Poiseuille flow viscometer

The membrane viscometer must use a membrane with a sufficiently well-defined pore so that the flow of isolated polymer molecules in solution can be analyzed as Poiseuille flow in a long capillary, whose length/diameter is j 10. As such the viscosity, T, of a Newtonian fluid can be determined by measuring the pressure drop across a single pore of the membrane, knowing in advance the thickness, L, and cross section. A, of the membrane, the radius of the pore, Rj., the flow rate per pore, Q,, and the number of pores per unit area. N. The viscosity, the maximum shear stress, cr. and the velocity gradient, y, can be calculated from laboratory measurements of the above instrumental parameters where Qj =... 

THE POISEUILLE EQUATION AND CAPILLARY VISCOMETERS 4.4a Flow Through Cylinders The Poiseuille Flow... 

Any of the flow processes described in sections 6.3, 6.4 and 6.5 can form the basis of absolute viscometers, so that there are viscometers using Poiseuille flow, rotating coaxial cylinders and the terminal velocity of falling spheres. 

One of the most widely used rheometer configurations is a simple variant of the capillary flow viscometer. In this device, a concentrated polymer solution or melt undergoes Poiseuille flow in a narrow capillary, length L and internal radius R, under the action of an external pressure P. The capillary exit is typically open to the atmosphere, such that a pressure difference Ap = P - produces the driving force that leads to fluid flow (Figure 8.3). If the volumetric flow rate of fluid through the capillary Q is known (measured), Poiseuille s equation can be used to determine the fluid s viscosity if the fluid is Newtonian. 

Earlier experiments involved the collection of SEC effluent aliquots to measure solution viscosity in batches with the very time consuming Ubbelohde drop-time type viscometers. A continuous capillary type viscometer was first proposed for SEC by Ouano. Basically, as shown in Figure 1, a single capillary tube with a differential pressure transducer was used to monitor the viscosity of SEC effluent at the exit of the SEC column. As liquid continuously flows through the capillary (but not through the pressure transducer), the detected pressure drop (AP) across the capillary provides the measure for the fluid viscosity (h) according to the Poiseuille s viscosity law ... 

Capillary Viscometers. Capillary flow measurement is a popular method for measuring viscosity (21,145,146) it is also the oldest. A liquid drains or is forced through a fine-bore tube, and the viscosity is determined from the measured flow, applied pressure, and tube dimensions. The basic equation is the Hagen-Poiseuille expression (eq. 17), where T is the viscosity, r the radius of the capillary, Ap the pressure drop through the capillary, V the volume of liquid that flows in time /, and L the length of the capillary. 

The principle of operation of capillary viscometers is described by the Poiseuille equation where the rate of liquid flow (VIt) through the viscometer can be determined by the following (Steffe, 1996) ... 

The capillary viscometer. The most common and simplest device for measuring viscosity is the capillary viscometer. Its main component is a straight tube or capillary, and it was first used to measure the viscosity of water by Hagen [28] and Poiseuille [60], A capillary rheometer has a pressure driven flow for which the velocity gradient or strain rate and also the shear rate will be maximum at the wall and zero at the center of the flow, making it a non-homogeneous flow. 

For low-viscosity Newtonian foods that can flow under nornial gravitational force, glass capillary viscometers can be used. Recalling that the magnitude of viscosity can be obtained by dividing the equation for shear stress by that for shear rate, one can derive from the Hagen-Poiseuille equation ... 

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

In both methods, Washburn s equation is used, which was derived from the Poiseuille equation to measure viscosity in capillary viscometers. The rate of volume flow (V/t) through a capillary tube with radius, rc, is given by the Poiseuille equation as... 

Perhaps the most familiar technique is the capillary-flow method. The working principle is the Hagen-Poiseuille relationship between the flow rate through a tube of fixed diameter, the pressure drop, and the viscosity. In practice, because the capillary diameter appears to the fourth power in the working equation and is difficult to determine accurately, capillary viscometers are usually calibrated with reference fluids such as water or reference oils that are available from viscometer manufacturers and some national laboratories. 

Two common methods for measuring viscosity are the cup and bob (Couette) and the tube flow (Poiseuille) viscometers. 

In a capillary viscometer, a piston of known weight presses the melt through a capillary with a specific diameter and length. The flow of a Newtonian fluid in a capillary obeys the Hagen-Poiseuille equation. 

The viscosity of a liquid or solution can be measured by using a viscometer whose design is based on the Hagen-Poiseuille law. Essentially, this involves the measurement of the flow rate of the liquid through a capillary tube which is part of the viscometer. Consequently, by measuring the flow time of the solution, t, and that of the pure solvent, to, the relative viscosity can be determined ... 

An alternative molecular weight-sensitive detector is the on-line viscometer. All current instrument designs depend upon the relationship between pressure drop across a capillary through which the polymer sample solution must flow and the viscosity of the solution. This relationship is based upon Poiseuille s law for laminar flow of incompressible fluids through capillaries ... 

Capillary viscometers provide an accurate means of observing viscosity effects in polymer solutions. There are numerous designs but the Ubbelohde dilution viscometer shown in Figure 2.3 is one of the most commonly used. The principles of measurement are based on the Poiseuille equation which relates the time required for the volume K of a liquid to flow through a... 

Experimentally, the viscosity of dilute polymer solutions is, in most cases, determined with glass capillary viscometers, making application of the Hagen-Poiseuille s law for laminar flow of liquids. The time required for a specific volume of a liquid to flow through a capillary of... 

The single-capillary viscometer (SCV) is represented in Fig. la. Its design is a direct extrapolation of classical viscometry measurement. It is composed of a small capillary, through which the solvent flows at a constant flow rate, and a differential pressure transducer (DPT), which measures the pressure drop across the capillary. SCV obeys Poiseuille s law and the pressure drop AP across the capillary depends on the geometry of the capillary, on flow rate Q, and on viscosity of the fluid rj according to... 

The automatic relative viscometer is ideally suited for measuring dilute polymer viscosities. It provides faster analysis and greater precision than is obtainable with conventional glass tube viscometers (Ubbelohde or Cannon-Fenske), which it replaces. The principle of operation is based on measurement of pressure drops due to the continuous forced flow of solvent and sample through two stainless steel capillary tubes placed in series. The pressure drop across each capillary tube obeys Poiseuille s law. The pressme drop is measured by a differential pressure transducer. The sample solution is loaded into a sample loop via a syringe pump and then pushed into one of the two capillaries. A steady-state condition is reached when the sample solution completely fills capillary 2, solvent remaining in capillary 1 at all times. The relative viscosity of the sample solution is determined simply and directly by the ratio of the pressure drops. From the measured relative viscosity, all other solution viscosity measurements can be calculated. Solution viscosities are determined by the viscosity of the sample relative to the reference solvent. The relative viscometer measures the solvent and sample viscosity simultaneously, so errors due to temperatme fluctuation and solvent variations are avoided. The main advantages of this approach are ... 

A further advantage of flow-mode testing is that the shear-rate magnitudes that would be encoimtered in a practical hydraulic device, often in excess of 40 000s, can be achieved [99]. However, the definition of shear rate needs to be subjected to scrutiny it is often derived from the Newto-nian/Poiseuille formula, albeit when plug flow is present [100]. In a Couette viscometer care must be taken to avoid plug flow the plug formed by radial... 

The values R, V. 1 can be made constant by using a capillary of known dimensions for all the liquids. A glass capillary viscometer can serve the purpose. If we measure the time of flow of two different liquids Uirough the same viscometer, then according to Poiseuille equation, the ratio of the viscosity coefiicients of the two liquids is given by... 

The flow behavior of non-Newtonian fluids is usually described by expressing either shear rate or viscosity as a function of shear stress. Absolute viscometers, either capillary or rotational, are used to perform the necessary measurements. In the capillary viscometer, the flow rate is measured as a function of applied pressure. Apparent viscosities calculated by means of Poiseuille s relation [Eq. (9)], are converted to true viscosities using the Weissen-berg-Rabinowitsch correction... 

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