Unraveling radial dependency effects in fiber thermal drawing

Fiber-based devices with advanced functionalities are emerging as promising solutions for various applications in flexible electronics and bioengineering. Multimaterial thermal drawing, in particular, has attracted strong interest for its ability to generate fibers with complex architectures. Thus far, however, the understanding of its fluid dynamics has only been applied to single material preforms for which higher order effects, such as the radial dependency of the axial velocity, could be neglected. With complex multimaterial preforms, such effects must be taken into account, as they can affect the architecture and the functional properties of the resulting fiber device. Here, we propose a versatile model of the thermal drawing of fibers, which takes into account a radially varying axial velocity. Unlike the commonly used cross section averaged approach, our model is capable of predicting radial variations of functional properties caused by the deformation during drawing. This is demonstrated for two effects observed, namely, by unraveling the deformation of initially straight, transversal lines in the preform and the dependence on the draw ratio and radial position of the in-fiber electrical conductivity of polymer nanocomposites, an important class of materials for emerging fiber devices. This work sets a thus far missing theoretical and practical understanding of multimaterial fiber processing to better engineer advanced fibers and textiles for sensing, health care, robotics, or bioengineering applications

Non-Newtonian effects on draw resonance in film casting

In this paper, the influence of non-Newtonian material properties on the draw resonance instability in film casting is investigated. Viscoelastic models of infinite width film casting are derived systematically following an asymptotic expansion and using two well-known constitutive equations: the Giesekus model and the simplified Phan–Thien/Tanner (PTT) model. Based on a steady state analysis, a numerical boundary condition for the inlet stresses is formulated, which suppresses the unknown deformation history of the die flow. The critical draw ratio in dependence of both the Deborah number and the nonlinear parameters is calculated by means of linear stability analysis. For both models, the most unstable instability mode may switch under variation of the control parameters, leading to a non-continuous change in the oscillation frequency at criticality. The effective elongational viscosity, which depends exclusively on the local Weissenberg number, is analyzed and identified as crucial quantity as long as the Deborah number is not too high. This is demonstrated by using a generalized Newtonian fluid model to approximate the PTT model. Based on such a generalized Newtonian fluid model, the effects of strain hardening and strain thinning are finally explored, revealing two opposing mechanisms underlying the non-Newtonian stability behavior

Der Einfluss von Prozess- und Materialparametern auf die Draw Resonance Instabilität

In this work, the influence of process and material parameters on the draw resonance instability in film casting and fiber spinning is investigated both theoretically and experimentally. Draw resonance generally occurs if the draw ratio, i.e., the ratio of outlet to inlet velocity, exceeds a critical value, and manifests itself in steady oscillations of the flow velocity and the geometric properties of the fibers and films. Several Newtonian and viscoelastic models for film casting and fiber spinning are derived and the critical draw ratio is determined by means of linear stability analysis in order to investigate the influence of various effects like gravity, inertia, neck-in and strain hardening on draw resonance. Moreover, physical mechanisms underlying the instability are revealed and alternative stability criteria are reviewed and extended. Employing control parameters with strong connection to practical application, the results are visualized in stability maps, which enable both a quick determination of the critical draw ratio and a partition of the parameter space into several dynamical regimes. The theoretical results are completed by an experimental study on draw resonance in fiber spinning. Using an effective relaxation time, the measured critical draw ratios can be well described by the theoretical predictions.n dieser Arbeit wird der Einfluss von Prozess- und Materialparametern auf die Draw Resonance Instabilität bei der Folienextrusion und beim Faserspinnen sowohl theoretisch als auch experimentell untersucht. Draw Resonance tritt im Allgemeinen auf, wenn das Abzugsverhältnis, also das Verhältnis zwischen Ausgangs- und Eingangsgeschwindigkeit, einen kritischen Wert überschreitet und äußert sich durch permanente Oszillationen in der Fließgeschwindigkeit und den geometrischen Eigenschaften der Fasern und Folien. Mehrere newtonsche und viskoelastische Modelle für die Folienextrusion und das Faserspinnen werden hergeleitet und das kritische Abzugsverhältnis wird mittels linearer Stabilitätsanalyse bestimmt, um den Einfluss verschiedener Effekte wie Gravitation, Trägheit, Neck-in und Dehnverfestigung auf die Draw Resonance zu untersuchen. Außerdem werden der Instabilität zu Grunde liegende physikalische Mechanismen aufgezeigt und alternative Stabilitätskriterien überprüft und erweitert. Unter Verwendung von Kontrollparametern mit engem Bezug zur praktischen Anwendung werden die Ergebnisse in Stabilitätskarten dargestellt, die sowohl eine schnelle Bestimmung des kritischen Abzugsverhältnisses als auch eine Aufteilung des Parameterraums in verschiedene dynamische Regimes ermöglichen. Die theoretischen Ergebnisse werden durch eine experimentelle Untersuchung der Draw Resonance beim Faserspinnen vervollständigt. Mit Hilfe einer effektiven Relaxationszeit können die gemessenen kritischen Abzugsverhältnisse gut durch die theoretischen Vorhersagen beschrieben werden

Combined influence of inertia, gravity and surface tension on the linear stability of Newtonian fiber spinning

The draw resonance effect appears in fiber spinning processes if the ratio of take-up to inlet velocity, the so-called draw ratio, exceeds a critical value and manifests itself in steady oscillations of flow velocity and fiber diameter. We study the effect of surface tension on the draw resonance behavior of Newtonian fiber spinning in the presence of inertia and gravity. Utilizing an alternative scaling makes it possible to visualize the results in stability maps of highly practical relevance. The interplay of the destabilizing effect of surface tension and the stabilizing effects of inertia and gravity lead to nonmonotonic stability behavior and local stability maxima with respect to the dimensionless fluidity and the dimensionless inlet velocity. A region of unconditional instability caused by the influence of surface tension is found in addition to the region of unconditional stability caused by inertia, which was described in previous works [M. Bechert, D. W. Schubert, and B. Scheid, Eur. J. Mech B 52, 68 (2015)EJBFEV0997-754610.1016/j.euromechflu.2015.02.005; Phys. Fluids 28, 024109 (2016)PHFLE61070-663110.1063/1.4941762]. Due to its importance for a particular group of fiber spinning applications, a viscous-gravity-surface-tension regime, i.e. negligible effect of inertia, is analyzed separately. The mechanism underlying the destabilizing effect of surface tension is discussed and established stability criteria are tested for validity in the presence of surface tension.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Practical mapping of the draw resonance instability in film casting of Newtonian fluids

The influence of viscosity and inlet velocity on the draw resonance instability of film casting processes is quantitatively analysed. By linear stability analysis of a Newtonian model including inertia and gravity effects, stability curves for different control parameter values are calculated numerically. For this purpose, we propose a scaling law which separates the fluidity, i.e. the reciprocal viscosity and the inlet velocity into two independent dimensionless parameters. This new scaling evidences a minimum of stability, separating two regimes of opposite behaviour: one for which increasing the inlet flow rate has a destabilizing effect due to viscosity and one for which increasing the inlet flow rate has a stabilizing effect due to gravity and inertia; increasing the fluidity has always a stabilizing effect. By fitting the stability curves with an appropriate postulated function, we are able to construct correlations between the critical draw ratio, the fluidity and the inlet velocity. For the first time regimes of negligible inertia or negligible gravity effects are revealed as well as a regime of unconditional stability. The proposed correlations for each of these regimes can further be used as an analytical solvable criterion for determining the onset of draw resonance in film casting.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

On the stabilizing effects of neck-in, gravity, and inertia in Newtonian film casting

We investigate the influence of the reduction of width along the stretching direction, the so-called neck-in effect, on the draw resonance instability in Newtonian film casting using a linear stability analysis of a model of reduced dimensionality including gravity and inertia forces. Proper scaling reveals the aspect ratio, i.e. the ratio of the initial film half-width to the film length, together with the fluidity and the inlet velocity as independent, dimensionless control parameters. Moreover, we introduce the local Trouton ratio as a measure for the type of elongational deformation, which can be uniaxial, planar, or a combination of both. In the case of purely uniaxial or planar deformations, a one-dimensional model is sufficient. The influence of the control parameters on the draw resonance instability, including a threshold to unconditional stability, is visualized by several stability maps. Special cases of viscous-gravity and viscous-inertia models are analyzed separately due to their practical importance. Gravity appears to influence the aspect ratio at which the critical draw ratio is maximum and amplifies the stabilizing effect of the neck-in. Inertia increases the stabilization due to neck-in, eventually leading to a window of unconditional stability within the analyzed region of aspect ratios. The mechanism underlying the complete suppression of draw resonance is presented, using exclusively steady state analysis. Additionally, the stabilizing mechanisms of gravity and neck-in are revealed. Known alternative stability criteria are extended to the case of finite width and their validity is tested in the presence of inertia, gravity, and finite aspect ratios.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Practical mapping of the draw resonance instability in film casting of Newtonian fluids

The influence of viscosity and inlet velocity on the draw resonance instability of film casting processes is quantitatively analysed. By linear stability analysis of a Newtonian model including inertia and gravity effects, stability curves for different control parameter values are calculated numerically. For this purpose, we propose a scaling law which separates the fluidity, i.e. the reciprocal viscosity and the inlet velocity into two independent dimensionless parameters. This new scaling evidences a minimum of stability, separating two regimes of opposite behaviour: one for which increasing the inlet flow rate has a destabilizing effect due to viscosity and one for which increasing the inlet flow rate has a stabilizing effect due to gravity and inertia; increasing the fluidity has always a stabilizing effect. By fitting the stability curves with an appropriate postulated function, we are able to construct correlations between the critical draw ratio, the fluidity and the inlet velocity. For the first time regimes of negligible inertia or negligible gravity effects are revealed as well as a regime of unconditional stability. The proposed correlations for each of these regimes can further be used as an analytical solvable criterion for determining the onset of draw resonance in film casting

Linear stability analysis of nonisothermal glass fiber drawing

The draw resonance effect appears in fiber drawing processes when the draw ratio, defined as the ratio between the take-up and the inlet velocities, exceeds a critical value. In many cases, inertia, gravity, and surface tension cannot be neglected, and a model combining all these effects is necessary in order to correctly describe the physics of the phenomenon. Additionally, it is also known that cooling can have a highly stabilizing effect on the draw resonance instability. However, a detailed analysis encompassing the effect of inertia, gravity, surface tension, and temperature is still lacking. Due to a destabilizing effect induced by geometry in the heat equation, we first show that the maximum critical draw ratio for fiber drawing can be two orders of magnitude lower than the one for the film casting problem when the heat transfer coefficient is assumed constant. By introducing a scaling making the fiber aspect ratio an independent parameter, we next show that the high value of the critical draw ratio encountered in industrial applications could be rationalized only if we consider that the heat transfer coefficient is not constant but depends on both the velocity and the cross-section area of the fiber. Within this framework, we show how the practical stability window is affected by the five control parameters: the draw ratio, the fiber aspect ratio, the inlet temperature, the convective heat transfer coefficient, and the stiffness of the non-homogeneous ambient temperature. We finally discuss the influence of radiative heat transfer on the stability.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Transport of flexible fibers in confined microchannels

When transported in confined geometries rigid fibers show interesting transport dynamics induced by friction with the top and bottom walls. Fiber flexibility causes an additional coupling between fiber deformation and transport and is expected to lead to more complex dynamics. A first crucial step for their understanding is the characterization of the deformed fiber shape. Here we characterize this shape for a fiber transported in a confined plug flow perpendicular to the flow direction using a combination of microfluidic experiments and numerical simulations. In the experiments, size, initial orientation, and mechanical properties of the fibers are controlled using microfabrication techniques and in situ characterization methods. The numerical simulations use modified Brinkman equations as well as full three-dimensional simulations. We show that the bending of a perpendicular fiber results from the force distribution acting on the elongated object and is proportional to the elasto-viscous number, which compares viscous to elastic forces. We quantitatively characterize the influence of the confinement on the fiber deformation. The precise understanding of the deformation of a flexible fiber in a confined geometry can also be used in future to understand the deformation and transport of more complex deformable particles in confined flows, such as vesicles or red blood cells