with the simple ‘dumbbell’ configuration in which two fluid drops with different sizes are connected by a long, thin and narrow conduit. We calculate the time scale required for one drop to drain into the other and how this depends both on the geometry of the pinned contact line and volume of fluid deposited into the drops. Our model therefore provides the mechanistic basis to design conduits with a particular fluid flux and/or shear stress, which are often key experimental constraints. Our asymptotic predictions are shown to be in excellent agreement with numerical simulations even for moderate aspect ratios (the ratio of conduit width to length). Next, we show how our results for the simple dumbbell configuration can be extended to predict the flow through networks of conduits with multiple drops and nodes, and hence may assist in their design and implementation. This new mathematical framework has the potential to increase the use of surface tension driven microfluidics across a wide range of disciplines as it allows alternate designs to be rapidly assessed.

Understanding flow behaviors of multiple droplets in complex non-Newtonian fluids is crucial in many science and engineering applications. In this study, a new and improved analytical solution is developed based on the free surface cell model for the flow drag of swamp of Newtonian fluid drops through a power-law fluid. The developed solution is accurate and compares well to the numerical solutions. The improvement involves a new quantification of shear stress boundary condition at the interface and a more consistent approximation in linearizing the power-law fluid flow governing equation. The Newtonian fluid solutions can be reasonably used to linearize the flow governing equation. The approximation of the boundary conditions at the interface, however, has a major impact on the model prediction. The main improvement in the new solution is observed under the condition of comparable viscosities of the Newtonian drops and the outside power-law fluid when the results are sensitive to the interface boundary condition. Under the two extreme conditions of high viscosity ratio (approaching particles) and low ratio (approaching bubbles), the present and existing solutions converge.

The thermal features of hybrid nano-powder turbulent motion through a pipe employing helical turbulator is numerically simulated via Finite Volume Method (FVM). The hybrid nanofluid (MWCNTs + Fe 3 O 4  + H 2 O) is obtained by uniformly dispersing MWCNTs + Fe 3 O 4 nanomaterials in H 2 O. The characteristics features of thermal energy transfer of hybrid nanofluid are investigated by varying the pitch ratio (P) of the helical turbulator and Reynolds number (Re) of the fluid. The outputs of the study are depicted in terms of contour plots of temperature, velocity, frictional irreversibility S gen,f , and thermal irreversibility S gen,th . The variation of S gen,f , and S gen,th with changing P and Re are also displayed by 3D plots. It is found that making the fluid more turbulent by increasing Re, the temperature of the fluid drops whereas the fluid velocity augments. The frictional irreversibility enhances, whereas the thermal irreversibility drops with the increasing turbulent motion. The decreasing P causes to drop the temperature of the higher turbulent fluid flow, while opposite effect is observed for smaller Re. The decreasing P causes to enhance the fluid mixing and thus augments the fluid velocity. S gen,f and S gen,th both augment with decreasing P. The comparison of current outputs with the older article shows an acceptable accuracy. The results of the present investigation will be useful in modelling of efficient thermal energy transfer systems.