Formulation design and rheology are critical for successful manufacturing via direct ink writing (DIW), thus linking rheology and printability is a growing area of research amongst the DIW and rheology communities. This work provides an extensive rheological investigation into the material strength, yielding and ‘recovery’ properties of graphite (Gr)-hydrogel based formulations. Using state-of-the-art Large Amplitude Oscillatory Shear (LAOS) techniques, Fourier Transform (FT) rheology and sequence of physical process (SPP) analysis, and 3-step ‘recovery’ tests we provide new insights on the yielding phenomenon, energy transitions and microstructural changes that the formulations undergo. The insights from the rheology experiments are combined with in situ and continuous monitoring during the printing process. From these analyses, we select rheological metrics or descriptors to quantify flowability, recoverability, and material strength. There is a threshold concentration of Gr powders (30 wt%) at which there is a shift in the yielding process. Below this threshold (for the F127 hydrogel and mixtures with low Gr content), perfect plastic dissipation ratio (ϕ) values are close to 0 in the LVR and then steeply increase to close to 1 after the cross-over in a narrow strain (and stress) space. As Gr concentration increases, and print quality gets worse, ϕ values consistently increase in the LVR and at any given γ₀, evidencing an increased energy dissipation throughout the flow transition region. Lissajous–Bowditch curves and SPP Cole–Cole plots illustrate these trends. The extent of the ‘recovery’ (quantified by the mutation time, λ_I, and the storage modulus ‘recovered’ after large deformations ) is also directly related to Gr content, with higher loading resulting in lesser recovery. Our findings provide a comprehensive set of metrics to characterise complex (yield stress) fluids for DIW using three property maps, one for each stage: flowability or yielding process, recoverability and material strength. The results demonstrate that considering these three maps holistically provides insightful trends to guide formulation design and assess performance in DIW.

Direct ink writing (DIW) is a three-dimensional (3D) printing technique exploited by researchers working in fields from scaffolds for energy applications to bioprinting. DIW's main strength is that it enables shaping advanced materials, if these materials can be formulated into complex fluids that meet the demands of the printing process. They must be extremely shear thinning soft solids, able to flow through narrow nozzles, recovering their structure upon deposition and retaining the predesigned 3D shape. Formulation design and rheology are critical, but these aspects can be overlooked due to the high specialization required. This work provides insight on the rheology and printability of complex yield-stress fluids through the study of linear and nonlinear behaviors using large-amplitude oscillatory shear rheology. We refine previous protocols and develop tools to understand the behaviors of formulations for DIW. We apply an existing mathematical framework to a library of carbon-based formulations for energy applications. Fourier transform analysis enables quantifying the onset and rising of higher harmonic contributions. Quantitative comparisons between different formulations are established using 3D harmonics maps, stress–strain plots, and material measures of nonlinearities [Fourier and Chebyshev coefficients, elastic moduli ${(G}_M^{\prime },{\hspace{0.17em}G}_L^{\prime }$ ), and dimensionless index of nonlinearity ($S$ )]. 3D Lissajous plots provide a qualitative alternative to interpretate the yielding transition. We create Ashby-type printability maps to guide formulation design and elucidate that non-printable formulations show distinctive features. This insight on yield-stress fluids for DIW is relevant to other applications and technologies: drilling fluids, gels, colloids, and foods.

Recent direct numerical simulations (DNS) and experiments in turbulent channel flow have found intermittent low- and high-drag events in Newtonian fluid flows, at $R{e}_{\tau }=u_{\tau }h/\nu$ between 70 and 100, where $u_{\tau }$, h and $\nu$ are the friction velocity, channel half-height and kinematic viscosity, respectively. These intervals of low-drag and high-drag have been termed “hibernating” and “hyperactive”, respectively, and in this paper, a further investigation of these intermittent events is conducted using experimental and numerical techniques. For experiments, simultaneous measurements of wall shear stress and velocity are carried out in a channel flow facility using hot-film anemometry (HFA) and laser Doppler velocimetry (LDV), respectively, for $R{e}_{\tau }$ between 70 and 250. For numerical simulations, DNS of a channel flow is performed in an extended domain at $R{e}_{\tau }$ = 70 and 85. These intermittent events are selected by carrying out conditional sampling of the wall shear stress data based on a combined threshold magnitude and time-duration criteria. The use of three different scalings (so-called outer, inner and mixed) for the time-duration criterion for the conditional events is explored. It is found that if the time-duration criterion is kept constant in inner units, the frequency of occurrence of these conditional events remain insensitive to Reynolds number. There exists an exponential distribution of frequency of occurrence of the conditional events with respect to their duration, implying a potentially memoryless process. An explanation for the presence of a spike (or dip) in the ensemble-averaged wall shear stress data before and after the low-drag (or high-drag) events is investigated. During the low-drag events, the conditionally-averaged streamwise velocities get closer to Virk’s maximum drag reduction (MDR) asymptote, near the wall, for all Reynolds numbers studied. Reynolds shear stress (RSS) characteristics during these conditional events are investigated for $R{e}_{\tau }$ = 70 and 85. Except very close to the wall, the conditionally-averaged RSS is higher than the time-averaged value during the low-drag events.

Understanding "yielding" of gels and other soft materials is critical for successful performance in many industries and research fields. However, it is known that not all yielding is the same, and that local structures and microscopic dynamics can be highly heterogeneous. Combining bulk measurements and direct visualization should enable us to map local flows and structural heterogeneities, and to connect their evolution with bulk rheological properties. We study the underlying microscopic dynamic behaviours of an F127 micellar cubic phase gel using rheo-optics. Bulk rheology experiments under large and small deformations are performed with fluorescence and polarized microscopy at the edge of the gap. Large amplitude oscillatory shear results are analyzed using Fourier-Transform rheology and the Sequence of Physical Processes. The structure-rheology analyses enable the correlation of the onset of nonlinearities with banding instabilities and the flow transition with the "slip-stick" theory previously proposed for cubic phases. Under large deformations, fracture is not consistent with the expected idealized yield behaviour. Birefringence analyses enable mapping the structural heterogeneity and the kinetics of structural transitions during the crystallization of the cubic structure. Combination of the flow and birefringence results reveals a connection between structural heterogeneity, transition kinetics, and fracture under large deformations.