Nonlinear travelling waves on a spiralling liquid jet

Părău, Emilian; Decent, Stephen; King, A. C.; Simmons, Mark; Wong, David

doi:10.1016/j.wavemoti.2006.05.004

Cited by 18 publications

(2 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, the apparent viscosity does not affect the steady solution at leading order, except in (3.26) and in a correction to p 1 in (3.25) which does not affect the trajectory, velocity, pressure or jet radius at leading order. This confirms the approach adopted in [16,17] and Pȃrȃu et al [22] also showed numerically that viscosity is not important to the trajectory except in very high viscosity liquids. The slender jet approximation in this case results in no shear across the jet at leading order.…”

Section: Asymptotic Form Of the Steady-state Solutionssupporting

confidence: 78%

Unstable waves on a curved non-Newtonian liquid jet

Hawkins

Gurney

Decent

et al. 2010

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

A spiralling slender non-Newtonian liquid jet emerging from a rapidly rotating orifice is examined. The effect of the non-Newtonian rheology on the trajectory of the jet and its linear instability are determined using a mixture of computational and asymptotic methods. The sizes of the droplets produced by this instability are determined by considering the most unstable wave mode. This enables a quantitative comparison between theoretical and experimental results to be made, by comparing droplet sizes predicted from the theory with experimental measurements. At lower Weber numbers some good points of agreement have been obtained. At higher Weber numbers jet break-up becomes increasingly complex and the possibility of break-up being due to absolute, rather than convective, instability is discussed.

show abstract

Section: Asymptotic Form Of the Steady-state Solutionssupporting

confidence: 78%

Unstable waves on a curved non-Newtonian liquid jet

Hawkins

Gurney

Decent

et al. 2010

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…The downstream boundary conditions for U, R and S are obtained by quadratic extrapolation of last interval mesh points. In this numerical simulation of the evolution of compound jet, our stopping criteria were taken to be the time at which the minimum dimensionless jet radius was 0.05 [14]. Using a value smaller than this, for example, 0.01 will not alter the resulting observations as close to breakup the evolution of the jet, in particular the radius, changes exponentially.…”

Section: Nonlinear Analysismentioning

confidence: 99%

Effects of gravity on the breakup and instability of a viscous compound jet

Afzaal

Uddin

Decent

et al. 2015

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Encapsulated droplet formation resulting from the rupture and breakup of a compound liquid thread has numerous applications in industry. Understanding the process through which a compound thread will breakup and form droplets of a desired size is thus of great relevance and may help in developing refined experimental techniques. In this paper, we investigate the breakup and the instability of a viscous compound thread falling under gravity. The governing equations are formulated and a reduced one-dimensional set of equations is obtained using an asymptotic approach. The steady-state solutions, which are dependent on the axial distance along the thread, are determined using a modified Newton's method. Thereafter, we present a linear temporal instability analysis to study the effects of how key parameters affect the structure and onset of rupture. Finally, we investigate the nonlinear behaviour of waves along the free surface through using a finite difference scheme based on the Lax-Wendroff method and we obtain the breakup times and the sizes of main and satellite droplets.

show abstract