Bavand Keshavarz

Stemflow hydrodynamics is the study of water movement along the exterior surface area of plants. Its primary goal is to describe water velocity and water depth along the stem surface area. Its significance in enriching the rhizosphere with water and nutrients is not in dispute. Yet, the hydrodynamics of stemflow have been entirely overlooked. This review seeks to fill this knowledge gap by drawing from thin film theories to seek outcomes at the tree scale. The depth‐averaged conservation equations of water and solute mass are derived at a point. These equations are then supplemented with the conservation of momentum that is required to describe water velocities or relations between water velocities and water depth. Relevant forces pertinent to momentum conservation are covered and include body forces (gravitational effects), surface forces (wall friction), line forces (surface tension), and inertial effects. The inclusion of surface tension opens new vistas into the richness and complexity of stemflow hydrodynamics. Flow instabilities such as fingering, pinching of water columns into droplets, accumulation of water within fissures due to surface tension and their sudden release are prime examples that link observed spatial patterns of stemflow fronts and morphological characteristics of the bark. Aggregating these effects at the tree‐ and storm‐ scales are featured using published experiments. The review discusses outstanding challenges pertaining to stemflow hydrodynamics, the use of dynamic similarity and 3D printing to enable the interplay between field studies and controlled laboratory experiments.

Aluminosilicate hydrogels are often considered to be precursors for the crystallisation of zeolites carried out under hydrothermal conditions.

This paper is associated with a video winner of a 2022 APS/DFD Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2022.GFM.V0115

We provide a canonical introduction to dual-junction-functionality associative polymer networks, which combine high and low functionality (f) dynamic cross-link junctions to impart load-bearing, dissipation, and self-repairing ability to the network. This unique type of network configuration offers an alternative to traditional dual-junction networks consisting of covalent and reversible cross-links. The high-f junctions can provide load-bearing abilities similar to a covalent cross-link while retaining the ability to self-repair and concurrently confer stimuli-responsive properties arising from the high-f junction species. We demonstrate the mechanical properties of this design motif using metal-coordinating polymer hydrogel networks, which are dynamically cross-linked by different ratios of metal nanoparticle (high-f) and metal ion (low-f) cross-link junctions. We also demonstrate the spontaneous self-assembly of nanoparticle-cross-linked polymers into anisotropic sheets, which may be generalizable for designing dual-junction-functionality associative networks with low volume fraction percolated high-f networks.

In this work, we mathematically derive the conditions for which empirical rheometric relations such as the Cox–Merz rule and Gleissle mirror relationship are satisfied. We consider the Wagner integral constitutive framework, which is a special limiting case of the Kaye–Bernstein Kearsley Zapas (K-BKZ) constitutive equation to derive analytical expressions for the complex viscosity, the steady shear viscosity, and the transient stress coefficient in the start-up of steady shear. We use a fractional Maxwell liquid model as the linear relaxation modulus or memory kernel within a non-linear integral constitutive framework. This formulation is especially well-suited for describing complex fluids that exhibit a broad relaxation spectrum and can be readily reduced to the canonical Maxwell model for describing viscoelastic liquids that exhibit a single dominant relaxation time. To incorporate the nonlinearities that always become important in real complex fluids at large strain amplitudes, we consider both an exponential damping function as well as a more general damping function. By evaluating analytical expressions for small amplitude oscillatory shear, steady shear, and the start-up of steady shear using these different damping functions, we show that neither the Cox–Merz rule nor the Gleissle mirror relation can be satisfied for materials with a single relaxation mode or narrow relaxation spectrum. We then evaluate the same expressions using asymptotic analysis and direct numerical integration for more representative complex fluids having a wide range of relaxation times and nonlinear responses characterized by damping functions of exponential or Soskey–Winter form. We show that for materials with broad relaxation spectra and sufficiently strong strain-dependent damping the empirical Cox–Merz rule and the Gleissle mirror relations are satisfied either exactly, or to within a constant numerical factor of order unity. By contrast, these relationships are not satisfied in other classes of complex viscoelastic materials that exhibit only weak strain-dependent damping or strain softening.

In this paper, we use ideas from fractional calculus to study the rheological response of soft materials under steady-shearing flow conditions. The linear viscoelastic properties of many multi-scale complex fluids exhibit a power-law behavior that spans over many orders of magnitude in time or frequency, and we can accurately describe this linear viscoelastic rheology using fractional constitutive models. By measuring the non-linear response during large step strain deformations, we also demonstrate that this class of soft materials often follows a time-strain separability principle, which enables us to characterize their nonlinear response through an experimentally determined damping function. To model the nonlinear response of these materials, we incorporate the damping function with the integral formulation of a fractional viscoelastic constitutive model and develop an analytical framework that enables the calculation of material properties such as the rate-dependent shear viscosity measured in steady-state shearing flows. We focus on a general subclass of fractional constitutive equations, known as the Fractional Maxwell Model, and consider several different analytical forms for the damping function. Through analytical and computational evaluations of the shear viscosity, we show that for sufficiently strong damping functions, for example, an exponential decay of fluid memory with strain, the observed shear-thinning behavior follows a power-law response with exponents that are set by the power-law indices of the linear fractional model. For weak damping functions, however, the power-law index of the high shear rate viscosity is set by the terminal behavior of the damping function itself at large strains. In the limit of a very weak damping function, the theoretical formulation predicts an unbounded growth of the shear stress with time and a continuously growing transient viscosity function that does not converge to a meaningful steady-state value. By determining the leading terms in our analytical solution for the viscosity at both low and high shear rates, we construct an approximate analytic expression for the rate-dependent viscosity. An error analysis shows that, for each of the damping functions considered, this closed-form expression is accurate over a wide range of shear rates.

Significance: Quantifying the viscoelastic properties of weak colloidal gels remains challenging due to the continuously aging nature of these pasty materials. Through time-resolved mechanical and structural spectroscopy and application of the time–connectivity superposition principle we construct the viscoelastic moduli of these gels over eight decades of effective material time. This protocol reveals the dual nature of the relaxation time spectrum with gel- and glass-like characteristics at large and small scales, respectively. The structure of the network at the critical gel point sets the underlying shape of the relaxation spectrum, which the aging material retains as a fixed skeleton. The observed nonergodic behavior suggests that the local arrest of clusters initiates from small scales and continuously evolves toward larger ones.

Free oscillations of synthetic and natural fibers in a torsional pendulum setup enable us to characterize the viscoelastic properties of soft fibers and their bulk viscoelastic coatings in a quantitative manner.