Naoya Yoshioka

On creeping flow of a visco-plastic fluid past a circular cylinder

Abstract The creeping flow of a Bingham fluid past a circular cylinder was analyzed by using variational principles. In consequence, the stress distribution which was represented in Eq. (23) and Table 1 was obtained from a maximum principle, and the velocity distribution which was represented in Eq. (41) and Table 1 was obtained from a minimum principle. The drag forces derived from these results are compared with those estimated by a slip-line analysis in Fig. 1. A characteristic peculiarity that the visco-plastic flow has a fluid region and a rigid region is illustrated in Fig. 3. It may be inferred that the result obtained from a maximum principle is useful.

The behavior of a swarm of particles moving in a viscous fluid

Abstract A significant bulk flow is thought to occur if a part of the body of a suspension, which has a different density from the density of the remainder of the suspension, is large enough in space however slight the difference may be. As a typical case, the slow motion of a swarm of particles in a viscous fluid was studied both theoretically and experimentally. Under a certain condition, the suspended particles formed a drop of suspension, in which the suspended particles and fluid moved as one body in the same way. The falling velocity of a spherical swarm of particles, which was called a drop of suspension, was measured and compared with a new theoretical prediction presented in this paper. It may be also noted that the theoretical model may be applicable to the flow due to density difference by means of replacement of the continuous mass by the damped mass which is regarded as consisting of particles.

On non-Newtonian flow past a sphere

The approximate solutions for flow of and Ostwald-de Waele fluid past a sphere at Re·0 = 60 and 1 ⩾ n ⩾ 0·8 are obtained by the use of an extended method of moments. As n decreases, (1) friction drag decreases, (2) pressure drag increases for flow past a blunt body, (3) total drag increases for flow past a sphere, (4) wake length increases for flow past a sphere, (5) separation point moves forward for flow past a sphere.

On Non-Newtonian Flow Through a Slit Plate

The flow through a two-dimensional orifice, i.e., a slit plate, in a two parallel plate channel involves two flow geometries of conversion and diversion. Both of them are widespread and important in the polymer processing of extrusion and injection mouldings. Therefore, there has been much discussion. Giesekus1,2 paid attention to the remarkable difference in the flow pattern between the converging flow and the diverging flow although the corresponding, creeping flow of a Newtonian fluid has a symmetric flow pattern on both the sides of the orifice plane. That asymmetry is one of the characteristic features of viscoelastic behaviors, as is also seen in the flow past a sphere.3 Most existing studies have been directed to the converging, entry flow in connection with the elongational flow, but the diverging, exit flow is also important. Thus, it would be interesting to correlate the pressure drop with the related flow pattern in each flow region, or, at least, to divide the additional pressure drop due to the existence of the orifice plate into the entrance and exit portions, if possible. Further points to be made clear are the difference in the pressure drop between the 2-dimensional, plane flow through a slit plate and the 3-dimensional, axisymmetric flow through an orifice, the critical condition for the onset of the steady oscillating flow, its period, and the change in the pressure drop with the onset of viscoelastic flow disturbances. The present work will be more or less concerned with these points.

An experimental investigation of viscoplastic flow past a circular cylinder at high Reynolds numbers

SummaryThe purpose of this work was to examine the high speed flow of viscoplastic fluid past a circular cylinder. Included in this work were measurements of the time-averaged wake length and the pressure and temperature distributions over the cylinder surface. The time-averaged wake length was very characteristic of viscoplasticity: The viscoplastic flow showed quite longer wake length than theNewtonian flow under certain conditions. It was found that there were the regions of stationary fluids adjacent to a cylinder and that they obstructed the heat transfer between the cylinder and fluid very much.ZusammenfassungDie vorliegende Arbeit befaßt sich mit der Untersuchung der Umströmung eines Kreiszylinders durch eine visko-plastische Flüssigkeit mit hoher Geschwindigkeit. Hierin eingeschlossen sind die Messung der mittleren Längenausdehnung des „Totwasser“-Gebiets sowie der Druck- und Temperaturverteilung über die Zylinderoberfläche. Die zeitlich gemittelte Längserstreckung des „Totwasser“-Gebiets stellt sich als eine für das visko-plastische Fließen charakteristische Größe heraus: Sie kommt erheblich größer heraus als fürnewtonsche Flüssigkeiten unter vergleichbaren Bedingungen. Man findet weiterhin am Zylinder anliegende stationäre Flüssigkeitsbereiche, welche die Wärmeübertragung zwischen Zylinder und Flüssigkeit sehr hemmen.

On Hole Pressure Error for Viscoelastic Fluids

It is a common practice to measure the fluid thrust normal to a solid wall through the small hole which is drilled in the surface of the wall. For viscoelastic flow, however, this experimental technique is not a common practice since some disturbance of the primary flow occures due to the hole, thus yielding in principle an error in measuring the undisturbed pressure. Therefore, there has been much discussion1,2 on this hole pressure error.

On the Determination of Normal Stress Difference by Capillary Tube Method

For the measurement of normal stress difference by the capillary tube method, the basic equations are derived under the following two assumptions.Assump. 1. Velocity profile is fully developed at the tube exit.Assump. 2. Exit pressure on the center-line of the tube is a function of shear stress at the wall.The results are shown in Table I. In this Table, the equations proposed by several investigators are also shown with their assumptions and approximations.By using the nondimensional group N defined by Eq. (5), which represents the ratio of inertia force to normal stress difference, the exit stress Pw(L) is expressed by Eq. (6). For the range of N<<1, Pw(L) is approximately equal to the normal stress difference Tn and increases with wall shear rate. Generally, Pw(L) depends on N as well as on wall shear rate, and cannot be considered as the material function. It may be anticipated that there is the range of N where Pw(L) becomes a decreasing function of N.Since the pressure term in Pw(L) cannot be neglected and it cannot be determined by the capillary tube method, it is impossible to determine each component of normal stress differences only by the capillary tube method.

Collection Efficiencies of Aerosols by Fibrous Paeked Bed under the Influence of Gravity

多分散エアロゾル (粒径3～13μ) の繊維充填層濾過実験で, 層入口および出口の粒度分布より任意の粒径に対する単一繊維捕集効率を求めた。この結果は重力, 慣性およびさえぎりを同時に考慮した孤立円筒理論捕集効率とかなり良い一致を示した。さらに, 低速度領域で粒径を小さくしていったとき, 重力支配域から拡散支配域へ移行する過程を定量的に考察した。その結果, この領域での全捕集効率は筆者らによる重力さえぎり効率とFriedlanderの半実験式の拡散項の和で表わされるとの結論を得た。

On the Relation between the Molecular Weight of Narrow-Distribution Polymers and Their Non-Newtonian Viscosity

The non-Newtonian viscosity derived from the previously proposed constitutive equation7) was expressed as follows, η(γ)=∫∞0H(λ)1/2α2[1/A(α)]dλ, A(α)=∫∞0e-x-α2x2dx, α2=1/2βλγwhere H(λ) was the relaxation spectrum and λ, γ, and β were the relaxation time, shear rate and a nondimensional parameter of order 1, respectively. When polymers are approximated in their narrow-distribution H(λ) byH(λ)={H1/1-δ00, λ0≤λ≤λ1, δ0=λ0/λ1 Otherwisethe non-Newtonian viscosity calculated from these equations can be superposed as shown in Fig. 1. If λ1 is replaced by the natural time λN defined by λN=η(0)J(0), which is more directly related to measurable quantities, the reduced shear rate in Fig. 1 becomesβδs/1+δ0λNγwhere J(0) is steady-state compliance and δs=1+1.8δ00.86.Prests data8) of J(0) are expressed in terms of entanglement density E as followsJ(0)/JRc=1.22E/1+0.22E, E=M/Mc or CM/(CM)cwhere JRc is the Rouse steady-state compliance at the critical molecular weight Mc. If this experimental equation is used with assumptions that β is independent of M and δ0-1=E, the relation between the characteristic time λch and M is to be expressed asλch∝η(0)E/1+0.34E.This is in the same relation as Graessleys, and is applied to the narrow distribution of polydimethyl siloxane melts9) with fairly good agreement as shown in Fig. 2. The solid line in this figure shows the viscosity curve at δ0=1 in Fig. 1.

Study on the Constant Pressure Filtration through Some Non-Plane Filter Leaves

円筒, 球, 園転惰円体などの非平面形状の炉葉による定圧游過方程式を非圧縮性ケークの仮定のもとに直交曲線座標系を用いて求め, これを湧葉内容積をケークが充満するまでの時間θM, それまでの浜液量QMおよび無次元化炉材抵抗β を用いると炉液量Qと炉過時間θ の関係はθ/θM=f (Q/QM, β) の形の式にまとめられなCaCO3スラリ一による実験結果はこの理論とかなりよく一致した.