Rivulet flow down a slippery substrate

A detailed analysis of small-scale locally unidirectional gravity-driven rivulet flow with prescribed volume flux down an inclined slippery substrate for a rivulet with either constant width (i.e., pinned contact lines) or constant contact angle is undertaken. In particular, we determine the effect of varying the Navier slip length λ (i.e., the strength of the slip at the solid-fluid interface) on the rivulet. The present analysis shows that the shape and size of the rivulet and the velocity within it depend strongly on the value of λ. Increasing the value of λ reduces the viscous resistance at the substrate and, hence, leads to a larger velocity within the rivulet, and so the prescribed flux is achieved with a smaller rivulet. In particular, in the limit of strong slip, λ → ∞, for a rivulet of a perfectly wetting fluid and a rivulet with constant width, the velocity becomes large and plug-like like O(λ1/2) ≫ 1, and the rivulet becomes shallow like O(λ-1/2) ≪ 1, while for a rivulet with positive constant contact angle, the velocity becomes large and plug-like like O(λ2/3) ≫ 1, and the rivulet becomes narrow like O(λ-1/3) ≪ 1 and shallow like O(λ-1/3) ≪ 1

Rivulet flow over and through a permeable membrane

Motivated by small-scale natural and industrial processes involving flow over and/or through a layer of a porous medium, a mathematical model for the steady gravity-driven flow of a rivulet of fluid with finite width over and through a permeable membrane is formulated and analyzed. The three-dimensional shape of the free surface of a rivulet with either fixed semiwidth or fixed contact angle is determined, and it is shown how the length, base area, and volume of the rivulet on the permeable part of the membrane depend on the physical properties of the system. In particular, whereas there is a physically realizable pendant rivulet solution only if the semiwidth does not exceed a critical value, there are physically realizable sessile and vertical rivulet solutions for all values of the semiwidth; moreover, a sessile rivulet with fixed semiwidth has a finite maximum possible length which is attained in the limit of a wide rivulet

Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure

We consider patterns formed in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes. We rigorously clarify some of the results obtained numerically by Honisch et al. [Langmuir 31: 10618-10631, 2015] and embed them in the general theory of thin-film equations. For the case of constant wettability, we elucidate the change in the global structure of branches of steady-state solutions as the average film thickness and the surface tension are varied. Specifically we find, by using methods of local bifurcation theory and the continuation software package AUTO, both nucleation and metastable regimes. We discuss admissible forms of spatially non-homogeneous disjoining pressure, arguing for a form that differs from the one used by Honisch et al.and study the dependence of the steady-state solutions on the wettability contrast in that case

The prevalence of sedentary behavior among university students in Saudi Arabia

Abstract Background A considerable body of research has demonstrated that reducing sitting time benefits health. Therefore, the current study aimed to explore the prevalence of sedentary behavior (SB) and its patterns. Methods A total of 6975 university students (49.1% female) were chosen randomly to participate in a face-to-face interview. The original English version of the sedentary behavior questionnaire (SBQ) was previously translated into Arabic. Then, the validated Arabic version of the SBQ was used to assess SB. The Arabic SBQ included 9 types of SB (watching television, playing computer/video games, sitting while listening to music, sitting and talking on the phone, doing paperwork or office work, sitting and reading, playing a musical instrument, doing arts and crafts, and sitting and driving/riding in a car, bus or train) on weekdays and weekends. Results SBQ indicated that the total time of SB was considerably high (478.75 ± 256.60 and 535.86 ± 316.53 (min/day) during weekdays and weekends, respectively). On average, participants spent the most time during the day doing office/paperwork (item number 4) during weekdays (112.47 ± 111.11 min/day) and weekends (122.05 ± 113.49 min/day), followed by sitting time in transportation (item number 9) during weekdays (78.95 ± 83.25 min/day) and weekends (92.84 ± 100.19 min/day). The average total sitting time of the SBQ was 495.09 ± 247.38 (min/day) and 58.4% of the participants reported a high amount of sitting time (≥ 7 hours/day). Independent t-test showed significant differences (P ≤ 0.05) between males and females in all types of SB except with doing office/paperwork (item number 4). The results also showed that male students have a longer daily sitting time (521.73 ± 236.53 min/day) than females (467.38 ± 255.28 min/day). Finally, 64.1% of the males reported a high amount of sitting time (≥ 7 hours/day) compared to females (52.3%). Conclusion In conclusion, the total mean length of SB in minutes per day for male and female university students was considerably high. About 58% of the population appeared to spend ≥7 h/day sedentary. Male university students are likelier to sit longer than female students. Our findings also indicated that SB and physical activity interventions are needed to raise awareness of the importance of adopting an active lifestyle and reducing sitting time