Capillary Penetration into Inclined Circular Glass Tubes

Meniscus Formation in a Vertical Capillary Tube

In this theoretical work, the energies associated with the formation of a meniscus in a small diameter capillary tube are analyzed. A mechanism for meniscus creation and an associated energy balance are proposed. Equations for work of wetting, surface energy, gravitational energy, and dissipation are derived. The relative magnitude of these quantities is compared, first to each other and then to energies from capillary rise. In capillary rise, the energy released as work of wetting is evenly split between gravitational energy stored in the liquid column and heat dissipated there. The analysis performed here suggests that meniscus formation is energetically distinct and more complex than capillary rise. In meniscus formation, most of the energy released as work of wetting is stored in the stretched air-liquid interface or dissipated in the bulk liquid; their relative distribution depends on the properties of the liquid and the tube.

Direct Measurement of Contact Angle Change in Capillary Rise

Capillary rise is important in many aspects of physical phenomena from transport in porous media to biotechnology. It is typically described by the Lucas-Washburn-Rideal equation (LWRE), but discrepancy between some experiments and the model still remains elusive. In this paper, we show that the discrepancy is simply from the contact angle change during the capillary rise with no help of any specific models, such as dynamic contact angle (DCA) models. To demonstrate this, we directly measure the contact angle change in the capillary rise for glycerol and carboxymethyl cellulose solutions as examples of Newtonian and non-Newtonian liquids. Unlike previous studies that used DCA models to explain the discrepancy, when the contact angle change is directly applied to the LWRE for all four tested fluids, the model agrees well with experimental data. The estimated contact angle from the capillary rise as a function of time is in good agreement with the directly measured contact angle within a narrow margin of error. To pinpoint the conditions for the discrepancy, we propose a new time scale when contact angle dynamics dominates. The contact angle dynamics that can be obtained from the macroscopic capillary rise may provide useful information for capillary flow in a more complicated geometry such as porous media.

Inertial capillary uptake of drops

Uptake of liquid drops into capillary tubes has been experimentally studied and quantitatively analyzed. In experiments, drops of water and aqueous glycerol (≤50 wt %) were drawn into cylindrical borosilicate glass and quartz tubes with an inner diameter of 0.50-0.75 mm. The meniscus height rise was measured using high-speed images captured at 4000 frames per second, and results within a conservatively defined inertial regime indicate constant uptake velocity. An increase in the inertial velocity with drop curvature was observed due to increasing Laplace pressure in the drop, as drop sizes were comparable to the width of the capillary tubes. Measured velocities were slower than predicted by a purely inertial-capillary model and best described by introducing a contact line friction, consistent with the observed variability and viscosity dependence of the results. Mean friction coefficients in borosilicate capillaries ranged from 169±1 for 50 wt % glycerol drops to 218±1 for water drops. Peaks in the instantaneous Laplace pressure caused by surface oscillations were also measured. Correlations with uptake velocity were qualitatively apparent, with a delay between peaks of similar magnitude to the inertial-capillary oscillation time.

Understanding and Modeling the Liquid Uptake in Porous Compacted Powder Preparations

Porous solid materials commonly undergo coating processes during their manufacture, where liquids are put in contact with solids for different purposes. The study of liquid penetration in porous substrates is a process of high relevance in activities in several industries. In particular, powder detergents are subject to coating with surfactants that will boost their performance, although this may affect the flowability and even cause caking of the particulate material, which can be detrimental to consumer acceptance. Here we present a methodology to make compacted preparations of powders relevant to detergent making and evaluate the internal structure of such porous substrates by means of X-ray microcomputed tomography. Liquid penetration in the preparation and the total mass uptake of fluid were monitored by a gravimetric technique based on a modified Wilhelmy plate method consisting of consecutive cycles. Taking into account the geometry of the system, two models were proposed to describe the liquid uptake based on the process being driven by mass (model 1) or pressure (model 2) gradients. A comparison between both from statistical and physical points of view led to the conclusion that the latter was more appropriate for describing the process and retrieving values of the permeability of the solid between 0.03 × 10^-12 and 0.95 × 10^-12 m². Finally, with the parameters retrieved from model 2, the force balance observed throughout the experiment was simulated satisfactorily.