Viscous Threads Research Articles

Humidity affects the extensibility of an orb-weaving spider's viscous thread droplets

The prey-capture threads found in most spider orb webs rely on viscous droplets for their stickiness. Each droplet is formed of a central mass of viscoelastic glycoprotein glue surrounded by an aqueous covering, both of which incorporate hydrophilic components. We found that the extensibility of droplets on Larinioides cornutus threads increased as humidity increased. However, the deflection of the droplets' supporting axial lines did not change, indicating that atmospheric water uptake increases glycoprotein plasticity, but not glycoprotein adhesion. The extensibility of droplets, along with that of the thread's supporting axial fibers, is responsible for summing the adhesion of multiple thread droplets. Therefore, daily changes in humidity have the potential to significantly alter the performance of viscous threads and orb webs.

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

AbstractThe nonlinear dynamics of a viscous filament surrounded by a second viscous fluid arranged in a core-annular configuration when a radial electric field acts in the annular region, are studied analytically and computationally using boundary element methods. The flow is characterized by the viscosity ratio, an electric Weber number measuring the strength of the electric field, a geometrical parameter measuring the thickness of the undisturbed annular region, as well as a computational parameter that fixes the wavenumber of the undulations. Axisymmetric solutions are computed by direct numerical simulations in the Stokes limit for general values of the parameters when the two fluids have equal viscosities, and an asymptotic theory is carried out to produce a novel evolution equation for thin film dynamics valid when the undisturbed annular thickness is small and the viscosity ratio is of order one. It is established (in agreement with previous computations in the absence of electric fields) that a sufficiently thick annulus enables thread breakup while a sufficiently thin one (approximately one fifth of the undisturbed thread radius for the case of equal viscosities, for instance) suppresses pinching and drives the interface to approach the tube wall asymptotically without actually touching it. The present simulations show that the electric field affects the dynamics drastically in several ways. First, it promotes interfacial wall touchdown in finite time and a comparison between direct simulations and the asymptotic solutions are in fair agreement. Second, the electric field acts to suppress pinching in the sense that solutions that lead to jet breakup due to a thick enough viscous annulus are driven to wall touchdown. When pinching takes place we find that the ultimate pinching solutions are self-similar and recover the non-electrified ones to leading order for the range of parameters studied.

Breakup of an electrified, perfectly conducting, viscous thread in an AC field

We study the axisymmetric breakup and satellite formation of slender jets surrounded by a concentrically placed cylindrical electrode and subjected to time-dependent AC electric fields. The jet is assumed to be a perfectly conducting viscous fluid and surrounded by a dielectric inviscid gas. We use the long-wave approximation to derive coupled evolution equations for the interface position and the axial velocity component, which accounts for electrostatic forcing. The electrostatic force in this case is large and competes with capillary forces near the rupture point, causing the interface to oscillate and the satellite to have shapes that are distinct from the DC case. In particular, our results indicate that it may be possible to use the AC field to control the number of satellites accompanying breakup as well as their size.

Constraints on the adhesion of viscous threads spun by orb-weaving spiders: the tensile strength of glycoprotein glue exceeds its adhesion

In this study we tested the hypothesis that a viscous thread releases its hold on a surface because its glycoprotein glue pulls from the surface and not because its elongating droplets break near their attachment to the surface. We compared the values obtained when three species' viscous threads adhered to four smooth surfaces, which differed in their total surface energy and in the proportions of their dispersion and polar energy components. Although water comprised 43-70% of the volume of these viscous droplets, only the dispersion surface energies of test materials and not their polar surface energies impacted thread adhesion. These results support the droplet pull-off hypothesis and are consistent with a previous finding that capillary force contributes little to thread adhesion. Just as a viscous thread's stickiness is constrained by the tensile strength of its supporting axial fibers, our findings suggest that glycoprotein adhesion is constrained by glycoprotein tensile strength.

Adhesive compatibility of cribellar and viscous prey capture threads and its implication for the evolution of orb‐weaving spiders

Evolution of orb-weaving spiders that comprise the Orbiculariae clade involved a transition in the composition of prey capture thread that has been challenging to explain. The primitive cribellar threads spun by members of the Deinopoidea subclade resemble the capture threads of their non-orb-web-weaving ancestors and are formed of thousands of fine, dry, protein cribellar fibrils. In contrast, the derived viscous capture threads spun by members of the Araneoidea subclade have regularly spaced, aqueous adhesive droplets. When second instar deinopoid spiderlings emerge from egg sacs they are unable to spin cribellar threads, and, therefore, do not construct orb-webs; whereas second instar araneoids spin capture threads and construct orb-webs. If, as we hypothesize, viscous material evolved to enable second instar spiderlings to construct orb-webs, early araneoids may have spun composite cribellar-viscous capture threads. To examine the functional feasibility of such intermediate capture threads, we compared the adhesion of cribellar threads, viscous threads, and combined cribellar-viscous threads. The stickiness of these combined threads was greater than that of native cribellar or viscous threads alone. The viscous material of Araneus marmoreus threads exhibited a substantial increase in stickiness when combined with cribellar fibrils and that of Argiope aurantia threads a small increase in stickiness when combined with cribellar fibrils. Thus, if early araneoids retained their ability to spin cribellar threads after having evolved glands that produced viscous material, their composite threads could have formed a functional adhesive system that achieved its stickiness at no loss of material economy.

The asymptotic structure of a slender dragged viscous thread

The behaviour of a viscous thread as it falls onto a moving belt is analysed in the asymptotic limit of a slender thread. While the bending resistance of a slender thread is small, its effects are dynamically important near the contact point with the belt, where it changes the curvature and orientation of the thread. Steady flows are shown to fall into one of three distinct regimes, depending on whether the belt is moving faster than, slower than or close to the same speed as the free-fall velocity of the thread. The key dynamical balances in each regime are explained and the role of bending stresses is found to be qualitatively different. The asymptotic solutions exhibit the ‘backward-facing heel’ observed experimentally for low belt speeds, and provide the leading-order corrections to the stretching catenary in theory previously developed for high belt speeds. The asymptotic stability of the thread to the onset of meandering is also analysed. It is shown that the entire thread, rather than the bending boundary layer alone, governs the stability. A balance between the destabilising reaction forces near the belt and the restoring force of gravity on the remainder of the thread determines the onset of meandering, and an analytic estimate for the meandering frequency is thereby obtained. At leading order, neutral stability occurs with the belt moving a little more slowly than the free-fall velocity of the thread, not when the lower part of the thread begins to be under compression, but when the horizontal reaction force at the belt begins to be slightly against the direction of belt motion. The onset of meandering is the heel ‘losing its balance’.

Breakup of an electrified viscous thread with charged surfactants

The dynamics and breakup of electrified viscous jets in the presence of ionic surfactants at the interface are investigated theoretically. Axisymmetric configurations are considered and the jet is surrounded by a concentrically placed cylindrical electrode, which is held at a constant voltage potential. The annular region between the jet and the electrode is taken to be a hydrodynamically passive dielectric medium and an electric field is set up there and drives the flow, along with other physical mechanisms including capillary instability and viscous effects. The jet fluid is taken to be a symmetric electrolyte and proper modeling of the cationic and anionic species is used by considering the Nernst–Planck equations in order to find the volume charge density that influences the electric field in the jet. A positively charged insoluble surfactant is present at the interface, and its evolution, as well as the resulting value of the local surface tension coefficient, is coupled with the voltage potential at the interface. The resulting coupled nonlinear systems are derived and analytical progress is made by carrying out a nonlinear slender jet approximation. The reduced model is described by a number of hydrodynamic, electrical, and electrokinetic parameters, and an extensive computational study is undertaken to elucidate the dynamics along with allied linear properties. It is established that the jet ruptures in finite time provided the outer electrode is sufficiently far away, and numerous examples are given where the dimensionless parameters can be used to control the size of the satellite drops that form beyond the topological transition, as well as the time to break up. It is also shown that pinching solutions follow the self-similar dynamics of clean viscous jets at times close to the breakup time. Finally, a further asymptotic theory is developed for large Debye layers to produce an additional model that incorporates the effects of surface charge diffusion. Numerical solutions establish that the presence of electrostatic and electrokinetic effects increases the sizes of satellites but have a rather weak influence on the time to rupture.

Discrete viscous threads

We present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which sheds light on the role of time-parallel transport in eliminating---without approximation---all but an O(n) band of entries of the physical system's energy Hessian. The result is a fast, unified, implicit treatment of viscous threads and elastic rods that closely reproduces a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluid-mechanical sewing machine. The novel implicit treatment also yields an order of magnitude speedup in our elastic rod dynamics.

Discrete viscous threads

We present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which sheds light on the role of time-parallel transport in eliminating---without approximation---all but an O ( n ) band of entries of the physical system's energy Hessian. The result is a fast, unified, implicit treatment of viscous threads and elastic rods that closely reproduces a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluid-mechanical sewing machine. The novel implicit treatment also yields an order of magnitude speedup in our elastic rod dynamics.

Effect of surface viscosity on the capillary instability of an annular layer or viscous thread

The capillary instability of two annular layers confined between two concentric cylinders is considered under conditions of Stokes flow. The inner cylinder, the outer cylinder or both cylinders may be absent, yielding an interior or exterior annular layer or a thread suspended in an infinite medium. The interface exhibits constant surface tension and develops viscous interfacial tensions due to the interfacial flow driven by the instability. A linear stability analysis for axisymmetric perturbations is carried out confirming the stabilizing effect of the surface viscosity over a broad range of conditions. In the case of a thread suspended in vacuum, the surface viscosity is not able to emulate an external medium viscosity. Numerical solutions of a simplified system of evolution equations for long waves using a particle method suggest that surface viscosity prevents thread break-up after a finite evolution time.

The role of granules within viscous capture threads of orb-weaving spiders

Sticky viscous prey capture threads form the spiral elements of spider orb-webs and are responsible for retaining insects that strike a web. These threads are formed of regularly spaced aqueous droplets that surround a pair of supporting axial fibers. When a thread is flattened on a microscope slide a small, opaque granule can usually be seen within each droplet. These granules have been thought to be the glycoprotein glue that imparts thread adhesion. Both independent contrast and standard regressions showed that granule size is directly related to droplet volume and indicated that granule volume is about 15% of droplet volume. We attempted to find support for the hypothesized adhesive role of granules by establishing an association between the contact surface area and volume of these granules and the stickiness of the viscous threads of 16 species in the context of a six-variable model that describes thread stickiness. However, we found that granule size made either an insignificant or a small negative contribution to thread stickiness. Consequently, we hypothesize that granules serve to anchor larger, surrounding layers of transparent glycoprotein glue to the axial fibers of the thread, thereby equipping droplets to resist slippage on the axial fibers as these droplets generate adhesion, elongate under a load, and transfer force to the axial fibers.

Model for Coiling and Meandering Instability of Viscous Threads

A numerical model is presented to describe both the transient and steady-state dynamics of viscous threads falling onto a plane. The steady-state coiling frequency w is calculated as a function of fall height H. In the case of weak gravity, w ~ H^{-1} and w ~ H are obtained for lower and higher fall heights respectively. When the effect of gravity is significant, the relation w ~ H^2 is observed. These results agree with the scaling laws previously predicted. The critical Reynolds number for coil-uncoil transition is discussed. When the gravity is weak, the transition occurs with hysteresis effects. If the plane moves horizontally at a constant speed, a variety of meandering oscillation modes can be observed experimentally. The present model also can describe this phenomenon. The numerically obtained state diagram for the meandering modes qualitatively agrees with the experiment.

Two new species of Hymenoepimecis (Hymenoptera: Ichneumonidae: Pimplinae) with notes on their spider hosts and behaviour manipulation

The wasp genera included in the Polysphincta genus-group develop exclusively as koinobiont ectoparasitoids of spiders, an unusual pattern within Hymenoptera. All known species of Hymenoepimecis attack orb-web spiders and Hymenoepimecis argyraphaga was previously described inducing a sudden modification of its host's web-building behaviour. Information on parasitoid–host interactions and even on host identities for most members of the genus-group, however, remain scarce. In this study we describe two new species of Hymenoepimecis and present information on their hosts, spiders of the genera Leucauge (Tetragnathidae) and Manogea (Araneidae). Cocoon webs of both host species are distinct from their normal webs. The modified cocoon web of Leucauge roseosignata constructed under the influence of Hymenoepimecis japi sp. nov. is very similar to the cocoon web described for Leucauge argyra. It is composed of three axes, including several radial threads each, and a hub used by the larva to attach the cocoon's suspension line. Spiral viscous threads, present in normal webs and in webs of parasitized spiders carrying larvae in the initial instars, are absent in cocoon webs. In the cocoon web of Manogea porracea the horizontal sheet is poorly structured and the cocoon is attached far from the spider's normal resting position, in an area composed of a densely tangled structure.

The adhesive delivery system of viscous capture threads spun by orb-weaving spiders

The sticky viscous capture threads in araneoid orb-webs are responsible for retaining insects that strike these webs. We used features of 16 species' threads and the stickiness that they expressed on contact plates of four widths to model their adhesive delivery systems. Our results confirm that droplets at the edges of thread contact contribute the greatest adhesion, with each successively interior droplet contributing only 0.70 as much adhesion. Thus, regardless of the size and spacing of a thread's large primary droplets, little adhesion accrues beyond a span of 20 droplets. From this pattern we computed effective droplet number (EDN), an index that describes the total droplet equivalents that contribute to the stickiness of thread spans. EDN makes the greatest positive contribution to thread stickiness, followed by an index of the shape and size of primary droplets, and the volume of small secondary droplets. The proportion of water in droplets makes the single greatest negative contribution to thread stickiness, followed by a thread's extensibility, and the area of flattened droplets. Although highly significant, this six-variable model failed to convincingly describe the stickiness of six species, a problem resolved when species were assigned to three groups and a separate model was constructed for each. These models place different weights on the variables and, in some cases, reverse or exclude the contribution of a variable. Differences in threads may adapt them to particular habitats, web architectures or prey types, or they may be shaped by a species' phylogeny or metabolic capabilities.

Daily and seasonal changes in the stickiness of viscous capture threads in Argiope aurantia and Argiope trifasciata orb‐webs

The spirally arrayed viscous capture threads of spider orb-webs are formed of small, regularly spaced adhesive droplets and are responsible for retaining insects that strike the web, giving a spider more time to subdue these prey. These sticky threads are deposited from the perimeter of the web inward. We tested the hypothesis that depletion of silk reserves during web construction affects the properties of capture threads spun by adult female Argiope aurantia and Argiope trifasciata. In both species the droplet volume (DV) per millimeter thread length was the same in outer and inner capture threads and in early and late season webs. However, the outer threads of both species were stickier than their inner threads and, consequently, had a greater stickiness per DV. Thus, dwindling silk reserves during web construction appeared to reduce the stickiness of both species' threads by changing the composition rather than the volume of their viscous droplets. In A. trifasciata, which we studied later in the fall than A. aurantia, there were also seasonal declines in both thread stickiness and stickiness per DV, which may result from either the depletion of silk reserves or the reallocation of these resources. Early season webs of A. trifasciata also had greater stickiness per square centimeter of capture area than late season webs, better equipping these early webs to retain insects.

Formation of miscible fluid microstructures by hydrodynamic focusing in plane geometries

We experimentally investigate the flow structures formed when two miscible fluids that have large viscosity contrasts are injected and hydrodynamically focused in plane microchannels. Parallel viscous flows composed of a central stream surrounded by symmetric sheath streams are examined as a function of the flow rates, fluid viscosities, and rates of molecular diffusion. We study miscible interfacial morphologies and show a route for manipulating viscous flow-segregation processes in plane microsystems. The diffusion layer at the boundary of an ensheathed fluid grows as function of the distance downstream and depends on the Péclet number. In particular, we observe diffusion-enhanced viscous ensheathing processes. In the presence of a constriction, we investigate the formation of a lubricated viscous thread in the converging flow and also the buckling morphologies of the thread in the diverging flow. This study, relevant to multifluid flow between a "thick" material and a "thin" solvent, demonstrates the possibility to further control steady and oscillatory miscible fluid microstructures.

Axisymmetric flow of two fluids in a pulsating pipe

The motion of a viscous thread surrounded by an annular viscous layer inside a pulsating cylindrical pipe whose radius is a periodic function of time is investigated. At zero Reynolds number, a stagnation-point-type solution may be written down in closed form. A Floquet linear stability analysis for Stokes flow reveals the pulsations either decrease or increase the growth rate of longwave disturbances depending on the initial radius of the thread. For a moderate-sized initial thread radius, increasing the amplitude of the pulsations decreases the critical wavenumber for instability to below the classical Rayleigh threshold. Increasing the viscosity contrast, so that the fluid in the annular layer becomes more viscous than the fluid in the thread, tends to decrease the growth rate of disturbances. In the second part of the paper, the basic stagnation-point-type flow at arbitrary Reynolds number is computed using a numerical method on the assumption that the interface is a circular cylinder at all times. During the motion, either the thread radius tends to increase and the thickness of the annular layer decreases, or else the thread tends to thin and the thickness of the annular layer increases, depending upon the initial conditions and the parameter values. For a judicious choice of initial condition, a time-periodic exact solution of the Navier–Stokes equations is identified.

Adhesive efficiency of spider prey capture threads

Cribellar capture threads are comprised of thousands of fine silk fibrils that are produced by the spigots of a spider's cribellum spinning plate and are supported by larger interior axial fibers. This study examined factors that constrain the stickiness of cribellar threads spun by members of the orb-weaving family Uloboridae in the Deinopoidea clade and compared the material efficiency of these threads with that of viscous capture threads produced by members of their sister clade, the Araneoidea. An independent contrast analysis confirmed the direct relationship between cribellar spigot number and cribellar thread stickiness. A model based on this relationship showed that cribellar thread stickiness is achieved at a rapidly decreasing material efficiency, as measured in terms of stickiness per spigot. Another limitation of cribellar thread was documented when the threads of two uloborid species were measured with contact plates of four widths. Unlike that of viscous threads, the stickiness of cribellar threads did not increase as plate width increased, indicating that only narrow bands along the edges of thread contact contributed to their stickiness. As thread volume increased, the gross material efficiency of cribellar threads decreased much more rapidly than that of viscous threads. However, cribellar threads achieved their stickiness at a much greater gross material efficiency than did viscous threads, making it more challenging to explain the transition from deinopoid to araneoid orb-webs.

The contribution of axial fiber extensibility to the adhesion of viscous capture threads spun by orb-weaving spiders

The viscous capture threads produced by over 4000 species of orb-weaving spiders are formed of regularly spaced aqueous droplets supported by a pair of axial fibers. These threads register increased stickiness when spans of increasing lengths contact a surface, indicating that adhesion is recruited from multiple droplets. This study examined threads produced by five species to test the hypothesis that axial fiber extensibility is crucial for this summation of adhesion. It did so by comparing the stickiness of unstretched threads with threads that had been elongated to reduce the extensibility of their axial fibers. As stretching these threads also increased the distance between their droplets, we measured the stickiness of stretched threads with contact plates whose widths were increased in proportion to the degree of thread elongation. We then accounted for the actual thread elongation achieved for each individual's threads and for differences in the five species' absolute thread extensibility. The results showed that in four species thread extensibility contributed positively to adhesion. For three species, thread extensibility and droplet volume together explained the mean per droplet adhesion of threads. Models based on these three species show that, as threads were elongated, increasing amounts of potential adhesion were lost to diminished axial fiber extensibility. These models indicate that approximately one-third of an unstretched viscous thread's stickiness accrues from the adhesive recruitment made possible by axial fiber extensibility.

Meandering instability of a viscous thread

A viscous thread falling from a nozzle onto a surface exhibits the famous rope-coiling effect, in which the thread buckles to form loops. If the surface is replaced by a belt moving with speed U , the rotational symmetry of the buckling instability is broken and a wealth of interesting states are observed [see S. Chiu-Webster and J. R. Lister, J. Fluid Mech. 569, 89 (2006)]. We experimentally studied this "fluid-mechanical sewing machine" in a more precise apparatus. As U is reduced, the steady catenary thread bifurcates into a meandering state in which the thread displacements are only transverse to the motion of the belt. We measured the amplitude and frequency omega of the meandering close to the bifurcation. For smaller U , single-frequency meandering bifurcates to a two-frequency "figure-8" state, which contains a significant 2omega component and parallel as well as transverse displacements. This eventually reverts to single-frequency coiling at still smaller U . More complex, highly hysteretic states with additional frequencies are observed for larger nozzle heights. We propose to understand this zoology in terms of the generic amplitude equations appropriate for resonant interactions between two oscillatory modes with frequencies omega and 2omega . The form of the amplitude equations captures both the axisymmetry of the U=0 coiling state and the symmetry-breaking effects induced by the moving belt.