Enhancement of the flow rate of shear-thinning liquids by low frequency vibrations

Dr. J. Ellenberger and Prof. R. Krishna

Introduction

The flow of a shear-thinning liquid through a capillary can be enhanced significantly by longitudinal, low frequency vibrations of the capillary.

The flow enhancement is dependant on the

The major objective of this experimental investigation is to test the influence of the above mentioned parameters on the enhancement of the flow rate.

EXPERIMENTAL

Experiments were carried out using a setup consisting of three interchangeable glass capillaries with a length L = 0.5 m and inner diameters of 1.155 mm, 2.156 mm and 3.961 mm respectively, a vibration exciter, a power amplifier, a high-speed video camera and a personal computer. A schematic representation of the set-up is shown in the figure below. The shear-thinning liquids flow from a 1L-glass vessel at constant external pressure into the capillary. The connection between the glass vessel and the capillary is a flexible silicone tube of 8 mm inner diameter and a length of 0.25 m. The glass capillaries were vertically mounted onto a shaft of an air-cooled vibration exciter (TIRAvib 5220, TIRA Maschinenbau GmbH, Germany). In this way, vertical displacements of the shaft at specific amplitudes (λ) and frequencies (f) fully corresponded to displacements of the capillary. The vibration exciter was coupled to a power amplifier and controlled from a personal computer using SignalCalc 550 Vibration Controller software (Data Physics Corporation, United States). The applied frequencies f ranged from 5 - 40 Hz and the amplitudes λ from 1.5 - 10 mm. The dimensionless vibration intensity Γ = λ (2 π f) 2/g was varied from 0.5 -14. The amplitude of vibration is defined as the absolute value of the maximum positive or negative displacement of the vibration exciter from its rest position. The vibration exciter was programmed to generate sinusoidal oscillations.

Small coal particles (0.5 g/L) with diameters dp in the range of 0.4 mm < dp < 0.72 mm have been added to the polymer solutions and high-speed video movies were made of the coal particles flowing through the centerline of the capillaries during vibration. The camera was a Photron Fast-ultima 40K high-speed video camera, which has the capability of recording at between 30 frames per second (fps) and 40500 fps. The camera was connected to a memory box, which allowed for movies being made to be instantaneously stored, as well as a display monitor, which permitted real-time viewing of the movies. Lighting for the movies was provided by a single Dedotec dedocool 250 W Halogen Photo Optic lamp. This lamp had the unique property of providing suffient illumination without increasing the ambient temperature. After each video recording, data obtained were transferred from the memory box to a PC for analysis.

The mass flow rate was determined by measuring the weight of liquid at the exit of the capillary during a certain time.

The experiments were carried out with aqueous solutions of two different polymers, i.e. Carboxy-methyl Cellulose and Polyacrylamide.

Schematic representation of the experimental set-up

EXPERIMENTAL SETUP PHOTOGRAPHS

Photographs of the setup used in carrying out experiments are shown below. Click on a photograph to view an enlarged version of it.


Vibration exciter capable of operating within a frequency range of 2 Hz to 5000 Hz with amplitudes of 0 to 12 mm zero-to-peak.

The capillary tube is tightly mounted onto the shaft at the top of the vibration exciter.

Picture of the experimental set-up.

The Photron Fastcam-ultima 40K high-speed camera. It has the capability of capturing video movies at rates ranging from 30 frames per second (fps) to 40500 fps.

TIRAvib amplifier used to amplify the input signal from computer system (shown above) to the vibration exciter.

Computer control system and video monitor used for programming the high-speed camera as well as analyzing movies made with it.

SAMPLE MOVIES OF A SHEAR-THINNING LIQUID

The movies 1 and 2, displayed below show the effect of low frequency vibration on the flow rate of an aqueous solution of polyacrylamide 0.5 wt% in a capillary of 2.156 mm inner diameter. Movie 1 shows the exit flow without vibration and movie 2 at a vibration frequency f of 15 Hz and a vibration amplitude λ of 5.0 mm zero-to-peak.The the flow rate of the polymer solution in movie 2 increases with a factor 3.54.

Movie 3 shows the movement of a small coal particle, added to the polymer solution, during vibration at f = 15 Hz and λ = 5.0 mm in the centerline of a capillary of 2.156 mm inner diameter. This movie clearly shows the phase-shift of the coal particle compared to the sinusoidal movement of the capillary.

The movies below are animated GIF previews. Click a preview movie to view the entire movie in full detail.


Movie 1: Polymer flow at no vibration. Play back is 3.75 times slower than real time.

Movie 2: Polymer flow at f = 15 Hz and λ = 5.0 mm. Play back is 3.75 times slower than real time.

Movie 3: Movement of a coal particle in the centerline of the capillary during vibration at f = 15 Hz and λ = 5.0 mm. Play back is 75 times slower than real time.


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