Haptic Perception of Viscosity
Wouter M. Bergmann Tiest1 , Anne C. L. Vrijling2 , and Astrid M. L. Kappers1
1
2
Helmholtz Institute, Utrecht University, The Netherlands
{w.m.bergmanntiest,a.m.l.kappers}@uu.nl
Royal Dutch Visio, National Foundation for the Visually Impaired and Blind, Huizen, The
Netherlands
[email protected]
Abstract. Viscosity is a liquid’s resistance against flow. Using a discrimination
experiment, the human ability to distinguish between different viscosities was
measured over the range of 200–20,000 mPa·s. Eight blindfolded subjects stirred
pairs of different silicone oils using a wooden spatula and had to indicate the
“thicker” of the two. The viscosity of the liquids was measured seperately using
a rheometer. Weber fractions for discrimination ranged from 0.3 at high viscosities to almost 1 at the lowest viscosity. For the higher viscosities, discrimination
could be described as Weber-like, but for the low viscosities, there seemed to be
a floor effect for the absolute threshold. The characterisation of the discrimination threshold as a function of viscosity is of fundamental interest in perception
research, but also of practical value for designers of haptic devices capable of
displaying viscosity.
Keywords: Kinaesthesia, Dynamic touch, Thresholds, Liquid, Weber fraction
1
Introduction
The viscosity or “thickness” of a liquid is a property that can be easily perceived haptically, as is noticable in the everyday context of stirring in a pot on the stove. But for
certain professionals, such as dough-makers or cooks, being able to accurately judge
viscosity is of great importance. Medical professionals should be able to correctly judge
the viscosity of texture-modified liquids that they prescribe to patients with orpharyngeal dysphagia. These patients have a delayed swallow initiation and benefit from thickened liquids that enter the pharynx slowly [1]. The cited study showed that information
on the product packaging was insufficient to reliably characterise the liquid’s viscosity,
whereas clinicians could perfectly discriminate between different viscosities by stirring
the liquids or by taking a sip. The importance of being able to rely on somesthetic
perception is clear.
Physically, viscosity is the internal resistance of a liquid against shear force. It is
expressed as the ratio between shear stress and shear rate. Shear stress is the amount
of force applied in the direction of shear per unit area (in N/m2 or Pa). Shear rate
is the gradient perpendicular to the force of the liquid’s moving speed (in m/s/m or
s–1 ). Viscosity is thus expressed in units of Pa·s. Water has a viscosity of 1 mPa·s. The
relationship between physical and perceived viscosity has been investigated for silicone
2
Wouter M. Bergmann Tiest, Anne C. L. Vrijling, and Astrid M. L. Kappers
liquids stirred with a rod [2]. This relationship could be described by a power law with
an exponent of 0.43. For manually stirred solutions of gum in water, the power law
exponent was found to be 0.33 [3]. In that same study, a very similar exponent of 0.34
was found for orally perceived viscosity, but the absolute viscosity was judged to be
somewhat higher in the mouth compared to stirring with the finger.
Concerning discrimination of different viscosities, early work was performed by
Scott Blair and Coppen using balls of bitumen that were handled under water [4]. They
found a Weber fraction of about 0.3 for 80 % correct discrimination. This was at a
very high viscosity of about 108 mPa·s. It is unknown if the same Weber fraction holds
for lower viscosities. Orally, the discrimination of viscosity has been tested using seven
mixtures of corn syrup and water, each differing a factor of about three in viscosity from
the next, in the range from 3 to 2240 mPa·s [5]. All could be identified above chance
level except the fifth (202 mPa·s). The fact that even with a difference in viscosity of a
factor of ∼ 3, mistakes were made indicates that at least for oral perception, which was
found to be quite comparable to manual perception [3], the Weber fractions for these
lower viscosities could be quite a bit higher than the value of 0.3.
Discrimination of the “viscosity” of a mechanical system (the ratio between force
and moving speed) has been investigated in a matching experiment using computercontrolled electrical motors for the range from 2 to 1024 N·m/s [6]. Weber fractions
ranged from 0.3 at the highest viscosity to 0.8 at the lowest. Although this type of
viscosity is different from that of a liquid, and is expressed in different units, the Weber
fraction at the high-viscosity end might be compared to and is found to be equal to
that reported by Scott Blair and Coppen [4]. This raises the question whether Weber
fractions for discrimination of the viscosity of liquids show a simular upward trend for
lower viscosities. It is the aim of the present paper to investigate this dependence of
Weber fractions on viscosity. This is done by performing discrimination experiments
with silicone liquids in the range from 78 to 31,000 mPa·s.
2
2.1
Methods
Subjects
Eight healthy adult subjects (5 male, age range 20–30 yrs, mean 24 yrs) participated
in the experiment. All subjects were strongly right-handed as determined by the Coren
test [7]. All subjects gave their informed consent before participating in the study. They
were paid for their time.
2.2
Stimuli
A set of 29 distinct viscosities, ranging from 78 mPa·s to 31,000 mPa·s were created by
mixing silicone liquids of standard viscosity (AK series, Wacker Chemie AG). The mixing ratios were determined from a diagram provided by the manufacturer. The diagram
displays a weight percentage scale which indicates the amount of high and low viscosity silicone liquids that have to be mixed to obtain the desired intermediate viscosity.
The density of the silicone liquids ranged from 9.6 × 10−4 kg/m3 to 9.7 × 10−4 kg/m3 .
250 ml of each mixture was poured into containers of 8 cm diameter and 8 cm height.
Haptic Perception of Viscosity
3
To determine their exact viscosity, the blended stimuli were measured with a rheometer (Physica Modular Compact Rheometer 300, Anton Paar GmbH). This measuring
system uses a cone-and-plate geometry (CP-50-1), with a cone angle of 1.001° and a
diameter of 49.95 mm. The total volume of the space between cone and plate is 0.57 ml.
The rheometer is equipped with a Peltier plate temperature unit that controls the temperature of 25°C over an extended time. Rotational measurements were performed in
which the shear rate was set to 100 s–1 and decreased to 0.1 s–1 in 10 steps. The total
measurement time of a stimulus is 100 s. The torque necessary to obtain the applied velocity is measured and converted to a shear stress by multiplying with a constant factor.
From these data, the viscosity was calculated at each shear rate. The calculated viscosities did not differ more than 1 % between the different shear rates. This means that
within this range, the stimuli behave as Newtonian liquids. The calculated viscosities
were averaged over the shear rates.
The stimulus set was made up out of 5 ranges of viscosity each consisting of a
reference stimulus and 6 test stimuli. The choice of the reference viscosities was based
on the Weber fractions reported by Jones and Hunter, which were fairly constant at
high viscosities, but increased with decreasing viscosity [6]. For this reason, we had
a dense spacing of reference stimuli at low viscosities, and only few reference stimuli
at high viscosities, see table 1. On a logarithmic scale, the spacing of the test stimuli
Table 1. Viscosities of the reference stimuli for the 5 ranges.
Range Reference stimulus (mPa·s) Ratio between subsequent test stimuli
1
199
1.51
2
449
1.44
3
938
1.35
4
1853
1.30
5
16060
1.25
was symmetric around the reference stimulus and equidistant within a range: there was
a constant ratio between the viscosities of subsequent test stimuli within a range, as
shown in table 1. These ratios were chosen such that the reference stimulus and the
most viscous test stimulus within a range differed by a factor of about 2.5 times the
value of expected Weber fractions based on pilot experiments.
2.3
Procedure
The subjects were blindfolded and comfortably seated at a table perpendicular to the
experimenter, see figure 1 (left). The subject was presented with pairs of stimuli. A
pair always contained a reference stimulus and one of the accompanying test stimuli.
At the beginning of the experiment the subject was informed that the task would be to
stir both liquids and indicate which of each pair was the more viscous, explained as the
“thicker”. The subject had to use the dominant hand (in all cases the right hand) to stir
with a wooden spatula (150 × 20 × 1.8 mm, with rounded ends). Subjects were allowed
to go back and forth between the stimuli, but this was not encouraged. The 6 pairs of
4
Wouter M. Bergmann Tiest, Anne C. L. Vrijling, and Astrid M. L. Kappers
10
test chosen
8
6
4
2
! " 125 mPa·s
0
200
#ref
300
500
700
viscosity !mPa·s"
1000
Fig. 1. Left: A schematic illustration of the setup. Right: A representative example of data points
and the psychometric function that was fitted to these data points. On the horizontal axis is the
viscosity on a logarithmic scale. On the vertical axis is the number of times that the test viscosity
was chosen to be the more viscous. σ is the difference between the 50 % and the 84 % point.
stimuli of each of the 5 ranges were presented 10 times in a pre-established random
order, different for each subject, for a total of 300 trials. These were performed in two
sessions of about 50 minutes and one session of 25 minutes, either on different days or
with sufficient time in between. No feedback was given during the sessions.
2.4
Analysis
Psychometric curves were determined by plotting the number of times that each test
stimulus was chosen as a function of its viscosity (µ) on a logarithmic scale. In a pair
where the test stimulus has lowest viscosity within the range, the test stimulus is expected to be chosen in none of the 10 trials to be the thickest. In a pair where the test
stimulus has the highest viscosity within the range, the test stimulus is expected to be
chosen in all 10 of the trials to be the thickest. In between, there is a transition from
0 to 10, the slope of which is a measure for the discrimination threshold. The psychometric curves were determined for each range and for each subject. The curves have
a characteristic sigmoid shape, which is often approximated by a cumulative Gaussian
distribution [8]. The discrimination threshold is then defined as the difference between
the centre of the distribution (50 % point) and −σ or +σ of the underlying Gaussian
distribution, corresponding to the 16 % and 84 % points, respectively. However, when
the discrimination is expected to be described by a constant Weber fraction, one should
not expect the thresholds (16 % and 84 % points) to lie at an equal absolute distance to
the left or to the right of the centre, but at an equal relative difference. That is, the ratio
between the 16 % and 50 % points should be equal to the ratio between the 50 % and
84 % points. A sigmoid function that satisfies this condition is given by
log µ/µref
f (µ) = 5 + 5erf √
.
2 log(σ/µref + 1)
Here, µref is the viscosity of the reference stimulus and σ/µref is the Weber fraction. On
a logarithmic scale, this function looks symmetrical. The function was fitted to the data
Haptic Perception of Viscosity
5000
threshold !mPa!s"
1
weber fraction
5
0.8
0.6
0.4
0.2
300
1000
3000
viscosity !mPa!s"
4000
3000
2000
1000
0
10000
300
1000
3000
viscosity !mPa!s"
10000
Fig. 2. Weber fractions (left) and absolute thresholds (right) averaged over subjects as a function
of reference viscosity. The error bars indicate the standard error of the sample mean.
of all subjects in all ranges. Figure 1 (right) shows a representative example of how the
function fits the data.
3
Results
The Weber fractions and absolute thresholds averaged over subjects are shown in figure
2. From about 2,000 mPa·s, the thresholds show Weber-like behaviour, but at lower
viscosities, the thresholds are much higher than would be expected from Weber’s law.
A repeated measures ANOVA on the Weber fractions showed a significant effect of
range (F4,28 = 15, p = 8.8 × 10−7 ). Bonferroni-corrected post-hoc tests showed that the
Weber fraction for the lowest range (199 mPa·s) differed significantly from all others
(p ≤ 0.017) except for the third range (938 mPa·s, p = 0.057). There were no significant
differences between other Weber fractions.
Since the behaviour is clearly not Weber-like, we will have a look at the absolute
thresholds as depicted in figure 2, right. For these also, a repeated measures ANOVA
showed a significant effect of range (F1.1,7.5 = 39, p = 2.8 × 10−4 , Greenhouse-Geisser
corrected value). Bonferroni-corrected post-hoc tests showed that only the thresholds
from the highest range (16060 mPa·s) differed significantly from the others (p ≤ 0.005);
the lower four ranges are not significantly different from each other.
4
Discussion and conclusions
One striking result is that the Weber fractions for the higher viscosities (0.29 ± 0.07,
SE) agree very well with those reported by Scott Blair and Coppen [4] and Jones and
Hunter [6], even though those values were measured in very different ways. Scott Blair
and Coppen used balls of bitumen which were handled directly by the subjects, whereas
in the present experiment the subject interacted with the stimulus through a rigid probe.
In that sense, the situation is perhaps more like that of Jones and Hunter, where subjects
moved a rod to and fro. In that experiment, like the present one, there was an increase in
Weber fractions for decreasing viscosity. Unfortunately, the two types of viscosity (of
6
Wouter M. Bergmann Tiest, Anne C. L. Vrijling, and Astrid M. L. Kappers
a liquid and of a mechanical system) cannot be directly compared, so we cannot check
whether the dependence on viscosity is the same.
Below about 2,000 mPa·s, the absolute thresholds do not seem to depend on viscosity. Apparently, there is a floor effect which does not allow the resolution of viscosity
perception to keep pace with viscosity itself. This does not coincide with a similar floor
effect in the perception of movement or force, so it is unlikely that the floor effect is
caused by limitations in force discrimination, as has been shown earlier [6]. Viscosity
perception is therefore not simply an integration of movement and force perception,
but (to some extent) a perceptual continuum in its own. By this we mean that viscosity
is considered to be a perceivable quantity in itself, and not (subconsiously) calculated
from other, more basic cues.
To conclude, we find a non-Weberlike dependence of discrimination thresholds on
viscosity, which transforms into Weber-like behaviour above 2,000 mPa·s. This will
enable designers of haptic interfaces to save on bandwidth during the display of low
viscosities, because human perception is relatively inaccurate in that range.
Acknowledgements. This work was supported by a grant from the Netherlands Organisation for Scientific Research (NWO). We thank ing. Emile Bakelaar (dept. of chemistry) for his assistance with the rheometer measurements.
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