A low-cost, open-source cylindrical Couette rheometer

Abstract

Rheology describes the flow of fluids from food and plastics, to coatings, adhesives, and 3D printing inks, and is commonly denoted by viscosity alone as a simplification. While viscometers adequately probe Newtonian (constant) viscosity, most fluids have complex viscosity, requiring tests over multiple shear rates, and transient measurements. As a result, rheometers are typically large, expensive, and require additional infrastructure (e.g., gas lines), rendering them inaccessible for regular use by many individuals, small organizations, and educators. Here, we introduce a low-cost (under USD$200 bill of materials) Open Source Rheometer (OSR), constructed entirely from thermoplastic 3D printed components and off-the-shelf electromechanical components. A sample fluid rests in a cup while a micro stepping motor rotates a tool inside the cup, applying strain-controlled shear flow. A loadcell measures reaction torque exerted on the cup, and viscosity is calculated. To establish the measurement range, the viscosity of four Newtonian samples of 0.1-10 Pa.s were measured with the OSR and compared to benchmark values from a laboratory rheometer, showing under 23% error. Building on this, flow curves of three complex fluids - a microgel (hand sanitizer), foam (Gillette), and biopolymer solution (1% Xanthan Gum) - were measured with a similar error range. Stress relaxation, a transient test, was demonstrated on the biopolymer solution to extract the nonlinear damping function. We finally include detailed exposition of measurement windows, sources of error, and future design suggestions. The OSR cost is ∼1/25th that of commercially available devices with comparable minimum torque (200 µN.m), and provides a fully open-source platform for further innovation in customized rheometry.

Fig. 1

Design of the OSR. The OSR comprises structural and electro-mechanical components, including a motor mount (tan), a cup-flexure-base (green), and a testing cylinder (light blue) with (a) an exploded view and (b) a vertical cross-section. The completed assembly is approximately 334 mm tall with the motor and 258 mm tall without the motor. The base is a 95 mm x 95 mm square anchored to a larger, stable base. (c–d) A zoomed-in view shows where the loadcell interfaces with the cup near the base (d) with a local contact point from a ball screw on a hard ceramic contact surface.

Fig. 2

Photographs of the built OSR. (a) Photographs show a fully assembled OSR and includes an approximate size scale, along with photographs of (b) the testing cylinder alone, (c) a fractal vane testing geometry, and (d) the cup and loadcell assembly with additional flexure locks in place (light blue).

Fig. 3

Finite element (FEA) modeling of flexure within the OSR. (a) A top view shows shearing of fluid in the gap between the cylinder and cup surface. (b) The flexure, resultingly, is designed to have one degree of freedom, rotation about θ_z, while being stiff in the vertical direction. (c) FEA of the flexure shows deformation under torque from low (blue) to high (red) displacement with nearly pure rotation. (d) A render of the assembly shows predominant torque load paths from the rotating central cylinder, in torsion through the loadcell and vertically through the flexure, down to the mechanically fixed ground plane.

Fig. 4

Measurement procedure using the OSR. (1) loading a sample fluid, (2) removing the flexure locks, (3) attaching the motor mount, (4) collecting data, and (5) disconnecting and cleaning the rheometer (with the flexure locks in place).

Fig. 5

Calibration of OSR torque measurement using a commercial rheometer. (a) The measured torque is shown as a function of the OSR loadcell sensor value, s, as calibrated by hanging weights (red points with a dark blue dashed fit line of s × 4.6 × 10⁻⁸ N.m) and as calibrated using the results from the DHR rheometer (green points with light blue fit line of s × 4.7 × 10⁻⁸ N.m). The lower torque limit of the DHR is shown as a solid horizontal black line. (b) A photograph shows the setup for calibrating the OSR with the DHR rheometer.

Fig. 6

Measurements of Newtonian fluids with the OSR. (a) Shear stress as a function of shear rate and (b) viscosity as a function of shear rate with (c) an evaluation of average values. In (a) and (b), points were measured by OSR, with the spread of data during data collection marked by dotted lines. Solid lines show the known, true value, and the grey region denotes minimum resolvable torque.

Fig. 7

Measurements of Non-Newtonian fluids with the OSR. Three non-Newtonian fluids were tested: a hand sanitizer, shaving cream, and 1% Xanthan gum solution in water showing, in order, (a,c,e) shear stress as a function of shear rate and (b,d,f) corresponding viscosity as a function of shear rate. For each plot, red data points show OSR measurements with a cylinder, with an error window from the spread of data during data collection marked with a red dashed line. A dash-dot blue line shows the baseline curve measured using a DHR rheometer. For (a,b) green data points mark data measured with an 8-arm fractal vane instead of a cylindrical geometry. In all relevant plots, red highlighting marks points most likely affected by slip, which presents as an apparent stress that is systematically lowered below a critical shear rate. A grey window marks the lower limit of measurement due to load cell noise, while a brown window marks regions within which inertia of the cylinder would affect measured data, calculated by Eq. 8.

Fig. 8

Stress relaxation of a non-Newtonian fluid with the OSR. (a) A set of step strain tests are shown in their entirety for Xanthan gum, first applying a step of the given strain γ followed by stress relaxation. (b) The relaxation modulus G as a function of time and applied strain is shown for times after the step is applied for all tests. (c) The extracted damping function h(γ) is referenced to 0.31 strain and compared to literature values for similar Xanthan gum solutions, from, with data collected by the OSR shown as red diamonds. The top horizontal axis shows the rotation angle of the cylinder in degrees corresponding to the strain.