---
title: Thinning-by-Spinning Mechanism
url: https://www.emergentmind.com/topics/thinning-by-spinning-mechanism
type: topic
---

# Thinning-by-Spinning Mechanism

Thinning-by-spinning denotes a family of mechanisms in which a rotational, spinning, or twist-related process reduces a characteristic transverse scale or a flow resistance. In published usage, the phrase is explicit in the rheology of dense chiral fluids, where microscopic self-spinning lowers macroscopic viscosity [2606.14311]. Closely related literatures use the same conceptual coupling for hydrodynamic film drainage during spin casting [1205.3295], centrifugally stretched jets in rotary jet-spinning [1110.1424], oscillation-enhanced helical elongation in electrospinning [1412.1121], anisotropic deswelling of bipolar liquid-crystal polymer microparticles into twisted spindles [1905.01149], and twist-controlled frictional locking in yarn [2110.04206]. This suggests that the term does not denote a single universal constitutive law; rather, it identifies several mechanistic routes by which spinning, twist, or helicity is coupled to thinning, slendering, or fluidization.

## 1. Terminology and conceptual scope

The meaning of “spinning” is context dependent. In spin casting, spinning is literal substrate rotation that drives radially outward flow and film thinning [1205.3295]. In rotary jet-spinning, spinning first ejects the jet and then sustains a centrifugally driven extensional flow that selects the fiber radius [1110.1424]. In electrospinning under driven perturbations, the relevant “spinning” is the imposed oscillation of the spinneret, which seeds bending instability and lengthens the jet trajectory [1412.1121]. In bipolar liquid-crystal polymer microparticles, the closest mechanism is not a hydrodynamic spinning process but a twist-assisted accommodation of anisotropic shrinkage [1905.01149]. In dense chiral fluids, spinning is microscopic self-rotation encoded through transverse pair forces, and the thinned quantity is viscosity rather than a geometric thickness [2606.14311].

The “thinning” is likewise not unique. It can mean reduction of film thickness \(h\), reduction of fiber radius \(r\), reduction of minor axis relative to major axis in spindle formation, or decrease of shear viscosity \(\eta\). In yarn mechanics, the phrase is again only approximate: twist creates a sufficiently slender, sufficiently twisted geometry in which friction is exponentially amplified, and the theory predicts an optimal yarn radius rather than a direct hydrodynamic thinning law [2110.04206]. A recurring theme across these otherwise disparate systems is that spinning or twist creates either extensional transport, geometric frustration, or an internal stress source that makes a transverse dimension or an effective resistance decrease.

## 2. Hydrodynamic–evaporative thinning in rotating films

For dilute-solution spin casting, the central thinning-by-spinning mechanism is hydrodynamic–evaporative. Rotation creates a radially outward velocity field in the thin film,
\[
u(r,z)=3K\,r\,z\left(h-\frac{z}{2}\right),
\qquad K=\frac{\omega^2}{3\nu},
\]
so liquid is continuously swept outward [1205.3295]. The corresponding volumetric flux induces a specific vertical advective field,
\[
\frac{dZ}{dt}=-K z^2(3h-z),
\]
which matters because the solvent is simultaneously removed at the free surface by evaporation. The film thickness therefore follows
\[
\frac{dh}{dt}=-2Kh^3-E.
\]
The cubic term is the hydrodynamic spin-off contribution, while \(E\) is the evaporative thinning rate.

This formulation produces a natural crossover thickness and timescale,
\[
h_{tr}=\left(\frac{E}{2K}\right)^{1/3},
\qquad
t_{sc}^*=(2E^2K)^{-1/3},
\]
and the scaled thinning law
\[
\frac{d\xi}{d\tau}=-\xi^3-1,
\qquad
\xi=\frac{h}{h_{tr}},
\qquad
\tau=\frac{t}{t_{sc}^*}.
\]
The process is therefore divided into a hydrodynamic regime at large \(h\), a crossover around \(h\sim h_{tr}\), and an evaporation-dominated regime at small \(h\) [1205.3295]. The same analysis identifies a Sherwood number,
\[
S=\frac{Eh_{tr}}{D}=E^{4/3}(2K)^{-1/3}D^{-1},
\]
which governs whether vertical composition stratification is diffusion dominated or evaporation dominated. In this setting, thinning-by-spinning is not merely centrifugal drainage; it is a coupled radial-outflow, vertical-advection, evaporation, and diffusion problem.

Thermal Marangoni forcing modifies the same classical picture without replacing it. In a rotating cylindrical container of PDMS, a cooler center and warmer edge generate a surface-tension gradient that drives inward surface flow, opposing centrifugal spin-off [1806.10595]. The lubrication equation contains centrifugal forcing, Marangoni forcing, gravity, capillarity, and disjoining pressure, and in the central thin-film region the isothermal limit recovers the Emslie-Bonner-Peck law
\[
\bar h(t)\sim \left(1+\frac{4}{3}\mathrm{Fr}^2 t\right)^{-1/2}.
\]
With thermal forcing, the reduced central-thickness equation becomes
\[
\frac{d\bar h}{dt}
=
-\frac{2}{3}\mathrm{Fr}^2\bar h^3
\left(
1-\frac{3c\,\mathrm{Ma}}{\mathrm{Fr}^2\,\bar h}
\right),
\]
so early-time thinning remains classical spin-off, but later-time thinning slows and can arrest at
\[
\bar h_*=\frac{3c\,\mathrm{Ma}}{\mathrm{Fr}^2}.
\]
This establishes an important boundary condition on the concept: spinning can be the dominant early-time thinning mechanism while other stresses control the late-time morphology [1806.10595].

## 3. Extensional draw-down in filament formation

In polymer melt spinning, thinning is the direct consequence of extensional draw-down under incompressibility. The one-dimensional slender-filament model uses cross-sectional area \(A(x,t)\) and axial velocity \(V(x,t)\), with mass conservation
\[
\frac{\partial A}{\partial t}+\frac{\partial(AV)}{\partial x}=0.
\]
At steady state,
\[
A(x)V(x)=\text{const},
\]
and with the nondimensional inlet condition \(A(0)=1\), \(V(0)=1\), and draw ratio \(\mathrm{Dr}=V(1)\), one obtains
\[
A(x)=\frac{1}{V(x)},
\qquad
A(1)=\frac{1}{\mathrm{Dr}}.
\]
The abstract conclusion is that “the fiber velocity and cross section area are determined solely by the draw ratio” [1609.00793]. The momentum balance,
\[
\mathrm{Re}\,A\left(\frac{\partial V}{\partial t}+V\frac{\partial V}{\partial x}\right)=\frac{\partial F}{\partial x},
\qquad
F=A\sigma,
\]
then determines how tension, inertia, and viscoelastic stress shape the profile and its stability. In the multiscale dumbbell formulation, each Lagrangian particle contains \(N_p=10^4\) Hookean dumbbells, equivalent to the upper-convected Maxwell fluid in the limit \(N_p\to\infty\) [1609.00793]. Here spinning means axial take-up, and thinning is kinematic draw-down supported by tensile stress.

Rotary jet-spinning realizes a different extensional route. A rotating reservoir ejects a polymeric jet once centrifugal forcing overcomes capillary retention, with threshold
\[
\Omega_{th}\sim \sqrt{\frac{\sigma}{a^2 s_0\rho}}.
\]
After ejection, the jet is stretched mainly by a centrifugally driven extensional flow. Combining mass conservation with a balance between viscous elongational stress and centrifugal forcing yields the principal radius law
\[
r\sim a\left(\frac{U\nu}{R_c^3\Omega^2}\right)^{1/2}
=
a\left(\frac{U\mu}{\rho R_c^3\Omega^2}\right)^{1/2}.
\]
The measured radii collapse against the predicted scaling variable, with empirical fit
\[
\left(\frac{a^2U\nu}{R_c^3\Omega^2}\right)^{1/2}\sim r^{1.09\pm0.05},
\]
and the reported radius range spans roughly \(150\) nm to \(3\,\mu\)m [1110.1424]. Surface tension primarily controls jet initiation and continuity, not radius selection in the successful regime. The minimum angular speed for fiber formation obeys
\[
\Omega_c\propto \mu^{-3},
\]
and the boundary between “beaded fibers” and “no fibers” is fit by
\[
\Omega\sim \mu^{-2.88\pm0.25}.
\]
Equally important, solvent evaporation is comparatively slow during flight, with \(t_{gap}/t_3\sim 10^{-4}\), so the jet becomes thin first because of spinning-induced extension and only later dries and solidifies [1110.1424].

Electrospinning under driven fast-oscillating perturbations uses yet another route. The spinneret injects the tail bead at
\[
X_N=N_sL\cos(\Omega t),\qquad
Y_N=N_sL\sin(\Omega t),\qquad
Z_N=h-L_{ins},
\]
thereby imposing a systematic off-axis perturbation [1412.1121]. Coulomb self-repulsion amplifies this perturbation into bending instability and three-dimensional helicoidal structures. Because the jet is incompressible,
\[
\pi a^2 l=\pi a_0^2 l_0,
\]
so longer helical paths imply smaller cross-sectional area. Increasing oscillation amplitude from roughly \(1.6\times10^{-4}\,\mathrm{cm}\) to \(1.6\times10^{-3}\,\mathrm{cm}\) leads to about a three-fold reduction in fiber thickness, with
\[
a_f/a_0=2.5\times10^{-3}\quad\text{for }N_s=5\times10^{-4},
\]
and
\[
a_f/a_0\approx 7.5\times10^{-4}\quad\text{for }N_s=5\times10^{-3}.
\]
Increasing frequency from \(10^5\) to \(10^6\,\mathrm{s}^{-1}\) yields roughly a three-fold decrease in thickness as well [1412.1121]. Here thinning-by-spinning is best understood as instability-mediated path elongation rather than direct radial squeezing.

## 4. Geometric twist-assisted slendering in soft solids and fibrous assemblies

In bipolar liquid-crystal polymer microparticles, deswelling from the spherical bipolar configuration causes the microparticle to contract anisotropically and twist in the process, resulting in a twisted spindle shaped structure [1905.01149]. The system consists of roughly \(100\,\mu\mathrm{m}\) diameter droplets fabricated from 5CB and RM257 in water with \(1\,\mathrm{wt}\%\) PVA and \(2\,\mathrm{wt}\%\) Irgacure 369 relative to RM257. Planar anchoring produces the standard bipolar spherical configuration, and UV polymerization fixes that anisotropic network. Extraction of 5CB with ethanol produces pronounced volume reduction, stronger contraction perpendicular to the boojum-to-boojum axis, and thus transformation into a spindle-like particle with boojums at the tips [1905.01149].

The transformation is explicitly two stage. For \(u<1.35\), shrinking proceeds mainly through inner folding or reduction of effective polymer-strand length with little twist. For \(u>1.35\), the particle increasingly shrinks by twisting, and the measured \(\beta(u)\) data for \(5\,\mathrm{wt}\%\) and \(20\,\mathrm{wt}\%\) RM257 collapse onto a common curve [1905.01149]. Representative equilibrium states for \(5\,\mathrm{wt}\%\) RM257 range from \(u=1.4\), \(\beta=11^\circ\) in pure chloroform to \(u=2.0\), \(\beta=44^\circ\) at \(\chi_{EthOH}=0.8\). The authors model the spiral texture by loxodromes on a spindle surface,
\[
z(r)=\pm a\sqrt{\left(1-\frac{r}{a}\right)\left(u^2+\frac{r}{a}\right)},
\]
with tangent direction
\[
\vu{\beta}=\cos\beta\,\vu{e}_r+\sin\beta\,\vu{e}_\theta.
\]
For a surface strand of fixed length \(l_0\), the twist–slenderness coupling is
\[
\beta=
\cos^{-1}\left[
\frac{a}{l_0}(1+u^2)\tan^{-1}(u^{-1})
\right].
\]
This predicts increased twist angle \(\beta\) with increasing aspect ratio \(u\). The article’s closest mechanistic description is therefore a geometric twist-assisted thinning mechanism arising from anisotropic shrinkage and fixed-length strand frustration, not angular momentum or forced spinning [1905.01149].

An allied geometric mechanism appears in yarn. Twisting makes each fiber follow a helix of radius \(r\) and reduced pitch \(p=P/(2\pi)\). For \(r\ll p\), the tension gradient contains an inward radial term,
\[
\frac{d\mathbf t}{dz}\simeq \frac{dt}{dz}\mathbf e_z-\frac{r}{p^2}t(z)\mathbf e_\rho,
\]
which acts as a twist-controlled harmonic potential [2110.04206]. Randomly oriented contact normals balance this inward force, and Coulomb friction then gives the local tension-transmission law
\[
\frac{dt}{dz}=\mu \frac{r}{p^2}t(z).
\]
Hence tension is amplified exponentially,
\[
t(L)=t_0\exp\!\left(\mu \frac{rL}{p^2}\right),
\]
or, in terms of total twist angle \(\theta=L/p\),
\[
t(L)=t_0\exp\!\left(\mu \frac{r\theta^2}{L}\right).
\]
The governing nondimensional parameter is the Hercules twist number,
\[
\mathcal H=\mu \theta^2\frac{R}{L},
\]
with critical threshold \(\mathcal H_c\simeq 30\) for locking. The theory then predicts an optimal yarn radius,
\[
R_{\mathrm{opt}}=\frac{2\mu \varepsilon_r \mathcal L}{\mathcal H_c},
\]
and for cotton gives \(R_{\mathrm{opt}}\simeq 80\,\mu\mathrm m\) and pitch \(P\simeq 1.2\,\mathrm{mm}\), close to the measured \(P\simeq 1.5\,\mathrm{mm}\) [2110.04206]. This is not thinning of a liquid, but it is a twist-controlled route to a slender, self-locking structure.

## 5. Rheological thinning-by-spinning in dense chiral fluids

The most explicit modern use of the term appears in dense chiral-fluid rheology. In a two-dimensional Lennard-Jones model with transverse interactions, microscopic self-spinning acts as an intrinsic source of fluctuations and shear, fluidizes a solid, weakens hexatic order, and lowers the apparent viscosity under shear [2606.14311]. The equations of motion are
\[
m\ddot{\mathbf r}_i+\Gamma \dot{\mathbf r}_i
=
\sum_{j\neq i}\left[\mathbf f_{ij}-\nabla_iU(r_{ij})\right]
+\Gamma \dot\gamma y_i \hat{\mathbf x}
+\sqrt{2\Gamma k_B T}\,\boldsymbol{\nu}_i,
\]
with transverse pair force
\[
\mathbf f_{ij}=-\Gamma \mathbf u_{ij},
\qquad
\mathbf u_{ij}
=
\omega \sigma_d^3\,\hat{\mathbf z}\times \frac{\mathbf r_{ij}}{r_{ij}^3}.
\]
The chirality parameter is
\[
\Omega=\frac{\Gamma\omega\tau^2}{m},
\]
and the viscosity is defined from the symmetrized off-diagonal stress,
\[
\eta
=
\frac{\langle \sigma_{xy}+\sigma_{yx}\rangle}{2\dot\gamma}
\equiv
\frac{\langle \sigma^{\rm s}\rangle}{\dot\gamma}.
\]

Two regimes are distinguished. In the solid regime, at \(\rho=0.7\), \(k_BT=0.35\), the passive system does not flow at low \(\dot\gamma\), while above a threshold in chirality the system develops a finite zero-shear viscosity [2606.14311]. In the liquid regime, at \(\rho=0.6\), \(k_BT=0.47\), increasing \(|\Omega|\) reduces \(\eta\). The linear-response viscosity is described by a generalized Green–Kubo relation,
\[
\eta
=
\frac{A}{k_B T_{\rm eff}(\Omega)}
\int_0^{+\infty}
\langle \sigma^{\rm s}(0)\sigma^{\rm s}(t)\rangle_0\,dt,
\]
where the effective temperature is obtained from
\[
k_BT_{\rm eff}=\frac{D}{\mu}.
\]
A key result is that \(T_{\rm eff}\) grows monotonically with \(\Omega\), so chirality can be coarse-grained as an effective heating and fluidization channel [2606.14311].

Beyond linear response, the flow curves collapse when expressed in terms of the ratio between imposed shear and spinning rates. Specifically, plotting
\[
\eta\,T_{\rm eff}(\Omega)
\quad\text{versus}\quad
\dot\gamma/|\Omega|
\]
produces a master curve up to large forcing [2606.14311]. At larger \(\dot\gamma\), this correspondence breaks down and handedness matters. For \(\Omega<0\), transverse interactions oppose the imposed shear handedness, string-like flow channels form earlier, and stresses are reduced beyond
\[
\dot\gamma^*\approx 0.2
\quad (\Omega=-10),
\]
whereas comparable behavior for \(\Omega>0\) appears only around
\[
\dot\gamma^*\approx 0.4
\quad (\Omega=10).
\]
This makes “thinning-by-spinning” literal at the rheological level: increasing microscopic spinning reduces macroscopic viscosity in a way quantitatively analogous to shear thinning over a broad regime [2606.14311].

## 6. Boundaries, misconceptions, and adjacent usages

A common misconception is that thinning-by-spinning always implies direct mechanical pulling by rotation. The literature does not support that as a universal statement. In bipolar liquid-crystal polymer microparticles, the authors do not claim that rotation itself actively pulls the body thin as in a mechanical spinner; instead, anisotropic contraction creates a geometric mismatch, and above a threshold aspect ratio the particle loses further volume predominantly through twisting rather than further strand shortening [1905.01149]. In electrospinning under oscillatory forcing, the thinner fiber arises because helical trajectories lengthen the jet path and increase elongation before deposition, not because oscillation directly squeezes the jet radially [1412.1121]. In dense chiral fluids, the thinned quantity is viscosity, and the mechanism is fluidization through transverse nonconservative pair forces and accelerated stress relaxation [2606.14311].

Another misconception is that spinning alone determines the final state. Thermal Marangoni forcing in rotating PDMS films shows that early-time thinning can remain classical spin-off while late-time dynamics and equilibrium thickness are set by inward thermocapillary transport [1806.10595]. Rotary jet-spinning likewise shows that successful fiber formation requires not only rotational stretching but also sufficiently slow capillary breakup, summarized by the experimentally verified boundary \(\Omega\sim \mu^{-2.88\pm0.25}\) [1110.1424]. In yarn, twist amplification depends on friction, pitch, fiber length, and rupture strain through the single parameter \(\mathcal H\), not on twist angle alone [2110.04206].

There is also a terminological boundary. The paper "Spin Swapping Transport and Torques in Ultrathin Magnetic Bilayers" does not use the phrase “Thinning-by-Spinning Mechanism” and instead analyzes a thickness-controlled crossover in spin transport [1511.03454]. Its core result is that spin Hall effect dominates in the diffusive limit \(d\gg \lambda\), whereas spin swapping dominates in the Knudsen regime \(d\lesssim \lambda\), with a qualitative change in torque symmetry from mostly damping-like to mostly field-like [1511.03454]. This is a related thickness–spin coupling, but it is not a thinning-by-spinning mechanism in the hydrodynamic, geometric, or rheological senses described above.

Taken together, these works support a precise but plural usage. Thinning-by-spinning can mean hydrodynamic spin-off of a liquid film, centrifugally driven extensional draw-down of a jet, helical path-length amplification in electrospinning, twist-assisted accommodation of anisotropic shrinkage, frictional self-locking in a slender twisted yarn, or chirality-induced viscosity reduction in dense active matter. What unifies them is not a single microscopic force law, but a recurrent coupling between rotation or twist and the reduction of a transverse scale or flow resistance.

Source: https://www.emergentmind.com/topics/thinning-by-spinning-mechanism