We study numerically the formation of long-lived transient shear bands during shear startup withi... more We study numerically the formation of long-lived transient shear bands during shear startup within two models of soft glasses (a simple fluidity model and an adapted 'soft glassy rheology' model). The degree and duration of banding depends strongly on the applied shear rate, and on sample age before shearing. In both models the ultimate steady flow state is homogeneous at all shear rates, consistent with the underlying constitutive curve being monotonic. However, particularly in the SGR case, the transient bands can be extremely long lived. The banding instability is neither 'purely viscous' nor 'purely elastic' in origin, but is closely associated with stress overshoot in startup flow.
We study theoretically the onset of shear banding in the three most common time-dependent rheolog... more We study theoretically the onset of shear banding in the three most common time-dependent rheological protocols: step stress, finite strain ramp (a limit of which gives a step strain), and shear startup. By means of a linear stability analysis we provide a fluid-universal criterion for the onset of banding for each protocol, which depends only on the shape of the experimentally measured timedependent rheological response function, independent of the constitutive law and internal state variables of the particular fluid in question. Our predictions thus have the same highly general status, in these time-dependent flows, as the widely known criterion for banding in steady state (of negatively sloping shear stress vs. shear rate). We illustrate them with simulations of the rolie-poly model of polymer flows, and the soft glassy rheology model of disordered soft solids.
We study theoretically the formation of shear bands in time-dependent flows of polymeric and worm... more We study theoretically the formation of shear bands in time-dependent flows of polymeric and wormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strain (or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally. For each protocol we perform a linear stability analysis to provide a fluid-universal criterion for the onset of shear banding, following our recent Letter 61. In each case this criterion depends only on the shape of the experimentally measured rheological response function for that protocol, independent of the constitutive properties of the material in question. (Therefore our criteria in fact concern all complex fluids and not just the polymeric ones of interest here. A separate manuscript 30 will explore them in a broad class of disordered soft glassy materials including foams, dense emulsions, dense colloids, and microgel bead suspensions.) An important prediction is that pronounced banding can arise transiently in each of these protocols, even in fluids for which the underlying constitutive curve of stress as a function of strain-rate is monotonic and a steadily flowing state is accordingly unbanded. For each protocol we provide numerical results in the rolie-poly and Giesekus models that support our predictions. We comment on the ability of the rolie-poly model to capture the observed experimental phenomenology, and on the failure of the Giesekus model.
Glassy polymers show "strain hardening": at constant extensional load, their flow first accelerat... more Glassy polymers show "strain hardening": at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a 'crinkle factor' describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.
We study numerically the formation of long-lived transient shear bands during shear startup withi... more We study numerically the formation of long-lived transient shear bands during shear startup within two models of soft glasses (a simple fluidity model and an adapted 'soft glassy rheology' model). The degree and duration of banding depends strongly on the applied shear rate, and on sample age before shearing. In both models the ultimate steady flow state is homogeneous at all shear rates, consistent with the underlying constitutive curve being monotonic. However, particularly in the SGR case, the transient bands can be extremely long lived. The banding instability is neither 'purely viscous' nor 'purely elastic' in origin, but is closely associated with stress overshoot in startup flow.
We study theoretically the onset of shear banding in the three most common time-dependent rheolog... more We study theoretically the onset of shear banding in the three most common time-dependent rheological protocols: step stress, finite strain ramp (a limit of which gives a step strain), and shear startup. By means of a linear stability analysis we provide a fluid-universal criterion for the onset of banding for each protocol, which depends only on the shape of the experimentally measured timedependent rheological response function, independent of the constitutive law and internal state variables of the particular fluid in question. Our predictions thus have the same highly general status, in these time-dependent flows, as the widely known criterion for banding in steady state (of negatively sloping shear stress vs. shear rate). We illustrate them with simulations of the rolie-poly model of polymer flows, and the soft glassy rheology model of disordered soft solids.
We study theoretically the formation of shear bands in time-dependent flows of polymeric and worm... more We study theoretically the formation of shear bands in time-dependent flows of polymeric and wormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strain (or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally. For each protocol we perform a linear stability analysis to provide a fluid-universal criterion for the onset of shear banding, following our recent Letter 61. In each case this criterion depends only on the shape of the experimentally measured rheological response function for that protocol, independent of the constitutive properties of the material in question. (Therefore our criteria in fact concern all complex fluids and not just the polymeric ones of interest here. A separate manuscript 30 will explore them in a broad class of disordered soft glassy materials including foams, dense emulsions, dense colloids, and microgel bead suspensions.) An important prediction is that pronounced banding can arise transiently in each of these protocols, even in fluids for which the underlying constitutive curve of stress as a function of strain-rate is monotonic and a steadily flowing state is accordingly unbanded. For each protocol we provide numerical results in the rolie-poly and Giesekus models that support our predictions. We comment on the ability of the rolie-poly model to capture the observed experimental phenomenology, and on the failure of the Giesekus model.
Glassy polymers show "strain hardening": at constant extensional load, their flow first accelerat... more Glassy polymers show "strain hardening": at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a 'crinkle factor' describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.
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Papers by Robyn Cooke