Viscous liquid

About: Viscous liquid is a research topic. Over the lifetime, 10655 publications have been published within this topic receiving 244865 citations. The topic is also known as: supercooled liquid & glassforming liquid.

On the Instability of a Cylindrical Thread of a Viscous Liquid Surrounded by Another Viscous Fluid

Abstract: 1—The dynamical theory of the instability of a long cylindrical column of an incompressible perfect liquid under the action of capillary force has been given by Rayleigh, neglecting the effect of the surrounding fluid. According to his results, if the column becomes varicose with wave-length λ , the equilibrium of the column is unstable, provided λ exceed the circumference 2π a of the cylinder, in accordance with the result of Plateau’s statical theory; and the degree of instability, as indicated by the value of q in the exponential eqt to which the motion is assumed to be proportional, depends upon the value of λ reaching a maximum when λ = 4.51 × 2 a . The case of a long cylindrical column of an incompressible viscous liquid has also been discussed by Rayleigh, again leaving out of consideration the effect of the surrounding fluid. Assuming the viscosity to be very great compared with the inertia and neglecting the effect of the latter, he has shown that for a very viscous liquid column the maximum instability occurs when the wave-length of the varicosity is very large in comparison with the radius of the cylinder, i. e ., when λ = ∞ theoretically. Quite recently G. I. Taylor has made interesting experimental researches, together with some theoretical investigations, upon the mode of formation of the cylindrical thread by the disruptive effect of the viscous drag of one fluid on the other, by putting a small drop of a viscous liquid in definable shearing fields of flow of another viscous liquid. He has thus thrown much light upon the mechanism of the formation of emulsions. In the course of his experiments he observed an interesting phenomenon, in one case when the ratio of the viscosity of the liquid forming the thread to that of the surrounding liquid is 0.91, that after the apparatus which was used to produce the field of flow was stopped the final thread gradually broke up into a number of small drops spaced at nearly regular intervals, although it had seemed quite stable while the apparatus was in motion. In connection with this interesting phenomenon, Professor G. I. Taylor kindly suggested to the writer a problem of investigating the character of the equilibrium of a long cylindrical thread of a viscous liquid surrounded by an­other viscous fluid under the action of interfacial surface tension as well as under the effect of viscous forces acting on the liquid inside the column by the surrounding viscous fluid. The effect of the latter is expected to play some important role in the phenomenon under con­sideration, although, as mentioned already, its effect had been neglected by Rayleigh in his investigation.

Analysis of the Swimming of Microscopic Organisms

Abstract: Large objects which propel themselves in air or water make use of inertia in the surrounding fluid. The propulsive organ pushes the fluid backwards, while the resistance of the body gives the fluid a forward momentum. The forward and backward momenta exactly balance, but the propulsive organ and the resistance can be thought about as acting separately. This conception cannot be transferred to problems of propulsion in microscopic bodies for which the stresses due to viscosity may be many thousands of times as great as those due to inertia. No case of self-propulsion in a viscous fluid due to purely viscous forces seems to have been discussed. The motion of a fluid near a sheet down which waves of lateral displacement are propagated is described. It is found that the sheet moves forwards at a rate 2π 2 b 2 /λ 2 times the velocity of propagation of the waves. Here b is the amplitude and λ the wave-length. This analysis seems to explain how a propulsive tail can move a body through a viscous fluid without relying on reaction due to inertia. The energy dissipation and stress in the tail are also calculated. The work is extended to explore the reaction between the tails of two neighbouring small organisms with propulsive tails. It is found that if the waves down neighbouring tails are in phase very much less energy is dissipated in the fluid between them than when the waves are in opposite phase. It is also found that when the phase of the wave in one tail lags behind that in the other there is a strong reaction, due to the viscous stress in the fluid between them, which tends to force the two wave trains into phase. It is in fact observed that the tails of spermatozoa wave in unison when they are close to one another and pointing the same way.

The transverse force on a spinning sphere moving in a viscous fluid

Abstract: The flow about a spinning sphere moving in a viscous fluid is calculated for small values of the Reynolds number. With this solution the force and torque on the sphere are computed. It is found that in addition to the drag force determined by Stokes, the sphere experiences a force FL orthogonal to its direction of motion. This force is given by .Here a is the radius of the sphere, Ω is its angular velocity, V is its velocity, ρ is the fluid density and R is the Reynolds number, . For small values of R, the transverse force is independent of the viscosity μ. This force is in such a direction as to account for the curving of a pitched baseball, the long range of a spinning golf ball, etc. It is used as a basis for the discussion of the flow of a suspension of spheres through a tube.The calculation involves the Stokes and Oseen expansions. A representation of solutions of the Oseen equations in terms of two scalar functions is also presented.

On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres

Abstract: Spatially periodic fundamental solutions of the Stokes equations of motion for a viscous fluid past a periodic array of obstacles are obtained by use of Fourier series. It is made clear that the divergence of the lattice sums pointed out by Burgers may be rescued by taking into account the presence of the mean pressure gradient. As an application of these solutions the force acting on any one of the small spheres forming a periodic array is considered. Cases for three special types of cubic lattice are investigated in detail. It is found that the ratios of the values of this force to that given by the Stokes formula for an isolated sphere are larger than 1 and do not differ so much among these three types provided that the volume concentration of the spheres is the same and small. The method is also applied to the two-dimensional flow past a square array of circular cylinders, and the drag on one of the cylinders is found to agree with that calculated by the use of elliptic functions.