Pouring viscous fluid out of a tipped container in minimal time

Emptying a container partially filled with viscous fluid can be a frustratingly slow process. It takes time for the fluid to even begin discharging after tipping the container to develop a draining film on the interior surface. To study the effects of the shape and the tipping angle of the container, we predict the time required for the fluid to begin discharging in two simple geometries. In addition, the volume of the fluid yet to be discharged at subsequent times is predicted to decrease as $t^{-1/2}$ or $t^{-1}$ for flow driven along a plane or corner, respectively. We compare these theoretical predictions with laboratory experiments and discuss how viscous fluids could be poured out most effectively.

Figure 1

Sketch of (a) a tipped container of rectangular cross section such that the bulk flow is along two planes and (b) a square container with a wedged base such that the bulk flow is along the wedge and a corner of the container. Each inset shows a cross section of the flow.

Figure 2

Rescaled time when fluid begins to pour out of (a) a flat edge of a square container and (b) a corner of a square container with a wedged base, plotted against the proportion of the container initially occupied by the fluid.

Figure 3

Proportion of glycerine ($G$) and golden syrup (GS) remaining along (a) flat edges of a square container and (b) corners of a square container with a wedged base, plotted on logarithmic scales against rescaled time.