# Kapillarwirkung

Interaktive Visualisierung der Kapillarwirkung und Jurins Gesetz - Erkunden Sie den Flüssigkeitsanstieg in engen Röhrchen, den Kontaktwinkel und die Kraftegleichgewichtsanalyse

> Kanonische Seite: https://elysiatools.com/de/visualizations/capillary-action

- **Kategorie:** Physics

## Überblick

Interactive visualization of capillary action and Jurin's Law - Comprehensive tool for understanding liquid behavior in narrow tubes. Features four visualization modes: (1) Single Tube Mode - Detailed capillary rise/fall simulation with real-time Jurin's law calculation h = 2γcosθ/(ρgr), accurate physical properties for 6 liquids (Water, Ethanol, Mercury, Olive Oil, Glycerol, Blood Plasma), 4 tube materials (Glass hydrophilic, Teflon hydrophobic, Paraffin hydrophobic, Plastic mixed) with different contact angles, animated liquid rise from 0 to equilibrium height, meniscus shape rendering (concave for θ < 90° wetting liquids, convex for θ > 90° non-wetting), surface tension vector visualization at meniscus interface, height measurement indicator with real-time mm display, and external liquid level reference line. (2) Tube Comparison Mode - Multi-tube side-by-side comparison showing inverse relationship between tube radius and capillary height (h ∝ 1/r), 4 preset tube radii (0.2mm, 0.5mm, 1.0mm, 1.5mm) with individual show/hide toggles, simultaneous height calculation and display for each tube, visual demonstration that halving radius doubles height, quantitative comparison with height labels for each tube, and practical understanding of why capillary action is significant in microscopic vessels (plant xylem: 10-100 μm). (3) Force Balance Mode - Detailed physics analysis showing equilibrium condition F↑ = F↓, upward surface tension force F↑ = 2πrγcosθ acting along circumference with green vector, downward gravitational force F↓ = ρπr²hg acting on liquid column with red vector, force magnitude calculation and display, center of mass indication for weight force, meniscus force application point visualization, and real-time force balance equation display with substituted values. (4) Jurin's Law Derivation - Step-by-step mathematical derivation with 5 interactive stages: Step 1 Force Balance (F↑ = F↓), Step 2 Surface Tension Force (F↑ = γ·L = γ·2πr·cosθ), Step 3 Gravitational Force (F↓ = m·g = ρ·V·g = ρ·πr²h·g), Step 4 Equate Forces (γ·2πr·cosθ = ρ·πr²h·g), Step 5 Solve for Height (h = 2γcosθ/(ρgr)). Each step includes visual diagram annotations on canvas showing parameters (h, r, θ), color-coded parameter highlights, and formula progression. Adjustable parameters: tube radius (0.1-2.0 mm), contact angle (0-180°), temperature (0-100°C) affecting surface tension, gravity (1.6-25.0 m/s²) showing planetary effects (Moon 1.6, Earth 9.8, Jupiter 24.8), liquid type selection, and tube material selection. Real-time statistics panel displays: capillary height h (mm), surface tension γ (mN/m), contact angle θ (°), tube radius r (mm), liquid density ρ (kg/m³), gravity g (m/s²), and live formula calculation with substituted values. Liquid properties panel shows: liquid name, wetting behavior (Hydrophilic θ<90°, Hydrophobic θ>90°, Neutral θ=90°), meniscus type (Concave, Convex, Flat), and tube material. Applications showcase 6 real-world uses: Plants (xylem water transport from roots to leaves), Paper & Fabric (ink absorption, sweat wicking), Inkjet Printing (microscopic nozzle ink delivery), Medical Testing (capillary tube blood samples, pregnancy tests), Sponges (porous water absorption), and Oil Recovery (migration through porous rock). Comprehensive educational content covering: What is capillary action? (liquid flow in narrow spaces without external forces, balance between surface tension and gravity), Jurin's Law historical context (James Jurin 1718, complete formula explanation, inverse radius relationship h ∝ 1/r), Role of contact angle (θ<90° wetting liquids rise with cosθ>0, θ>90° non-wetting liquids fall with cosθ<0, θ=90° no capillary effect), Effect of tube radius (microscopic significance, plant xylem applications, demonstrated in comparison mode), Wetting vs Non-wetting (water in glass θ≈30° strong rise, mercury in glass θ≈140° depression, material dependence), Gravity effects (Moon 6× higher rise, Jupiter 40% lower rise, space applications), and Limitations of Jurin's Law (5 assumptions: cylindrical tube, constant contact angle, complete wetting, no evaporation, static equilibrium). Formula display uses mathematical notation with fraction rendering for h = (2γcosθ)/(ρgr). Responsive design with mode selection panel, main canvas (600px height), statistics panel (380px width), controls grid, comparison options, derivation steps panel, and applications grid. Multi-language support (zh, en, es, fr, de, ru, pt) with complete translations. Canvas-based rendering with smooth rise animation, gradient liquid colors per liquid type, realistic meniscus curves, force vector arrows, parameter annotations, and grid overlay option.

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